Experimental Control Science
Methodology, Algorithms, Solutions
Zhiqiang Gao, Ph.D.
Center for Advanced Control Technologies
Cleveland State University
December 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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Center for Advanced Control Technologies
From Applied Research
to
Advanced 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
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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
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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-lock
Brake System
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Turbofan engine
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A Non-isothermal CSTR
AT
• CV: product
concentration CA
Feed
AC
• MV: Coolant flowrate qc
qc
Coolant
Product, CA
dC A q
 E
 (C Af  C A )  k0C A exp  
dt
V
 RT
 H
dT q
 (T f  T )  
 C p
dt V

 c C pc

  C pV

• Difficulties:

 c (t )


 E
 k0C A exp  
 RT


 c (t )

 


hA
h (t )   Tcf  T 
 qc 1  exp  

q

C
pc
 
 c

– Strong nonlinearity
– Time varying
parameters: c(t) h(t)
(catalyst deactivation
and heat transfer fouling)
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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
• Introduction
• Questions
• Research Direction
• Methodology
• Active Disturbance Rejection
• Advanced Technologies
• Take Aways
• Open 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?
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An Art of Practice?
Hidden Technology?
Mathematics?
Engineering Science?
Control Science?
Natural Science?
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Where does control belong?
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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
• Introduction
• Questions
• Research Direction
• Methodology
• Active Disturbance Rejection
• Advanced Technologies
• Take Aways
• Open Problems
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Theory vs. Practice
A Historical Perspective
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Looking back
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PID (N. Minorsky)
Nyquist
Bode
Kalman
…
• Ho
• Han
1922
1932
1940
1961
1982
1989/1999
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Classical Control Era
Control
Practice
Control
Research
Mathematics
Control
Theory
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Modern Control Era
Control
Practice
Control
Research
Mathematics
unobservable
uncontrollable
Control
Theory
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<The Structure of Scientific Revolutions>
by Thomas S. Kuhn
Research:
Science:
• A strenuous and devoted
attempt to force nature
into the conceptual boxes
supplied by professional
education
• Suppresses fundamental
novelties because they
are necessarily
subversive of its basic
commitments.
• Most scientists are
engaged in mopping up
operations
• Predicated on the
assumption that the
scientific community
knows what the world is
like.
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Outline
• Introduction
• Questions
• Research Direction
• Methodology
• Active Disturbance Rejection
• Advanced Technologies
• Take Aways
• Open 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-conjectureexperiment-theory-validation”
• Carried out by BOTH theorists and
experimentalists
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Experiment
Discover
Theorize
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Reconnect
Control
Practice
Control
Research
Mathematics
Control
Theory
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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
• Introduction
• Questions
• Research Direction
• Methodology
• Active Disturbance Rejection
• Advanced Technologies
• Take Aways
• Open 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
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Modeling: Uncertainty Reduction
Example: modeling  design tuning
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Passive Disturbance Rejection
Example: PID tuning
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Active Disturbance Rejection
Example: 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
Plant:
y  f ( y, y, w)  u
Modeling:
f ( y, y, w)
in analytical form
Design Goal:
y  g ( y, y )
Control Law:
u   f ( y, y, w)  g ( y, y )
Examples:
pole placement; feedback linearization
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Industry Practice
With f ( y, y, w) unknown, u  l ( y ,
y)
y  f ( y, y, w)  l ( y, y )  g ( y, y )
The PID example
y  f (t , y, y, w)  ( K p e  K I  edt  K De)
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
f ( y, y, w)  y  u
• Estimating f ( y, y, w) in real time
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Active Disturbance Rejection
Augmented plant in state space: x1  y, x2  y, x3  f ( y, y, w)
y  f ( y, y, w)  u

Extended State Observer (Han)
 x1  x2
 x  x  u,
3
 2

 x3  f
y  x

1
 z1  z2  1 g1 ( z1  y )

 z2  z3   2 g 2 ( z1  y )  u
 z   g ( z  y)
3 3 1
 3
z1  x1 z2  x2 z3  x3  f
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Active disturbance compensation
 x1  x2

 x2  f  u
y  x
1

u  u0  z3
z3  f
f (t ) or f ( x1 , x2 , w)?
 x1  x2

 x2  u0
y  x
1

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Observer Comparison
y  f ( y, y, w)  u
Luenberge Observer
Extended State Observer
w(t)
w(t)
y(t)
u(t)
Plant
ŷ
ŷ
Plant
ŷ
Luenberger
State Observer
y(t)
u(t)
ŷ
fˆ
Extended
State Observer
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Observer Comparison
y  f ( y, y, w)  u
Luenberger Observer
Extended State Observer
• Needs expression of f
• Model-based
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• For LTI systems only
Estimates y, dy/dt, and f
Model-independent
Linear or nonlinear
TI or TV
One-parameter tuning
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y
(n)
 f ( y, y, w)  u

u   fˆ  u0

y ( n )  u0
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Active Disturbance Rejection Control
ADRC
• Generalized disturbance rejection:
– Internal disturbance: system dynamics
– External disturbance
– Combined into f
• Easily tuned
– Z. Gao, ACC2003
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Bandwidth-based Tuning
transient profile and output
2
bandwidth: 4 rad/sec
bandwidth: 20 rad/sec
transient profile
1
0
0
1
2
3
error
4
5
6
0
1
2
control3signal
4
5
6
0
1
2
3
time second
4
5
6
1
position
2
y
z1
0.5
1
0
0
1
2
3
velocity
4
5
6
2
dy/dt
z2
1
0
2
0
-1
0
1
2
3
4
disturbance
and unknown
dyanmics
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6
1
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0
f
z3
0
-1
-50
0
1
2
3
time second
4
5
6
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Hardware Test: torque disturbance
Torque Disturbance Rejection
Rev. 1.5
Position
ADRC
1
PID
0.5
0
0
2
4
6
8
Rev. 0.1
10
12
10
12
PID
Position error
0
ADRC
-0.1
0
2
4
6
8
Volts 5
ADRC
Control Command
0
PID
-5
0
2
4
6
8
10
12
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Performance of the disturbance observer
Total disturbance and its estimation
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20
a(t)
f(t)
z3(t)
10
0
-10
-20
-30
0
1
2
3
4
5
Time (sec.)
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Motion Control Demo
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Outline
• Introduction
• Questions
• Research Direction
• Methodology
• Active Disturbance Rejection
• Advanced Technologies
• Take Aways
• Open Problems
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Algorithms
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Nonlinear PID
Discrete Time Optimal Control
Active Disturbance Rejection
Single Parameter Tuning
Wavelet Controller/Filter
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Technologies
• 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)
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Take Aways
• Think outside “the box”
• Active disturbance rejection
• From problems to methods to
methodology
gao@csuohio.edu
http://cact.csuohio.edu
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Open Problems
• Characteristics of ESO
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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
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