1 experimental control science methodology, algorithms, solutions zhiqiang gao, ph.d. center for...
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Experimental Control Science
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 Research to
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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A Non-isothermal CSTR
• CV: product concentration CA
• MV: Coolant flowrate qc
• Difficulties: – Strong nonlinearity– Time varying
parameters: c(t) h(t) (catalyst deactivation and heat transfer fouling)
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0
0
( ) exp ( )
( ) exp ( )
1 exp ( )
AAf A A c
f A cp
c pcc 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
Coolant
Feed
q c
Product, CA
AT
AC
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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 Direction Research 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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Outline• IntroductionIntroduction
• QuestionsQuestions
• Research Direction
• MethodologyMethodology
• Active Disturbance RejectionActive Disturbance Rejection
• Advanced TechnologiesAdvanced Technologies
• Take AwaysTake Aways
• Open ProblemsOpen Problems
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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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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 devoted attempt to force nature into the conceptual boxes supplied by professional education
• Most scientists are engaged in mopping up operations
Science:
• Suppresses fundamental novelties because they are necessarily subversive of its basic commitments.
• Predicated on the assumption that the scientific community knows what the world is like.
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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 and experimentalists
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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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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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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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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
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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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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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• 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 to
methodology
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