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Control Systems Lab - SC4070
Organization, Modeling Recap and Lab Overview
Dr. Manuel Mazo Jr.Delft Center for Systems and Control (TU Delft)[email protected].:015-2788131
TU Delft, February 10, 2014(slides modified from the original drafted by Robert Babuska)
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Outline
1 Course Organization and Content
2 Short Recap on System Modeling, Identification andPractical Control Synthesis
3 Overview of Laboratory Setups
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Outline
1 Course Organization and Content
2 Short Recap on System Modeling, Identification andPractical Control Synthesis
3 Overview of Laboratory Setups
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Control Systems Lab SC4070
Lecturer: Manuel Mazo Jr.Lab Assistants: Yiming Wan
Harsh Shukla
Questions on theory, class organization Lecturer
Questions on models, implementation Lab Assistants
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Control Systems Lab SC4070
4 lecturesMonday 10-02 2014, 3mE-CZ F, 15:45-17:30Friday 14-02 2014, 3mE-CZ D, 15:45-17:30Friday 21-02 2014, 3mE-CZ D, 15:45-17:30
(TBC) Monday 24-02 2014, 3mE-CZ F, 10:45-12:30
1 lab demoMonday 17-02 2014, 3mE 34 F-0-420, 15:45-17:30
home preparation, laboratory sessions
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Control Systems Design Lab
Lab: Room 3mE 34 F-0-420
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Groups and Setups
Group Names Lab Setup Schedule of Lab
A
B
C
D
E
...
Lab groups are formed by three students. Send via email:
1. names, 2. student numbers, 3. emails of the three members
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Course Objectives
Recall control system design techniques
Applymethodologies to a real process:
first in simulations then on the actual experimental setup
Understandtheory,develophands-on experience
Prerequisites and background
Introduction to Modeling and Control Basics of Classical Control Engineering
Basics of Control Systems Design Experience with MATLAB and Simulink
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Outline of the lectures
(I). Logistics, introduction, modeling
(II). Dynamical systems, modeling and identification
(III). Control design methods
(III and IV). Matlab & Simulink, implementation
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Home work and Laboratory sessions
follow lectures and lab demo (first two weeks)
form group, choose laboratory setup (first week)
implement a Simulink model (home)
calibrate model (estimate parameters) to match process (lab)
identify a black-box model (lab), compare with above (home)
design a controller for the simulation model (home)
test and tune the controller on the process (lab)
Discuss with the lecturer / lab assistants your plans along the way, and the
possible theory / lab problems you may encounter.
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Assesment
Work is done in groups of three students.
Participation to lab sessions.
Presentation of results.(Week 12 (week of March 17th))
Written report.(Deadline: Friday morning, 28-03-2014) max 10 pages clear and complete stating exact contributions of each group member
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Tips for presentations and reports
Include Table of content, Introduction and Conclusions
Motivate all choices made (e.g., sampling, design parameters)
Compare simulation and real-time results, evaluate critically
Plots:
label axes (variables and units), provide figure captions use the Matlab function plot, do not paste Simulink scopes
Write concisely, do not include much theoretical background
Stress own experience, inventions, lessons learnt
Presentations: do not explain mathematical models in detail, doexplain what is measured and actuated
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Course Material
Book (background on control theory):Franklin, Powell, and Emami-Naeini.Feedback Control of Dynamic Systems.
Fifth Edition, Prentice Hall, 2006.
Slides and handouts:available on the WEBhttp://www.dcsc.tudelft.nl/sc4070
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Course Material
Book (elements of digital control):Astrom K.J. and Wittenmark B.:Computer Controlled Systems 3ed.
Prentice Hall, 1997.(Chapters 1 9)
Matlab/Simulink Software
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C
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Course information on the Web
Public website: www.dcsc.tudelft.nl/sc4070
Course information
Material, files
Important dates, notifications sent via BlackBoard
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S h d l
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Schedule
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St d L d
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Study Load
Week 7 8 9 10 11 12 13 Total
Lectures 4 4 8Home prep. 10 10 10 10 6 46
Laboratory 5 5 5 15Presentation 8 3 11Report 8 12 20
Total 14 14 15 15 19 11 12 100
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S i t t t t f h
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Some important concepts to refresh
Frequency IO models, transfer functions
State-space models
Linearization of nonlinear models
State feedback
Observers, output feedback
Digital control
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M tl b d Si li k
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Matlab and Simulink
software is available via BlackBoard and on faculty desktops
Matlab basics (plot, load, save, M-files, etc.)
Control toolbox:
LTI class (ss, tf, zpk) time-domain and frequency analysis (step, bode) control design tools (place, acker)
Simulink (interface between computer and experimental device)
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O tli
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Outline
1 Course Organization and Content
2
Short Recap on System Modeling, Identification andPractical Control Synthesis
3 Overview of Laboratory Setups
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S bje t f the e feedb k t l
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Subject of the course: feedback control
outputs
Process
inputs
disturbances
reference
Controller
feedback
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Digital implementation
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Digital implementation
design + implementation of computer-controlled systems
y(t)u(t)
Computer
ProcessAlgorithm
Clock
{ ( )}u t{ ( )}y tk kA-D D-A
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How to obtain a process model?
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How to obtain a process model?
1 physical, mechanistic modeling
1 use first principles differential equations (possibly
nonlinear)2 linearize around an operating point3 discretize to interface with controller
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How to obtain process model?
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How to obtain process model?
1 physical, mechanistic modeling
1 use first principles differential equations (possiblynonlinear)
2 linearize around an operating point3
discretize/digitalize to interface with controller2 from data, system identification
1 measure inputoutput data (around single operating point)2 define model structure (order), mostly linear3 estimate model parameters from data (e.g., via least
squares)
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Example: Physical Modeling of a DC
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Example: Physical Modeling of a DCMotor
V
T
J
,
R L
+
V = Kb
b
-
+
-
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Example: Physical Modeling of a DC
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Example: Physical Modeling of a DCMotor
V
T
J
,
R L
+
V = Kb
b
-
+
-
L didt
+Ri=V Vb , Vb=K=K d
dt
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Example: Physical Modeling of a DC
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Example: Physical Modeling of a DCMotor
V
T
J
,
R L
+
V = Kb
b
-
+
-
L didt
+Ri=V Vb , Vb=K=K d
dt
Jd2
dt2 bd
dt =T , T =Ki
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Modeling: Euler-Lagrange equation
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Modeling: Euler-Lagrange equation
Let T and Vbe the kinetic and potential energy of a system, then one can
use the following equations to obtain the dynamics equations of the system:
L(x) =T(x) V(x)
d
dt
L
x
=
L
x
Example: mass-spring system
T(x) = mx2
2
V(x) = kx2
2
Applying the Euler-Lagrange equation results into:
mx= kx
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Example: System Identification
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Example: System Identification
y
Process
u
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Example: System Identification
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Example: System Identification
Input data
u
t
y
Process
u
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Example: System Identification
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Example: System Identification
y
Output data
t
Input data
u
t
y
Processu
u(1), u(2), . . . , u(N) y(1), y(2), . . . , y(N)
y(t) =G(s)u(t)
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Controller Design in
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Controller Design inIndustrial Practice
Order the controller.
Unpack and connect.
Turn the knobs (e.g. PID) until it works.
This is of course slightly exaggerated, notable exceptions exist:aerospace, mechatronics, automotive, process/chemical . . .
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Controller Design in
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Controller Design inIndustrial Practice
Order the controller.
Unpack and connect.
Turn the knobs (e.g. PID) until it works.
This is of course slightly exaggerated, notable exceptions exist:aerospace, mechatronics, automotive, process/chemical . . .
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Controller Design in
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Controller Design inIndustrial Practice
Order the controller.
Unpack and connect.
Turn the knobs (e.g. PID) until it works.
This is of course slightly exaggerated, notable exceptions exist:aerospace, mechatronics, automotive, process/chemical . . .
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Controller Design in
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Controller Design inIndustrial Practice
Order the controller.
Unpack and connect.
Turn the knobs (e.g. PID) until it works.
This is of course slightly exaggerated, notable exceptions exist:aerospace, mechatronics, automotive, process/chemical . . .
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In-Class Controller design procedure
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g p
Develop a mathematical model of the process.
Implement the model for simulation purposes, estimate parameters.
Analyze dynamic properties of the system.
Determine the specifications (objective) for the controller.
Design a controller to comply with specs.
Test controller in simulations, redesign (if necessary).
Implement on the process, test, evaluate.
At least, this is the desired situation . . .
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In-Class Controller design procedure
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g p
Develop a mathematical model of the process.
Implement the model for simulation purposes, estimate parameters.
Analyze dynamic properties of the system.
Determine the specifications (objective) for the controller.
Design a controller to comply with specs.
Test controller in simulations, redesign (if necessary).
Implement on the process, test, evaluate.
At least, this is the desired situation . . .
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In-Class Controller design procedure
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Develop a mathematical model of the process.
Implement the model for simulation purposes, estimate parameters.
Analyze dynamic properties of the system.
Determine the specifications (objective) for the controller.
Design a controller to comply with specs.
Test controller in simulations, redesign (if necessary).
Implement on the process, test, evaluate.
At least, this is the desired situation . . .
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In-Class Controller design procedure
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Develop a mathematical model of the process.
Implement the model for simulation purposes, estimate parameters.
Analyze dynamic properties of the system.
Determine the specifications (objective) for the controller.
Design a controller to comply with specs.
Test controller in simulations, redesign (if necessary).
Implement on the process, test, evaluate.
At least, this is the desired situation . . .
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In-Class Controller design procedure
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Develop a mathematical model of the process.
Implement the model for simulation purposes, estimate parameters.
Analyze dynamic properties of the system.
Determine the specifications (objective) for the controller.
Design a controller to comply with specs.
Test controller in simulations, redesign (if necessary).
Implement on the process, test, evaluate.
At least, this is the desired situation . . .
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In-Class Controller design procedure
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Develop a mathematical model of the process.
Implement the model for simulation purposes, estimate parameters.
Analyze dynamic properties of the system.
Determine the specifications (objective) for the controller.
Design a controller to comply with specs.
Test controller in simulations, redesign (if necessary).
Implement on the process, test, evaluate.
At least, this is the desired situation . . .
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In-Class Controller design procedure
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Develop a mathematical model of the process.
Implement the model for simulation purposes, estimate parameters.
Analyze dynamic properties of the system.
Determine the specifications (objective) for the controller.
Design a controller to comply with specs.
Test controller in simulations, redesign (if necessary).
Implement on the process, test, evaluate.
At least, this is the desired situation . . .
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In-Class Controller design procedure
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Develop a mathematical model of the process.
Implement the model for simulation purposes, estimate parameters.
Analyze dynamic properties of the system.
Determine the specifications (objective) for the controller.
Design a controller to comply with specs.
Test controller in simulations, redesign (if necessary).
Implement on the process, test, evaluate.
At least, this is the desired situation . . .
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Outline
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1 Course Organization and Content
2 Short Recap on System Modeling, Identification andPractical Control Synthesis
3 Overview of Laboratory Setups
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Inverted pendulum / wedge setup
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Inverted wedge
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ac M, J
m
b
g
ukm
d
d = 1
m
kmu ma bd+md
2 +mgsin()
= 1
J+ma2 +md2 mad 2 mdd+mga sin()
+mgdcos() +Mgcsin()
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Parameters for inverted wedge
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Symbol Parameter Value
g acceleration due to gravity 9.81 ms2
a height of track 0.11 mc distance from COG to axis 0.045 mm mass of cart 0.49 kgM mass of balance 3.3 kgJ inertia of balance 0.42 kgm2
km input-to-force gain 5.0 Nb damping coefficient 4 to 10 kgs1
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Inverted pendulum
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m, l, J
d
b
M
g
uk
m
= 1J+ml2
mglsin() mldcos()
d = 1
M+m
kmu+ ml
2 sin() bd ml cos()
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Parameters for inverted pendulum
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Symbol Parameter Value
g acceleration due to gravity 9.81 ms2
l half length of pendulum 0.30 mm mass of pendulum 85 or 210 g
J inertia of pendulum 1
3 ml
2
M mass of cart 0.49 kgkm input-to-force gain 5.0 Nb damping coefficient 4 to 10 kgs1
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Helicopter setup
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Helicopter
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u
+ = K1u
+b+K2sin = f() ( approximation . . .= K3)
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Propeller nonlinearity
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u
y
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Gantry crane
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Gantry crane
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Gantry crane
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Rotational pendulum
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Rotational Pendulum
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m1
m2
l2
l1
m2g
m1g
motor
M()+C(, )+G() = kmu
0
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Rotational Pendulum: matrices
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M() =
P1+ P2+ 2P3cos 2 P2+ P3cos 2
P2+ P3cos 2 P2
C(, ) = b1 P32sin 2 P3(1+ 2)sin 2
P31sin 2 b2
G() =
g1sin 1 g2sin(1+ 2)
g2sin(1+ 2)
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