experimental control science1 experimental control science methodology, algorithms, solutions...
TRANSCRIPT
1
Experimental ControlScience
Methodology, Algorithms, Solutions
Zhiqiang Gao, Ph.D. Center for Advanced Control Technologies
Cleveland State UniversityDecember 24, 2004
http://cact.csuohio.edu
2
Outline• Introduction
• Questions
• Research Direction
• Methodology
• Active Disturbance Rejection
• Advanced Technologies
• Take Aways
• Open Problems
3
From Applied Researchto
Advanced Technologies
Center for Advanced Control Technologies
http://cact.csuohio.edu
4
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
5
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
6
Sponsors• NASA• Rockwell Automation• Kollmorgen• ControlSoft• Federal Mogul• AlliedSignal Automotive• Invacare Co.• Energizer• Black and Decker• Nordson Co.• CAMP
7
NASA Intelligent PMAD Project
8
Web Tension Regulation
9
Truck Anti-lockBrake System
10
Turbofan engine
11
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
12
Nonlinear 3-Tank Fault Id. Problem
6 possible faults 2 inputs 3 outputs
13
CACT Mission• Define, Articulate, Formulate
Fundamental Industrial Control Problems
• Solutions and Cutting Edge Technologies
• Performance and Transparency
• Synergy in Research and Practice
14
Outline•• IntroductionIntroduction
• Questions
•• Research DirectionResearch Direction
•• MethodologyMethodology
•• Active Disturbance RejectionActive Disturbance Rejection
•• Advanced TechnologiesAdvanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
15
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?
16
How do we describe it?
• An Art of Practice?• Hidden Technology?• Mathematics?• Engineering Science?• Control Science?• Natural Science?
17
Where does control belong?
• Electrical Engineering• Mechanical Engineering• Chemical Engineering• Aerospace Engineering• System Engineering• Mathematics• Biology?
18
Is there a theory-practice gap?
Control Theory
⇓
Engineering Problem Solving
?
19
Can theory be driven by practice?
New Theory
⇑ ?
Engineering Problem Solving
20
Outline•• IntroductionIntroduction
•• QuestionsQuestions
• Research Direction
•• MethodologyMethodology
•• Active Disturbance RejectionActive Disturbance Rejection
•• Advanced TechnologiesAdvanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
21
Theory vs. Practice
A Historical Perspective
22
Looking back
• PID (N. Minorsky) 1922• Nyquist 1932• Bode 1940• Kalman 1961 …• Ho 1982• Han 1989/1999
23
Classical Control Era
ControlPractice
ControlResearch
ControlTheory
Mathematics
24
Modern Control Era
ControlPractice
ControlResearch
ControlTheory
MathematicsResearch
Theory
unobservable
uncontrollable
25
<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.
26
Outline•• IntroductionIntroduction
•• QuestionsQuestions
•• Research DirectionResearch Direction
• Methodology
•• Active Disturbance RejectionActive Disturbance Rejection
•• Advanced TechnologiesAdvanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
27
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
28
Experiment Discover Theorize
29
Reconnect
ControlPractice
ControlResearch
ControlTheory
Mathematics
30
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
31
The Paradox of theRobust Control Problem
Making model-dependent controldesign independent of the model
32
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
33
Is the solution to the robust control problemoutside the existing control theory?
34
Problem Reformulation
reconnect theory to practice
35
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
36
Outline•• IntroductionIntroduction
•• QuestionsQuestions
•• Research DirectionResearch Direction
•• MethodologyMethodology
• Active Disturbance Rejection
•• Advanced TechnologiesAdvanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
37
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?
38
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?
39
Disturbance Rejection
• Modeling: Uncertainty ReductionExample: modeling ⇒ design ⇒ tuning
• Passive Disturbance RejectionExample: PID tuning
• Active Disturbance RejectionExample: Invariant Principle, ADRC (Han)
40
A Motion Control Case Study
( , , )y f y y w u= +&& &
41
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:
42
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
= + + +
= !
"&& & &
43
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&
44
Getting around modeling
• Adding a sensor
• Estimating in real time
( , , )f y y w y u= !& &&
( , , )f y y w&
45
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= + !&& &
46
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
47
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
48
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= +&& &
49
!
!
( ) ( , , )ny f y y w u= +&
0
ˆu f u= ! +
( )
0
ny u!
50
Active Disturbance Rejection ControlADRC
• Generalized disturbance rejection:– Internal disturbance: system dynamics– External disturbance– Combined into f
• Easily tuned– Z. Gao, ACC2003
51
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
52
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
53
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)
54
Motion Control Demo
55
Outline•• IntroductionIntroduction
•• QuestionsQuestions
•• Research DirectionResearch Direction
•• MethodologyMethodology
•• Active Disturbance RejectionActive Disturbance Rejection
• Advanced Technologies
•• Take AwaysTake Aways
•• Open ProblemsOpen Problems
56
Algorithms
• Nonlinear PID• Discrete Time Optimal Control• Active Disturbance Rejection• Single Parameter Tuning• Wavelet Controller/Filter
57
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= + +! &
58
Discrete Time Optimal Control Law1 2
0
1 2
2
0
0
2 0
2 0
(( , , , )
;
8 | |
( ), | |2
/ , | |
( ), | |
, | |
u fst x x r h
d rh d hd
y x hx
a d r y
a dx sign y y d
a
x y h y d
r sign a a d
fst ar a dd
=
= =
= +
= +
!"+ >#
= $# + %&
>"#
= !$%#&
1
2
0
( 1) ( ) ( )
| ( ) |
1 0, ,
0 1
(0)
0
0f
x k Ax k Bu k
u k r
x hx A B
x h
x x
x
+ = +
!
= = =" # " # " #$ % $ % $ %& ' & '& '
=
" #= $ %& '
59
Comparison of switching curves
Details
60
• 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
61
Take Aways
• Think outside “the box”
• Active disturbance rejection
• From problems to methods tomethodology
http://[email protected]
62
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
63
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