234111 – Introduction to Computer Science1 הצטרפות לרשימת התפוצה של הקורס.
Experimental Control Science1 Experimental Control Science Methodology, Algorithms, Solutions...
Transcript of Experimental Control Science1 Experimental Control Science Methodology, Algorithms, Solutions...
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Experimental ControlScience
Methodology, Algorithms, Solutions
Zhiqiang Gao, Ph.D. Center for Advanced Control Technologies
Cleveland State UniversityDecember 24, 2004
http://cact.csuohio.edu
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Outline• Introduction
• Questions
• Research Direction
• Methodology
• Active Disturbance Rejection
• Advanced Technologies
• Take Aways
• Open Problems
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From Applied Researchto
Advanced Technologies
Center for Advanced Control Technologies
http://cact.csuohio.edu
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Center for Advanced Control Technologies
Zhiqiang Gao, Director
Sridhar Ungarala, Chemical Engineering
Daniel Simon, Embedded Control Systems, Electrical Engineering
Paul Lin, Mechanical Engineering.
Yongjian Fu, Software Engineering
Sally Shao, Mathematics
Jack Zeller, Engineering Technology
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Past Projects• Temperature Regulation• Intelligent CPAP/BiPAP• Motion Indexing• Truck Anti-lock Brake System• Web Tension Regulation• Turbine Engine Diagnostic• Computer Hard Disk Drive• Stepper Motor Field Control• 3D Vision Tire Measurement• Digitally Controlled Power Converter
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Sponsors• NASA• Rockwell Automation• Kollmorgen• ControlSoft• Federal Mogul• AlliedSignal Automotive• Invacare Co.• Energizer• Black and Decker• Nordson Co.• CAMP
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NASA Intelligent PMAD Project
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Web Tension Regulation
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Truck Anti-lockBrake System
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Turbofan engine
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A Non-isothermal CSTR
• CV: productconcentration CA
• MV: Coolant flowrate qc
• Difficulties:– Strong nonlinearity– Time varying
parameters: φc(t) φh(t)(catalyst deactivationand heat transferfouling)
11( )
0
0
( ) exp ( )
( ) exp ( )
1 exp ( )
AAf A A c
f A c
p
c pc
c h cf
p c pc
dC q EC C k C t
dt V RT
dT q H ET T k C t
dt V C RT
C hAq t T T
C V q C
!
!"
"!
" "
# $= % % %& '
( )
# $%* # $= % + %& ' & '& ' ( )( )
+ ,# $ # $+ % % %- .& ' & '& ' & '- .( ) ( )/ 0
Coolant
Feed
q c
Product, CA
AT
AC
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Nonlinear 3-Tank Fault Id. Problem
6 possible faults 2 inputs 3 outputs
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CACT Mission• Define, Articulate, Formulate
Fundamental Industrial Control Problems
• Solutions and Cutting Edge Technologies
• Performance and Transparency
• Synergy in Research and Practice
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Outline•• IntroductionIntroduction
• Questions
•• Research DirectionResearch Direction
•• MethodologyMethodology
•• Active Disturbance RejectionActive Disturbance Rejection
•• Advanced TechnologiesAdvanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
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Questions
• What is control & where does it belong?
• What is a good controller & how to find it?
• Does a theory-practice gap exist? Why?
• Can theoretical advance be driven by practice?
• What is the most fundamental control problem?
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How do we describe it?
• An Art of Practice?• Hidden Technology?• Mathematics?• Engineering Science?• Control Science?• Natural Science?
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Where does control belong?
• Electrical Engineering• Mechanical Engineering• Chemical Engineering• Aerospace Engineering• System Engineering• Mathematics• Biology?
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Is there a theory-practice gap?
Control Theory
⇓
Engineering Problem Solving
?
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Can theory be driven by practice?
New Theory
⇑ ?
Engineering Problem Solving
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Outline•• IntroductionIntroduction
•• QuestionsQuestions
• Research Direction
•• MethodologyMethodology
•• Active Disturbance RejectionActive Disturbance Rejection
•• Advanced TechnologiesAdvanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
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Theory vs. Practice
A Historical Perspective
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Looking back
• PID (N. Minorsky) 1922• Nyquist 1932• Bode 1940• Kalman 1961 …• Ho 1982• Han 1989/1999
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Classical Control Era
ControlPractice
ControlResearch
ControlTheory
Mathematics
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Modern Control Era
ControlPractice
ControlResearch
ControlTheory
MathematicsResearch
Theory
unobservable
uncontrollable
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<The Structure of Scientific Revolutions>by Thomas S. Kuhn
Research:
• A strenuous and devotedattempt to force natureinto the conceptualboxes supplied byprofessional education
• Most scientists areengaged in mopping upoperations
Science:
• Suppresses fundamentalnovelties because theyare necessarilysubversive of its basiccommitments.
• Predicated on theassumption that thescientific communityknows what the world islike.
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Outline•• IntroductionIntroduction
•• QuestionsQuestions
•• Research DirectionResearch Direction
• Methodology
•• Active Disturbance RejectionActive Disturbance Rejection
•• Advanced TechnologiesAdvanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
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Control as an Experimental Science
• Y.C. Ho, IEEE AC, Dec. 1982
• “Control” as experimental science (the 3rd dimension w.r.t. the gap)
• Experiment vs. Application(detective vs. craftsman)
• “observation-conjecture-experiment-theory-validation”
• Carried out by BOTH theorists andexperimentalists
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Experiment Discover Theorize
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Reconnect
ControlPractice
ControlResearch
ControlTheory
Mathematics
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The Han Paradigm
• Is it a Theory of Control or a Theory of Model?
• Paradox of Robust Control
(Godel’s Incompleteness Theorem)
• An Alternative Design Paradigm
– Explore Error-Based Control Mechanisms
– Active Disturbance Rejection
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The Paradox of theRobust Control Problem
Making model-dependent controldesign independent of the model
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GÖdel’s Incompleteness Theorem
“Within any formal system of axioms,such as present day mathematics,questions always persist that canneither be proved or disproved on thebasis of the axioms that define thesystem.” --paraphrased by S. Hawking
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Is the solution to the robust control problemoutside the existing control theory?
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Problem Reformulation
reconnect theory to practice
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Making Problem Definition Realistic
• Assumptions on the plant:– What is the minimum info needed for design?– What info is available in practice?
• Design Objectives:– Absolute requirements– Criteria of optimality (judgment for comparison)
• Design Constraints:– Actuator/sensor/digital controller– Hard and soft constraints
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Outline•• IntroductionIntroduction
•• QuestionsQuestions
•• Research DirectionResearch Direction
•• MethodologyMethodology
• Active Disturbance Rejection
•• Advanced TechnologiesAdvanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
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Questions
• What is control & where does it belong?
• What is a good controller & how to find it?
• Does a theory-practice gap exist? Why?
• Can theoretical advance be driven by practice?
• What is the most fundamental control problem?
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Uncertainty principle in control?
• Kalman Filter: uncertainty of measurement
• Industry Control: uncertainty of dynamics
• Disturbance: dynamics beyond the math model
• Disturbance ⇔ Uncertainty
• Control ⇔ Disturbance Rejection?
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Disturbance Rejection
• Modeling: Uncertainty ReductionExample: modeling ⇒ design ⇒ tuning
• Passive Disturbance RejectionExample: PID tuning
• Active Disturbance RejectionExample: Invariant Principle, ADRC (Han)
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A Motion Control Case Study
( , , )y f y y w u= +&& &
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Model-Based Method
( , , )y f y y w u= +&& &
Modeling: in analytical form
Design Goal:
Plant:
( , , )f y y w&
( , )y g y y=&& &
( , , ) ( , )u f y y w g y y= ! +& &
Examples: pole placement; feedback linearization
Control Law:
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Industry Practice
( , , ) ( , ) ( , )y f y y w l y y g y y= + !&& & & &
The PID example
With unknown,( , , )f y y w& ( , )u l y y= &
( , , , ) ( )p I Dy f t y y w K e K edt K e
e r y
= + + +
= !
"&& & &
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The Han Methods
• Beyond PID ⇒ Nonlinear PID ⇒ Time Optimal Control ⇒ Discrete Time Optimal Control ⇒ Find other error-based designs
• Find a way around modeling ( , , )f y y w&
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Getting around modeling
• Adding a sensor
• Estimating in real time
( , , )f y y w y u= !& &&
( , , )f y y w&
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Active Disturbance Rejection
1 2
2 3
3
1
,
x x
x x u
x f
y x
=!"
= +"#
="" =$
&
&
&&
Augmented plant in state space:
Extended State Observer (Han)
1 2 31 2 3 z x z x z x f! !! =
1 2 1 1 1
2 3 2 2 1
3 3 3 1
( )
( )
( )
z z g z y
z z g z y u
z g z y
!
!
!
= " "#$
= " " +%$ = " "&
&
&
&
1 2 3, , ( , , )x y x y x f y y w= = =& &
( , , ) y f y y w u= + !&& &
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Active disturbance compensation
1 2
2 0
1
x x
x u
y x
=!"
#$" =%
&
&
1 2
2
1
x x
x f u
y x
=!"
= +#" =$
&
&
0 3
3
u u z
z f
= !
"
1 2( , , )?( ) or f x x wf t
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Observer Comparison
Luenberge Observer Extended State Observer
Plant
y(t)
w(t)
Extended
State Observer
u(t)Plant
y(t)
w(t)
Luenberger
State Observer
u(t)
yy
y& y&
( , , )y f y y w u= +&& &
f
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Observer Comparison
Luenberger Observer
• Needs expression of f• Model-based• For LTI systems only
Extended State Observer
• Estimates y, dy/dt, and f• Model-independent• Linear or nonlinear• TI or TV• One-parameter tuning
( , , )y f y y w u= +&& &
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!
!
( ) ( , , )ny f y y w u= +&
0
ˆu f u= ! +
( )
0
ny u!
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Active Disturbance Rejection ControlADRC
• Generalized disturbance rejection:– Internal disturbance: system dynamics– External disturbance– Combined into f
• Easily tuned– Z. Gao, ACC2003
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Bandwidth-based Tuning
0 1 2 3 4 5 60
1
2position
y z1
0 1 2 3 4 5 6-1
0
1
2velocity
dy/dtz2
0 1 2 3 4 5 6-50
0
50disturbance and unknown dyanmics
time second
f z3
0 1 2 3 4 5 60
1
2transient profile and output
bandwidth: 4 rad/sec bandwidth: 20 rad/sectransient profile
0 1 2 3 4 5 60
0.5
1error
0 1 2 3 4 5 6-1
0
1
2control signal
time second
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Hardware Test: torque disturbance
0 2 4 6 8 10 120
0.5
1
1.5
0 2 4 6 8 10 12-0.1
0
0.1
0 2 4 6 8 10 12-5
0
5
Torque Disturbance Rejection Rev.
Rev.
Volts
Position
Position error
Control Command
ADRC
ADRC
ADRC
PID
PID
PID
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Performance of the disturbance observer
0 1 2 3 4 5-30
-20
-10
0
10
20
30
a(t)
z3(t)
Total disturbance and its estimation
Time (sec.)
f(t)
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Motion Control Demo
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Outline•• IntroductionIntroduction
•• QuestionsQuestions
•• Research DirectionResearch Direction
•• MethodologyMethodology
•• Active Disturbance RejectionActive Disturbance Rejection
• Advanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
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Algorithms
• Nonlinear PID• Discrete Time Optimal Control• Active Disturbance Rejection• Single Parameter Tuning• Wavelet Controller/Filter
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Nonlinear PID
• Error driven, not model-based• Nonlinear “proportional” term gp(e)
– Small error, large gain– Reduce the role of integrator
• Nonlinear integral control– Reduce phase lag– Maintain zero s.s. error and good disturbance rejection
• Nonlinear differentiator– Noise immunity
( ) ( ) ( )p p I i D du K g e K g e dt K g e= + +! &
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Discrete Time Optimal Control Law1 2
0
1 2
2
0
0
2 0
2 0
(( , , , )
;
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=
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1
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x k Ax k Bu k
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x
+ = +
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= = =" # " # " #$ % $ % $ %& ' & '& '
=
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Comparison of switching curves
Details
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• Manufacturing (Motion, Web Tension, CNC)
• Power Electronics (Motor, PMAD, Converters)
• Aircraft (Flight, Jet Engine)
• Process Control (CSTR)
• Biomedical (Ankle)
• Health/fault Monitoring (A benchmark prob.)
• Automobile (Truck ABS)
Technologies
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Take Aways
• Think outside “the box”
• Active disturbance rejection
• From problems to methods tomethodology
http://[email protected]
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Open Problems• Characteristics of ESO
– Convergence,– Rate of Convergence,– Boundedness– Bound of error– Order estimation– b0 estimation (Initial results)
• Practical Optimality (Initial results)• Reformulation of process control problems• Cybernetics
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A Research Alliance• Practitioners/Researchers/Mathematicians
• Discover (both practitioners and theoreticians)
• Theorize– Prove stability and convergence– Generalize a particular solution/method– Establish a new kind of theory
• Validate– Verify the new theory against other problems– Define the range of applicability