Embracing Opportunity in Imperfection: Is simulation the...

1copy 2011 The MathWorks Inc

Opportunity in Embracing ImperfectionIs simulation the real thing

Pieter J MostermanSenior Research ScientistDesign Automation Department

Adjunct ProfessorSchool of Computer Science

2

In your opinion what lasting legacy has YACC brought to language development

YACC made it possible for many people who were not language experts to make little languages (also called domain-specific languages) to improve their productivity Also the design style of YACC - base the program on solid theory implement the theory well and leave lots of escape hatches for the things you want to do that dont fit the theory - was something many Unix utilities embodied It was part of the atmosphere in those days and this design style has persisted in most of my work since then

Interview with Stephen C Johnson in ldquoThe A-Z of programming languages YACCrdquo Computerworld 09072008httpnewsidgnocwartcfmid=094E3B6E-17A4-0F78-311509693E8E95C1





4

The importance of computation

Together with theory and experimentation computational science now constitutes the ldquothird pillarrdquo of scientific inquiry

5


Resolved That the House of Representativesmdash3) encourages the expansion of modeling and simulation as a tool

and subject within higher education4) recognizes modeling and simulation as a National Critical

Technology

6

Agenda

Outline Model-Based Design Problem statement A solution approach Outlook

7

The science in engineering a system

Discard detail but keep pertinent behavior

experimentation theoryhttpimagesjscnasagov

8


Where is the heat

But often no analytical solution

experimentation theory

9

experimentation theory computation


A computational solution

10




Not much heat at the nozzles hellip letrsquos change the material hellip

11





12

Computational methods to add more detail

Same computational approximationInformation beyond what is in a first principles model

13

Same computational approximation


14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16

Computational methods are not that mature

17


ldquo hellip engineers used Crater during STS-107 to analyze a piece of debris that was at maximum 640 times larger in volume than the pieces of debris used to calibrate and validate the Crater modelrdquoH W Gehman Jr et alldquoReport of Columbia Accident Investigation Board Volume Irdquo National Aeronautics and Space Administration August 2003

Dr Scott LiebermanmdashAP PhotoTyler Morning Telegraph

18

httptatwitudelftnlnwusersvuikinformationfig06gif

Technology maturation a comparison

Brooklyn Bridge

Tacoma Narrows BridgeSzeacutechenyi Chain Bridge

ldquoComputational Science Demands a New Paradigmrdquo Douglass E Post and Lawrence G Votta Physics Today 2005

Conservative Cautious improvement

1849 1883 1940

hellip till failure

httpblogteacollectioncomthe-lion-on-szechenyi-chain-bridge-3067

httphelpforsnarodruUSANew_Yorknew_york_2html

19


Brooklyn Bridge Akashi-Kaikyō Bridge



Conservative Cautious improvement Firm methodology

1849 1883 1940 1998

hellip till failure

httpwwwlibwashingtoneduspecialcollexhibitstnbhttpblogteacollectioncomthe-lion-on-szechenyi-chain-bridge-3067

httphelpforsnarodruUSANew_Yorknew_york_2html httpwwwweirdlyoddcom10-tallest-bridges-in-the-world

20

Premise

Approximation is not the culpritndash Model-Based Design is successfully exploiting computation ndash But still very ad hoc lots of testing required

Embrace the imperfectionndash Create better models without reducing the approximationndash Use computational methods to

Enhance model information Enhance domain information Analyze and design complex execution engines

ndash Requires precise definition of the execution semantics Differential equations difference equations discrete event etc Approximations

Treat computation as equal to experiment and theory

21

Agenda


22

Design of an engineered system

23

Increasingly more detail

24

Target stack

System behavior

25

Target stackHost stack

Simulation studies

26

Host stack Target stack

Model-Based Design

27


Model-Based Design

28


Executable specifications

29


Model elaboration

Elaborate

30


Automatic code generation

Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest

Raises level of abstraction

Enables continuous testing

Model-Based Design

32

Mapping an application

General purpose

Application specific

Sing

le a

pplic

atio

n

Application to be implemented

Technology divergence

33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n

Compile technology into application

35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n

Reuse shared transformation technology

37



General purpose

Sing

le a

pplic

atio

n

Modular timing engine to enable reuse

38

Agenda


39

Computer Automated Multiparadigm Modeling for technology reuse

F0

SY SE

FM

SY SE For graphical syntax often a meta model is used

A syntax a semantic domain and a mapping

40

Define semantics as a syntactic transformationmdashsemantic anchoring

FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT

SY SE Transformation model

Target semantic domain must be subsumed

41

Modeling a model transformation

42


43


44

Model-Based Design


45

Model-Based Design


46

Can we develop a unifying semantic domain

Multi-domain models comprise many formalisms hellip

F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x

Modeling a physical system

vx

From first principles hellip Hookersquos Law

Newtonrsquos SecondC

xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=

=An ideal oscillator

49

v

x


vx

Letrsquos develop a numericalsolver to compute a solution hellip



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50

Numerical integration

kt

kx

)( txfx =

kkkke htxtxtx )()()(ˆ 1 +=+

Euler step h in time along

1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+

Trapezoidal average the end points

53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


Taylor series expansion for error analysis

)(2

)(1

)()()( 321 kk

kk

kkk hOhtxhtxtxtx +++=+

56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+ke tεWhen x(t) changes little hk can be large

57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε

Change step size based on estimate 211 2

)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58

Sophisticated solver hellip

Letrsquos compute a solution to the ideal oscillator

We can make the error small hellip but only locally

v

x

vx

59



We can make the error small hellip but only locally It accumulates for lsquolong timersquo behavior So hellip how come the JSF flies

v

x

vx

60

Engineering an embedded system

physical theoretical

dttdvmtF )()( =

validate

In collaboration with Hans Vangheluwe McGill University

computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63


Create executable models in all phases

64


Make the computational approximation the primary design deliverablemdashthe real thing

65

So that gets the job done hellip but hellip

More than 50 of the modeling effort is in verification validation and testing

Semantics of models is buried in the execution engine Engine code base is extensive and complex

ndash Interaction of approximationsndash Interaction and interfacing of different formalisms

How can we mature the field Model the semantics of the execution engine

66

Agenda


67

system

model

model

systemunder study

So what is a model anyway

Jean Beacutezivin

ldquoEverything is a modelrdquo

Jean-Marie Favre

ldquoNothing is a modelrdquo

Pieter J Mosterman

ldquoNothing is not a modelrdquo

systemmodel

system under study

model

system


68

Computer Automated MultiparadigmModeling

(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe

ldquoModel everythingrdquo

systemmodel

system under study

model

system


69

With the most appropriate formalism

At the most appropriate level of abstraction


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70

Host stack Host stack Target stack

analyzebehavior

Modeling the execution engine

71

Host stack


72

Host stack

Create abstractions in the simulation stack hellip

specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze

Analyze as little as possible

declarative model

75

Host stack

analyzedesign

reuse

Further facilitate design reuse hellip

declarative model

76

A declarative formalism with fix-point semantics

1z21

Constant Gain Delay Scope

1 55

ndash Repeated application of a monotonically increasing partial function converges to a fixed point

77


1z21


1 6 5125


78


1z21

Constant Gain Delay Scope5

02 0003 04 01


ndash One implementation is a data dependency schedule

1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80

Dynamic systems evolve over time

Sequences of fix-point evaluations Define input and output signals as (potentially infinite)

streams of valuesndash Stream(Type) = Type Stream(Type)

Delay as a function applicationndash Delay x0 u = x0 u

ndash A variable has a lsquoclockrsquo that encodes its sample time

1z2 4 7 hellip5

5 2 4 hellip

81

Multiple rates a potential problem hellip

Streams are only practical if we can limit the stream entries being accessed

Not this

even+

x4x3x2

x4

x0+x0 x1+x2 x2+x4 hellip x0 x1 x2 x3 x4 hellip

x0 x1 x2 x3 x4 hellip

82

Clock calculus to detect

Require compatible clocks the synchronous assumption

Match against base clock

even+

x0 x1 x2 x3 x4 hellipx0 x1 x2 x3 x4 hellip

T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip

T F T F T hellip T T T T T hellip 0 pad

x0 x2 x4 hellip x0 0 x2 0 x4 hellip

84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T

A multi-rate system example

1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBaseFind greatest common divisor (Ts)

85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

T F T F T TFT T T T T T T

87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source

Ts = 2 (s)T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T

T F T F T F TRTT T T T T T T

89

Can we use this framework to define a variable-step solver

Separatendash Time (explicit)ndash Evaluations (ordered)

Time as a function of evaluations

90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation



Time as a function of evaluationsndash Step is variable

t(0)t(1)

t(2)

95

evaluation



Time as a function of evaluationsndash Step is variablendash Step may be 0

t(0)t(1)

t(2)t(3)

96

evaluation



Time as a function of evaluationsndash Step is variablendash Step may be 0ndash Step may be negative

Time may recedet(0)t(1)

t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98

A stream based functional solver

minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration

Trapezoidal integration

99

previous increment


minusminusminusminus= sum =

otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus

minusminus+minusminus

minus+minus=

e

it ipihiuiuihiuiuey1

)1(2

)3()2()3(2

)1()()1()(

( ) toleheueheueued ltminusminusminusminusminus+minus

= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)

Rate transition a function of time

1s2Gain Integrator Scope

hold (t)

Now we can create a variable step solver inside 1s that maps onto the synchronous paradigm

Dynamically compute lsquoholdrsquo output as an argument of time

No predetermined sequence of output values

)()( sTtuty =

t

101

Unifying formalisms with different semantics

Newtonrsquos Law and Hookersquos Lawndash Differential equations as before

Control behaviorndash Sampled data (periodic Ts=05)

Contact behaviorndash Discontinuous changes hellip

Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102

Modeling the contact behavior

Simultaneous inequalities

Finite state machine

free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103

Computational simulation

Position vs time Time vs evaluations (detail)


104



Simultaneous inequalities Finite state machine

105




106

But time is a function of evaluations


Which t should tevent really map ontoball

smoothfloorsmoothball

eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107

Different choice of semantics

50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion

evaluated onaccepted time step

always evaluated

108

Comparing with an analytic solution

032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion

evaluated on acceptedtime step

analytic solution

always evaluated

Justyna Zander Pieter J Mosterman Greacutegoire Hamon and Ben Denckla ldquoOn the Structure of Time in Computational Semantics of a Variable-Step Solver for Hybrid Behavior Analysis in the Proceedings of the IFAC World Congress Milan Italy August 2011

109

Characteristics of the semantic domain

Declarativendash Purely functional (no side effects)

Ordered evaluations Untimed

ndash Time as explicit function t(e)ndash Time is not strictly increasing

Broadly applicable to dynamic systemsndash Differential equations difference equations discrete events

Pieter J Mosterman Justyna Zander Greacutegoire Hamon and Ben Denckla Towards Computational Hybrid System Semantics for Time-Based Block Diagrams in 3rd IFAC Conference on Analysis and Design of Hybrid Systems (ADHS09) A Giua C Mahulea M Silva and J Zaytoon (eds) pp 376-385 Zaragoza Spain September 16-18 2009 plenary paper

110

Agenda


111

Conclusions

Computation the good and not so goodbull Quantitative approximationndash Potential for higher quality models

Exploit computational methodsndash We must formalize the computational execution semanticsndash Model at a declarative level

Define solvers using a functional stream-based approachndash Precise computational semantics of the execution engine

112

Opportunities

First principles in computational form New generation of modeling and simulation tools

ndash More robust in less time (less bugs more reliable and consistent approximation)

Bring disciplines togetherndash Engineering Computer Science Physics Mathematics

Exploit the abstractionndash Automatic code generation ndash Computational methods for

Analysis Design Synthesis

113

Control synthesis using model checking

114


115

A counterexample

Pieter J Mosterman Justyna Zander Greacutegoire Hamon and Ben Denckla A Computational Model of Time for Stiff Hybrid Systems Applied to Control Synthesis in Control Engineering Practice in press

116

A counterexample


117

Controlled acceleration of mounted component

0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments

Justyna Zander Harvard University

Fraunhofer Institute FOKUS Berlin

Greacutegoire HamonMathWorks

Ben DencklaIndependent Thinker

Hans VangheluweUniversity of Antwerp

McGill University

Many thanks for their continuing collaboration

119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

2

In your opinion what lasting legacy has YACC brought to language development

YACC made it possible for many people who were not language experts to make little languages (also called domain-specific languages) to improve their productivity Also the design style of YACC - base the program on solid theory implement the theory well and leave lots of escape hatches for the things you want to do that dont fit the theory - was something many Unix utilities embodied It was part of the atmosphere in those days and this design style has persisted in most of my work since then

Interview with Stephen C Johnson in ldquoThe A-Z of programming languages YACCrdquo Computerworld 09072008httpnewsidgnocwartcfmid=094E3B6E-17A4-0F78-311509693E8E95C1





4



5




Technology

6

Agenda


7




8


Where is the heat



9




10





11





12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119





4



5




Technology

6

Agenda


7




8


Where is the heat



9




10





11





12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

5




Technology

6

Agenda


7




8


Where is the heat



9




10





11





12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

6

Agenda


7




8


Where is the heat



9




10





11





12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

7




8


Where is the heat



9




10





11





12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

8


Where is the heat



9




10





11





12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

9




10





11





12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

10





11





12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

11





12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

12



13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

13



14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

14

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

15

Model quality

information

appr

oxim

atio

nanalytic

computation

decreasingerror

error level

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

16


17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

17




18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

18



Brooklyn Bridge




1849 1883 1940

hellip till failure



19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

19






1849 1883 1940 1998

hellip till failure



20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

20

Premise






21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

21

Agenda


22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

22


23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

23


24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

24

Target stack

System behavior

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

25


Simulation studies

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

26


Model-Based Design

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

27


Model-Based Design

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

28



29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

29


Model elaboration

Elaborate

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

30



Elaborate

Synthesize

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

31


ExploreVerifyTest

Elaborate

Synthesize

ExploreVerifyTest

ExploreVerifyTest



Model-Based Design

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

32


General purpose


Sing

le a

pplic

atio

n



33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

33


General purpose

Sing

le a

pplic

atio

n


34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

34



General purpose

Sing

le a

pplic

atio

n


35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

35



General purpose

Sing

le a

pplic

atio

n

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

36



General purpose

Sing

le a

pplic

atio

n


37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

37



General purpose

Sing

le a

pplic

atio

n


38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

38

Agenda


39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

39


F0

SY SE

FM



40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

40


FISE

SY

F0

SY SE

FM

SY SE

TL R

IL R

IL R

IhelliprArr

FT



41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

41


42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

42


43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

43


44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

44

Model-Based Design


45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

45

Model-Based Design


46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

46



F0

SY SE

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

47



F0

SY SE

FU

SY

SE

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

48

v

x


vx



xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

49

v

x


vx




xxF 0minusminus=

maF =

A bit of calculus

dttdxtv

dttdvta

)()(

)()(

=

=

Cxtx

dttdvm

dttdxtv

0)()(

)()(

minusminus=


50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

50


kt

kx

)( txfx =



1+kt

1+kxkx

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

51


kt

kx

)( txfx =



1+kt

1+kx

1ˆ +kx1+kε

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

52


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

53


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

54


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+


55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

55


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

56


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk



57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

57


kt

kx

)( txfx =



1+kt

1+kx1+kε

kkk

kkt htxtxtxtx2

)()()()(ˆ 11

++= +

+



)(2

)(1

)()()( 321 kk

kk


)( 1+kt tε


)()(ˆ)(ˆ kk

ktke htxtxtx

asympminus ++

)( 1+ke tε

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

58




v

x

vx

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

59




v

x

vx

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

60



dttdvmtF )()( =

validate


computational

verify

void main () int i

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

61



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

62



dttdvmtF )()( =

validate


computational

validate

verify

void main () int i

refine

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

63



64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

64



65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

65






66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

66

Agenda


67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

67

system

model

model

systemunder study


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


systemmodel

system under study

model

system


68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

68


(CAMPaM)


Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

69




Jean Beacutezivin


Jean-Marie Favre


Pieter J Mosterman


Hans Vangheluwe


systemmodel

system under study

model

system


70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

70


analyzebehavior


71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

71

Host stack


72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

72

Host stack


specification

implementation

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

73

Host stack


declarative model

imperative model

implementation

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

74

Host stack

analyze


declarative model

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

75

Host stack

analyzedesign

reuse


declarative model

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

76


1z21


1 55


77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

77


1z21


1 6 5125


78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

78


1z21


02 0003 04 01



1z21


1 6 5125

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

79


1 6 5121z21


02 0003 04 01



1z21


1 6 5125

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

80






1z2 4 7 hellip5

5 2 4 hellip

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

81



Not this

even+

x4x3x2

x4



82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

82




even+


T T T T T hellip

T F T F T hellip

x0 x2 x4 hellip

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

83




even+


T T T T T hellip



84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

84

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)


85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

85

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

86

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase

Ts


87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

87

2 7 3 hellip

Source

Ts = 2 (s)

T T T T T T T


1z2Gain Delay Scope

Ts = 1 (s)

SourceDelayBase


88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

88

hold

2 7 3 hellip

Source



1z2Gain Delay Scope

Ts = 1 (s)

Source

DelayBase

T F T F T TF

T T T T T T T


89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

89




90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

90




T T T T T T T

Ts

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

91




Ts2Ts

time

T T T T T T T

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

92

evaluation




time

Ts2Ts

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

93

evaluation




t(0)

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

94

evaluation




t(0)t(1)

t(2)

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

95

evaluation




t(0)t(1)

t(2)t(3)

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

96

evaluation





t(2)t(3)

t(4)

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

97

evaluation





t(2)t(3)

t(4)

t(5)

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

98


minus= sum =

otherwiseeoddif

eyihiuey

e

e

ie

)()1(

)()()( 1

( )sum =

minus+minus=

e

itihiuiuey

1 2)1()()1()(

Euler integration


99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

99

previous increment



otherwiseeoddif

eyipihiuihiuey

e

e

ie

)()1(

)()2()2()()()( 1

( ) ( )sum =minus


minus+minus=

e


)1(2

)3()2()3(2

)1()()1()(


= )2()2(2

)3()2()3()(

previous increment

Euler integration


Error computation

increment

increment

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

100

2 7 3 hellip

Source

Ts = 2 (s)



hold (t)




)()( sTtuty =

t

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

101





Fpull

R C

m

Fg

x=0Ffloorx

==

=else

kifkif

kFpull

0110020

)(

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

102




free contact

0ltx

0gex

lt

+minus=

otherwisetxif

CtxtRvtFfloor

0)(

0

)()()(

0)( =tFfloor

+minus=

CtxtRvtFfloor)()()(

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

103




104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

104




105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

105




106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

106





eventevent

eventeventfloor

metF

geta

otherwiseetxif

CetxetRvetF

))(())((

0))((

0

))(())(())((

+=

lt

+minus=

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

107


50 100 150 200 250 300-01

-008

-006

-004

-002

0

002

004

evaluations

posi

tion


always evaluated

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

108


032 034 036 038 04 042 044 046-012

-01

-008

-006

-004

-002

0

002

time

posi

tion


analytic solution

always evaluated


109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

109







110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

110

Agenda


111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

111

Conclusions




112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

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Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

112

Opportunities






113


114


115

A counterexample


116

A counterexample


117


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Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

113


114


115

A counterexample


116

A counterexample


117


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acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

114


115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

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-10

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acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

115

A counterexample


116

A counterexample


117


0 001 002 003 004 005-20

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-10

-5

0

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acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

116

A counterexample


117


0 001 002 003 004 005-20

-15

-10

-5

0

time

acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

117


0 001 002 003 004 005-20

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acce

lera

tion

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

118

Acknowledgments






McGill University


119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

119

reg


Slide Number 2




Agenda








Model quality

Model quality





Premise

Agenda



System behavior

Simulation studies

Model-Based Design

Model-Based Design


Model elaboration


Model-Based Design







Agenda






Model-Based Design

Model-Based Design





















Agenda












































Agenda

Conclusions

Opportunities



A counterexample

A counterexample


Acknowledgments

Slide Number 119

Embracing Opportunity in Imperfection: Is simulation the...

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