Control Engineering Laboratory PORT-BASED MODELING · PDF fileControl Engineering Laboratory...

7182005 Summerschool Bertinoro17-23 July 2005

copy PC Breedveld1

Control Engineering Laboratory

PORT-BASED MODELING OF DYNAMIC SYSTEMS

fundamental concepts and bond graphs

PORT-BASED MODELING OF DYNAMIC SYSTEMS

fundamental concepts and bond graphs

Peter BreedveldPeter Breedveld

Control Engineering Laboratory Faculty of Electrical Engineering Mathematics and Computer ScienceUniversity of Twente Netherlands

pcbreedveldutwentenl

Some remarksSome remarks

copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (2)

bullbull Role of concepts (lsquointellectrsquo multiple views)Role of concepts (lsquointellectrsquo multiple views)bullbull Ports from a historical energy point of viewPorts from a historical energy point of view

(energy states)(energy states)bullbull Focus on linear motion and fixed axis rotation Focus on linear motion and fixed axis rotation

simple configuration constraints no need for simple configuration constraints no need for abstract geometrical concepts (like in the rest of abstract geometrical concepts (like in the rest of the course)the course)

bullbull Separation between configuration state and energy Separation between configuration state and energy statestatestructures influence of kinematic constraintsstructures influence of kinematic constraints

General OutlineGeneral Outline


bullbull Background and historyBackground and historybullbull Introduction to ports bonds and Introduction to ports bonds and

physical domainsphysical domainsbullbull Introduction to bond graph modelingIntroduction to bond graph modeling

causality domaincausality domain--independence etcindependence etc

Assumed prerequisitesAssumed prerequisites


bullbull Some experience inSome experience inndashndash Block diagram modelsBlock diagram modelsndashndash Numerical simulation (methods)Numerical simulation (methods)ndashndash Linear and nonlinear analysisLinear and nonlinear analysisndashndash Basic physics (electrical circuits simple Basic physics (electrical circuits simple

rigid body mechanisms principles of rigid body mechanisms principles of thermodynamics etcthermodynamics etc

IntroductionIntroduction


ndashndash Modular modeling (prevailing trend in Modular modeling (prevailing trend in modeling and simulation of complex modeling and simulation of complex physical systems)physical systems)

bullbull represented as a network interconnection of represented as a network interconnection of ideal elementsideal elements

ndashndash AdvantagesAdvantagesbullbull flexibilityflexibilitybullbull rere--usability of model partsusability of model partsbullbull physical insightphysical insightbullbull support for automated modelingsupport for automated modelingbullbull fundamental to systems and control theoryfundamental to systems and control theory



ndashndash DisadvantagesDisadvantagesbullbull equations of motion obtained directly from equations of motion obtained directly from

network modeling are oftennetwork modeling are oftenndashndash complicatedcomplicatedndashndash without apparent structurewithout apparent structurendashndash will easily contain will easily contain algebraic constraintsalgebraic constraints arising arising

from the interconnection of the subfrom the interconnection of the sub--systemssystemsbullbull no problem for digital simulation butno problem for digital simulation butbullbull may not be very wellmay not be very well--suited to analysis and suited to analysis and

control purposes (nonlinear systems)control purposes (nonlinear systems)

Course objectivesCourse objectives


ndashndash particular type of network modeling viz particular type of network modeling viz portport--based modelingbased modeling

bullbull subsub--systems are interacting through power systems are interacting through power exchange represented by pairs of exchange represented by pairs of conjugated variablesconjugated variables

bullbull unified way to deal with systems from unified way to deal with systems from different physical domains (eg mechanical different physical domains (eg mechanical and electrical) and electrical)

bullbull resulting systems of equations possess an resulting systems of equations possess an underlying generalized Hamiltonian underlying generalized Hamiltonian structure leading to the geometric notion of structure leading to the geometric notion of a porta port--Hamiltonian systemHamiltonian system



bullbull exploiting the underlying Hamiltonian exploiting the underlying Hamiltonian structure offers many possibilities forstructure offers many possibilities for

ndashndash analysisanalysisndashndash simulationsimulationndashndash controlcontrol

of complex physical systemsof complex physical systemsbullbull illustrated in variety of application areasillustrated in variety of application areasbullbull possible extension to classes of possible extension to classes of

distributeddistributed--parameter systemsparameter systems


AppetizerNewton cradle example


bullbull ExperimentExperiment

bullbull 2020--sim sim demdemoobullbull AnimationAnimation


Dual role exampleFalling and bouncing object


bullbull generally considered as conceptually generally considered as conceptually complexcomplexndashndash switching models switching models reinitializationreinitialization timing timingndashndash energy bookkeepingenergy bookkeepingndashndash prone to sign errorsprone to sign errors

bullbull portport--based approach with explicit based approach with explicit structure allows conceptually simple structure allows conceptually simple solutionsolution

AimAim


bullbull System theoretic approach to physical system dynamics System theoretic approach to physical system dynamics based onbased onndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics

bullbull shown how as a resultshown how as a resultndashndash variables and relations describing physical systems may be variables and relations describing physical systems may be

classifiedclassifiedndashndash models may be organized as (lsquoportmodels may be organized as (lsquoport--based approachrsquo)based approachrsquo)

bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a a

generalized networkgeneralized networkndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy gy

and entropyand entropybullbull special attentionspecial attention

ndashndash role of analogiesrole of analogiesndashndash analogue behavioranalogue behavior

Fundamental issuesFundamental issues


bull introduction amp some philosophybull Why physical systems modelingbull What is physical systems modelingbull Context of explanation (focus of engineering

physics) versus justification (focus of math)bull elements and components theory buildingbull synthesis between classical approaches

bull choice of variablesndashndash mechanical versus thermodynamic mechanical versus thermodynamic

frameworkframework


lsquoWhyrsquoThree-world meta-model


bullbull Real worldReal world (assuming existence of (assuming existence of lsquolsquoobjectiveobjectiversquorsquoenvironmentenvironmentrsquorsquo))

bullbull Conceptual worldConceptual world (in our brain)(in our brain)bullbull lsquolsquoPaperPaperrsquorsquo worldworld including electronically stored including electronically stored

datadata

ndashndash Only invia the paper worldOnly invia the paper worldbullbull CommunicationCommunicationbullbull SupportSupportbullbull SystematizationSystematization

ndashndash exchangeable abstractionsconcepts gtgtgtexchangeable abstractionsconcepts gtgtgtndashndash importance of importance of symbolssymbols amp amp notation notation (representation)(representation)


lsquoWhyrsquoAre physical concepts lsquorealrsquo


bullbull For exampleFor examplendashndash energy time momentum causalityhellipenergy time momentum causalityhellip

bullbull In a context of In a context of justificationjustification NONObullbull In a context of In a context of discoverydiscoveryexplanationexplanation

YES YES but rather lsquoreally usefulrsquo than but rather lsquoreally usefulrsquo than just lsquorealrsquojust lsquorealrsquo


lsquoWhyrsquoThe useless lsquoquest for truthrsquo


bullbull A model is necessarily A model is necessarily incompleteincompletelsquolsquoall models are wrongall models are wrongrsquorsquo but but lsquolsquotruthtruthrsquorsquo is is notnot

what countswhat countsbullbull The issue is whether a model is The issue is whether a model is

competentcompetent (to solve a problem in a (to solve a problem in a given given problem contextproblem context in the most in the most generic sense of the word)generic sense of the word)

What is a modelWhat is a model


Some sort of abstraction Some sort of abstraction (in the (in the lsquolsquopaperpaperrsquorsquo world)world) that enablesthat enablesbullbull insight insight in in the real world counterpartthe real world counterpartbullbull communicationcommunication about about the real world counterpartthe real world counterpartbullbull observationobservation of of the real world counterpartthe real world counterpartbullbull troubleshootingtroubleshooting of of the real world counterpartthe real world counterpartbullbull designdesign of new aspects related to the real world counterpartof new aspects related to the real world counterpartbullbull modificationsmodifications of of the real world counterpartthe real world counterpartbullbull lsquolsquoexplanationexplanationrsquorsquo of of functionalityfunctionality of the real world counterpartof the real world counterpartbullbull measurementmeasurement of of the real world counterpartthe real world counterpart

but most importantly that is but most importantly that is bullbull competentcompetent to solve a given problem and make decisions to solve a given problem and make decisions

related to the real worldrelated to the real world

ModelingModeling


bull Given a specific problem context the decision process to obtain a competent model to solve this problem

bull Approaches between two extremesndashndash a priori knowledgea priori knowledgendashndash lsquolsquoblack boxblack boxrsquorsquo (also an axiomatic concept with a priori (also an axiomatic concept with a priori

assumptions)assumptions)bullbull concept concept lsquolsquoinputinputrsquorsquo implicitly contains model of imposing some implicitly contains model of imposing some

action with negligible back effect (action with negligible back effect (lsquolsquohigh input impedancehigh input impedancersquorsquo))bullbull concept concept lsquolsquooutputoutputrsquorsquo implicitly contains model of measurement implicitly contains model of measurement

with negligible effect on the system being observed (with negligible effect on the system being observed (lsquolsquolow low output impedanceoutput impedancersquorsquo))

bullbull after a competent inputafter a competent input--output relation is found it is not output relation is found it is not open for modifications or physical interpretationopen for modifications or physical interpretation

lsquoSpecialrsquo stateslsquoSpecialrsquo states


PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature

ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)

ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)

Model representationModel representation


bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent

bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)

bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including

the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc

Role of representationsRole of representations


Process timeProcess timeversusversus

processprocessinging timetime

A

A

A

A

A

T

T

T

T

T

a

b

c

d

e

x1

x2

x3

x4

x5

SequentialSequential

A

T

T

A

x

t

x1 x5x4

x3x2

SimultaneousSimultaneous

What are we trying to describeWhat are we trying to describe


bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))

ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics

bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))

bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)

electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain

ndashndash configurationconfiguration

Physical systems modelingPhysical systems modeling


bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)

bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))

ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat

bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction

bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial

time amp uncertaintytime amp uncertainty


bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on

counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)

ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty

bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)

ndashndash dialectic conceptsdialectic concepts


concepts oflsquostatersquo amp lsquochangersquo


bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more

than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to

spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics

Contents of the sequelContents of the sequel


bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of

energyenergybullbull (Computational) Causality(Computational) Causality

Modeling pitfallsModeling pitfalls


bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo

bullbull Model depends on problem contextModel depends on problem context

bullbull Competent modelsCompetent models

bullbull Analogies are not identitiesAnalogies are not identities

bullbull Avoid implicit assumptionsAvoid implicit assumptions

bullbull Avoid model extrapolationAvoid model extrapolation

bullbull Confusion of components with elementsConfusion of components with elements

Port-based modelingPort-based modeling


bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)

bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations

bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)

bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for

demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs


Physical components versus ideal elements



Physical component versus ideal elements





Component mounterComponent mounter



Physical components versus conceptual elements


physical componentphysical componentpiece of rubber hosepiece of rubber hose

dominant behaviordominant behaviorbullbullwhen falling when falling ideal massideal massbullbullwhen pulling load when pulling load ideal springideal springbullbullfor vibration isolation for vibration isolation ideal resistorideal resistorbullbulletcetc

lsquoParasiticrsquo elementslsquoParasiticrsquo elements


bullbull Next to dominant behaviorNext to dominant behavior

In engineering modelsIn engineering models


bullbull Avoid implicit assumptions eg aboutAvoid implicit assumptions eg aboutndashndash problem contextproblem context

ndashndash referencereference

ndashndash orientationorientation

ndashndash coordinatescoordinates

ndashndash metricmetric

ndashndash lsquonegligiblersquo phenomena etclsquonegligiblersquo phenomena etc

bullbull Avoid model extrapolationAvoid model extrapolationndashndash danger of ignoring earlier assumptionsdanger of ignoring earlier assumptions

bullbull Focus at competence not lsquotruthrsquoFocus at competence not lsquotruthrsquo


Intuitive introduction of the lsquoportrsquo concept


ideal ideal motormotor

J

ideal ideal inertiainertiaideal ideal

transmissiontransmission

ideal current ideal current sourcesource

P

potentiometerpotentiometer

Dominant behaviorDominant behavior

(not necessarily competent in each context)(not necessarily competent in each context)

Simple modelSimple model



Addition of relevant parasitic behavior


Depending on Depending on problem problem contextcontext

Polymorphic Polymorphic modelingmodeling

What are portsWhat are ports


MECH

J

ii∆∆uu11

ii ii

∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33

ωω ωω

PP ==∆∆uusdotsdot ii(power)(power)

PP ==∆∆TTsdotsdotωω(power)(power)

ii∆∆uu44

∆∆TT11

ωω

electrical portselectrical ports

mechanical portsmechanical ports


Comparison with familiar model views


Iconic diagramsIconic diagrams(lsquoideal physical modelsrsquo)(lsquoideal physical modelsrsquo)

R L

C

R

K=1CFext

Usource

i v

F m

electricalelectrical mechanicalmechanical

Iconic diagram symbolsIconic diagram symbols


Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent



C-type storage

I -type storage

(M)R (dissipation

irreversible transduction)

Se (effort source)

Sf (flow source)

TF (transformer)

Iconic diagramsIconic diagrams


bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure

1

i

2020--simsim

iconicon

TF (transformer)TF (transformer)


Common block diagram models


R L

C

R

K=1CFext

Usource

i v

F m




Note not all signals Note not all signals are physically are physically

meaningful variablesmeaningful variables

Ports in iconic diagramsPorts in iconic diagrams


R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m

Ports in block diagramsPorts in block diagrams


Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable

Structure as multiportStructure as multiport


Different formsDifferent forms




Compact amp domain independentCompact amp domain independent


Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1

Structure explicitlyStructure explicitly

representedrepresented

as multiportas multiport

JUNCTIONJUNCTION

Ports in bond graph viewPorts in bond graph view


C

R

Se

I

1

Bond graphsBond graphs


Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)


Analog simulation withOP-AMPS



BondsBonds

Energy exchange = powerEnergy exchange = power

Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy

C ICompact notationCompact notation

bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds

Ports and power bondsPorts and power bonds


bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)

mass-spring systemmass-spring system


Dynamic conjugationDynamic conjugation


bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in

equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion

ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration

Power conjugationPower conjugation


= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct

ndashndash sumsum in case of scattering variablesin case of scattering variables

part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p


Conjugate variables amp corresponding statesConjugate variables amp corresponding states


Basic dynamic behaviorsamp mnemonic codes


bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)

bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)

bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction

bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf

bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY

bullbull gtgt gtgt 9 basic elements9 basic elements

Orientation conventionsOrientation conventions


bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))

bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules

minimizes sign errorsminimizes sign errors


Convention on effort and flow positions


Basic one-port elementsBasic one-port elements



Basic two- and multiport elements



Constitutive relations not necessarily linear


eg zener diodeeg zener diodedominant behaviordominant behavior

irreversible irreversible transduction transduction (resistor)(resistor)

with nonlinear with nonlinear constitutive relationconstitutive relation

R


Other form of non-linearityModulation


eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)

MR

capstancapstan


Bilateral signal flow (computational causality)


2 possibilities2 possibilities

NotationNotation


Causal strokeCausal stroke

Back to the exampleBack to the example


C

R

Se

I

1



C

R

Se

I

1

2020--sim demosim demo

Causal port propertiesCausal port properties


bullbull FixedFixed causalitycausality

bullbull PreferredPreferred (integral) causality(integral) causality

Causal constraintsCausal constraints


Arbitrary causalityArbitrary causality


Causality assignmentCausality assignment


Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via

constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo

ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)

ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))

ExampleExample


Se GY

II

R

1

R

1

2nd order loop2nd order loop

1st order loop1st order loop1st order loop1st order loop

bullbullImportant modeling feedbackImportant modeling feedback

bullbullAutomatic in 20Automatic in 20--simsim

bullbullVisible in bond graph causalityVisible in bond graph causality

bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams

J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω

Positive orientationPositive orientation


orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection

Causality does NOT affect orientationCausality does NOT affect orientation


Basic form of physical modelsBasic form of physical models


second lsquolawrsquoirreversible

transformation

boundaryaddition

structureconstraint relationsdistribution reversible

transformationtransport

first lsquolawrsquoconservation lsquolawsrsquo

storage

interfaces and structurehave to satisfy basic laws in degenerate way

storage = 0 production = 0 Basic lsquolawsrsquo

constitutive relationsdetermine particular occurrence (instantiation)


Thermodynamic approachThermodynamic approach

Energy balanceEnergy balance

for the totalfor the total

systemsystem

Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy

lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)

bullbull Difference is used to find the entropy productionDifference is used to find the entropy production

bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)

System boundarySystem boundary

Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)

GJSGJSGJS

Power continuous Power continuous junction structurejunction structure

Structure is Structure is conceptualconceptual


Mechanical versus Thermodynamic framework


Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)

CC--SGYSGY--CC

Only relaxation Only relaxation behavior Cbehavior C--RR

Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)

OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics

Symplectic gyratorSymplectic gyrator


bullbull Unit gyratorUnit gyrator

bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0

C11 C12C12 C22 SGYC 0Multiport


Symplectic GYratorSymplectic GYrator


bullbull Mechanical (Mechanical (xxpp))

ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)

bullbull Electrical network (Electrical network (qqλλ))

ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)

SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i

Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo


Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal

C1 SGY 1 I

R1 SGY 1 R

1 SGY TF SGY 0 1 TF 0

SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY


Basic model structure(generalized bond graph)


AntiAnti--reciprocal reciprocal part (generalized part (generalized

gyrator)gyrator)

Weighted Junction Weighted Junction Structure Structure

(reciprocal)(reciprocal)

Simple Junction Simple Junction Structure (generalized Structure (generalized

KirchhoffKirchhoff laws)laws)

Weighted part (generalized Weighted part (generalized transformer)transformer)

Generalized Junction Generalized Junction Structure (power Structure (power

continuous)continuous)Boundary conditionsBoundary conditions

(sources)(sources)

Energy storageEnergy storageIrreversible Irreversible transformationtransformation

(entropy production)(entropy production)


Mechanical framework of variables



Generalized thermodynamic framework of variables


q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow

eeffort generalized state

electric icurrent

uvoltage charge

magnetic uvoltage

icurrent magnetic flux linkage

thermal Ttemperature

fSentropy flow

entropy

chemical microchemical potential

fNmolar flow

number of moles




f flow


elasticpotential translation

vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum

elasticpotential rotation

ωangular velocity

Ttorque angular displacement

kinetic rotation Ttorque

ωangularvelocity

angularmomentum

elastic hydraulic ϕvolume flow

ppressure

volume

kinetic hydraulic ppressure

ϕvolume flow

momentum of a flow tube

θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d

Energy as starting pointEnergy as starting point


bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables

bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash

bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species

( ) ( )1 i nE E q E q q q= =

( ) ( )1 1 i k i kE H q p H q q q p p p= =

( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=


Configuration influence on energetic structure


bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force

ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)

ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms

(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation

ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)

( ) ( )

E q xF q x

xpart

=part

Modulated capacitorModulated capacitor


System (boundary) definitionSystem (boundary) definition


bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo

N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo

V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries

NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally

LagrangianLagrangian (eg network of tubes)(eg network of tubes)

lsquoClassical network casersquolsquoClassical network casersquo


bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters

bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order

homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts

(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and

extensive descriptionextensive description

If not a networkIf not a network


bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible

bullbull Example balloonExample balloon

Part of a tube networkPart of a tube network


daxialV=0(V not a convected property)daxial Nne0

dradialN=0dradial Vne0(flexible tube local changes)

System boundary definitionSystem boundary definition


bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates

bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant

ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion

restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element

destroys the topologyrsquodestroys the topologyrsquo


SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on

ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics

bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as

bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized

networknetwork

ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy

bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable

ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)

bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher

PORT-BASED MODELING OF DYNAMIC SYSTEMS fundamental concepts and bond graphs

Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling

Model representation

Physical systems modeling

Contents of the sequel

Modeling pitfalls

Port-based modeling




Component mounter


lsquoParasiticrsquo elements

In engineering models


Simple model


What are ports


Iconic diagram symbols


Iconic diagrams



Ports in iconic diagrams


Ports in block diagrams

Structure as multiport

Different forms

Different forms

Compact amp domain independent


Ports in bond graph view

Bond graphs


Bonds

Ports and power bonds

mass-spring system

Dynamic conjugation

Power conjugation

Conjugate variables amp corresponding states


Orientation conventions


Basic one-port elements





Notation

Back to the example

Back to the example

Causal port properties

Causal constraints

Arbitrary causality

Causality assignment

Example

Positive orientation

Causality does NOT affect orientation

Symplectic gyrator

Symplectic GYrator


Modulated capacitor

Example nonlinear 3-port C

Regular causal form in thermodynamics

Desired integral causal form

Form requires T0 not S0

Concluding remarks

Some remarksSome remarks


bullbull Role of concepts (lsquointellectrsquo multiple views)Role of concepts (lsquointellectrsquo multiple views)bullbull Ports from a historical energy point of viewPorts from a historical energy point of view

(energy states)(energy states)bullbull Focus on linear motion and fixed axis rotation Focus on linear motion and fixed axis rotation

simple configuration constraints no need for simple configuration constraints no need for abstract geometrical concepts (like in the rest of abstract geometrical concepts (like in the rest of the course)the course)

bullbull Separation between configuration state and energy Separation between configuration state and energy statestatestructures influence of kinematic constraintsstructures influence of kinematic constraints











































AimAim














frameworkframework






datadata




















ModelingModeling























A

A

A

A

A

T

T

T

T

T

a

b

c

d

e

x1

x2

x3

x4

x5


A

T

T

A

x

t

x1 x5x4

x3x2



















































































J




P













MECH

J

ii∆∆uu11

ii ii

∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33

ωω ωω



ii∆∆uu44

∆∆TT11

ωω







R L

C

R

K=1CFext

Usource

i v

F m







C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks











































AimAim














frameworkframework






datadata




















ModelingModeling























A

A

A

A

A

T

T

T

T

T

a

b

c

d

e

x1

x2

x3

x4

x5


A

T

T

A

x

t

x1 x5x4

x3x2



















































































J




P













MECH

J

ii∆∆uu11

ii ii

∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33

ωω ωω



ii∆∆uu44

∆∆TT11

ωω







R L

C

R

K=1CFext

Usource

i v

F m







C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks






frameworkframework






datadata




















ModelingModeling























A

A

A

A

A

T

T

T

T

T

a

b

c

d

e

x1

x2

x3

x4

x5


A

T

T

A

x

t

x1 x5x4

x3x2



















































































J




P













MECH

J

ii∆∆uu11

ii ii

∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33

ωω ωω



ii∆∆uu44

∆∆TT11

ωω







R L

C

R

K=1CFext

Usource

i v

F m







C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks






datadata




















ModelingModeling























A

A

A

A

A

T

T

T

T

T

a

b

c

d

e

x1

x2

x3

x4

x5


A

T

T

A

x

t

x1 x5x4

x3x2



















































































J




P













MECH

J

ii∆∆uu11

ii ii

∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33

ωω ωω



ii∆∆uu44

∆∆TT11

ωω







R L

C

R

K=1CFext

Usource

i v

F m







C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks


















ModelingModeling























A

A

A

A

A

T

T

T

T

T

a

b

c

d

e

x1

x2

x3

x4

x5


A

T

T

A

x

t

x1 x5x4

x3x2



















































































J




P













MECH

J

ii∆∆uu11

ii ii

∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33

ωω ωω



ii∆∆uu44

∆∆TT11

ωω







R L

C

R

K=1CFext

Usource

i v

F m







C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks
















A

A

A

A

A

T

T

T

T

T

a

b

c

d

e

x1

x2

x3

x4

x5


A

T

T

A

x

t

x1 x5x4

x3x2



















































































J




P













MECH

J

ii∆∆uu11

ii ii

∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33

ωω ωω



ii∆∆uu44

∆∆TT11

ωω







R L

C

R

K=1CFext

Usource

i v

F m







C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks


















































































J




P













MECH

J

ii∆∆uu11

ii ii

∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33

ωω ωω



ii∆∆uu44

∆∆TT11

ωω







R L

C

R

K=1CFext

Usource

i v

F m







C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks










MECH

J

ii∆∆uu11

ii ii

∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33

ωω ωω



ii∆∆uu44

∆∆TT11

ωω







R L

C

R

K=1CFext

Usource

i v

F m







C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks





R L

C

R

K=1CFext

Usource

i v

F m







C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks






C-type storage

I -type storage

(M)R (dissipation


Se (effort source)

Sf (flow source)

TF (transformer)




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks




1

i

2020--simsim

iconicon





R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks




R L

C

R

K=1CFext

Usource

i v

F m








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks








R L

C

R

K=1CFext

Usource

i v

F m



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks



R L

C

R

K=1C

Fext

Usource

i

v

F

m












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks












Source

Coil

Capacitor

Resistor

Source

Mass

Spring

Damper

Domain dependent



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks



I

C

R

Se

I

C

R

1Se

Domain independent

1




JUNCTIONJUNCTION



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks



C

R

Se

I

1








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks








BondsBonds



















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks















part part= = + = +

part part

part= =

partpart

= =part

sum sum sum sumddd

d d d

d effort

d

d flow

d

jii i j j

i ji j i j

ji j

i

ii j

j

pqE E EP e f e f

t q t p t

pEe e

q t

q Ef f

t p































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks































R





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks





MR

capstancapstan





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks





NotationNotation





C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks



C

R

Se

I

1



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks



C

R

Se

I

1
















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks















ExampleExample


Se GY

II

R

1

R

1







J

u

i u

i

u

i

u

i

u

i

T

ω

T

ω









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks









transformation

boundaryaddition




storage








systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks





systemsystem







GJSGJSGJS







CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks





CC--SGYSGY--CC







bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks




bullbull SGYSGY

bullbull Multiport

r = 1GY0 0C C

SGY0 0C C

0 -1+1 0









SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks







SGY0 0C C

SGY0 0C C

part=

partpotEex

dd

=potxft

part=

partkinEep

dd

=kinpft

dd

= minuspFt

=potf v

=pote F=kine v

dd

= minuspFt

λpart

=partmagEe

ddλ

=magft

ddλ

minus = ut

=mage i

dd

=elecqft

=elecf i

part=

partelecEeq=elece u

ddλ

minus = ut

=mage i




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks




C1 SGY 1 I

R1 SGY 1 R


SGY GY SGY 1 1 GY 1

SGY1

1 TF 0SGY1

1 GY 1

0GY

TF 1

1 0SGY SGY1

0

SGY

1

1

0

1 0

0

SGY SGY0

1

SGY

1 0

1

1

0

0

Se SGY 1

0Sf SGY

Sf 1

Se 0

I 0 C0 SGY





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks





gyrator)gyrator)








(sources)(sources)









q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks







q f t= int d

q i t= int d

λ = intu td

int= tSS f d

int= tNN f d

f flow


electric icurrent

uvoltage charge

magnetic uvoltage



fSentropy flow

entropy


fNmolar flow

number of moles




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks




f flow



vvelocity

Fforce displacement

kinetic translation

Fforce

vvelocity momentum


ωangular velocity



ωangularvelocity

angularmomentum


ppressure

volume


ϕvolume flow


θ = int ωdt

b T t= int d

V t= int ϕd

dp tΓ = int

p F t= int d

x v t= int d

q f t= int d






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks






( ) ( )1 i nE E q E q q q= =


( ) ( ) E U q U V S N= =

( ) ( )( )( )

1

1 1

i m

i m

E U q U V S N

U V S N N N

U V S N N N Nminus

= = =

= =

=

( ) ( )( )

2

2

i n

i n

U U q U S q q q

S S U q q q

= =

=









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks









( ) ( )

E q xF q x

xpart

=part





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks





































networknetwork






Some remarks

General Outline

Introduction

Introduction

Course objectives

Aim

Fundamental issues

Modeling




Modeling pitfalls

Port-based modeling




Component mounter





Simple model


What are ports




Iconic diagrams







Different forms

Different forms




Bond graphs


Bonds


mass-spring system

Dynamic conjugation

Power conjugation










Notation

Back to the example

Back to the example


Causal constraints

Arbitrary causality


Example



Symplectic gyrator

Symplectic GYrator


Modulated capacitor





Concluding remarks

Control Engineering Laboratory PORT-BASED MODELING · PDF fileControl Engineering Laboratory...

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