Bridging the theory-practice gap
through problem reformulation:
a motion control case study
Zhiqiang Gao, Ph.D.
Center for Advanced Control Technologies
Cleveland State University
June 24, 2004
www.cact.csuohio.edu
1
Outline
• Introduction
• The Theory-Practice Gap
• An Experimental Science
Approach to Control Research
• Problem Reformulation
• Conclusions
2
Center for Advanced Control Technologies
From Applied Research
to
Advanced Technologies
www.cact.csuohio.edu
3
CACT Mission
• Define, Articulate, Formulate
Fundamental Industrial Control Problems
• Solutions and Cutting Edge Technologies
• Performance and Applicability
• Synergy in Research and Practice
4
Center for Advanced Control Technologies
FACULTY:
Dr. Zhiqiang Gao, Director of CACT, ACRL and AERL
Dr. Daniel Simon, Director of the Embedded Systems Laboratory in
Electrical Engineering.
Dr. Paul Lin, Director of the 3D Optical Measurement Laboratory in
Mechanical Engineering.
Dr. Yongjian Fu, Software Engineering
Dr. Sally Shao, Mathematics
Prof. Jack Zeller, Engineering Technology, 40 yrs+ experience, P.E.
5
Center for Advanced Control Technologies
Doctoral Candidate Researchers:
Frank Goforth
Robert Miklosovic
Zhan Ping
Wankun Zhou
Aaron Radke
Chunming Yang
Qing Zheng
Sri Kiran Kosanam
Masters Candidate Researchers:
Eric Dittmar
Bharath Endurthi
Hrishikesh Godbole
Sai Kiran Gumma
Qing Guo
Ivan Jurcic
Srujan Kusumba
Mike Gray
Xiaolong Li
Ramgopal Mushini
Nuha Nuwash
Tong Ren
Bhavinkumar Shah
Chirayu Shah
Madhura Shaligram
6
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
AlliedSignal Automotive
Invacare Co.
Energizer
Rockwell Automation
Kollmorgan
ControlSoft
Black and Decker
Nordson Co.
CAMP
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NASA Intelligent PMAD Project
9
Networked Power Converters
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Case Study: Web Tension
Regulation
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Case Study:
Truck Anti-lock
Brake System
12
Case Study: Computer Hard
Disk Drive
13
We build it, test it, and make it work.
We apply our research using
our partner’s products.
15
We get results: Wavelet
control for robust machines.
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We get results: Advanced motor
field control reduces cost.
17
We get results: Model Independent
control design & tuning.
18
We write the software.
19
We have staff from the
“School of Hard Knocks”.
20
It All Comes Down To Mathematics
• Level of abstraction
• Clarity in thinking
• Theory and guidance
21
Theory vs. Practice
A Historical Perspective
22
The Classical Control Era
Control
Practice
Control
Research
Mathematics
Control
Theory
23
The Modern Control Era
Control
Practice
Control
Research
Mathematics
Control
Theory
24
The transition did go quietly
25
4/1964 IEEE Trans. Automatic Control
Editorial
“In recent years, there has been
considerable discussion about the
gap which appears to exist between
control theory and its application…”
“It appears that the problem of the
gap is a control problem in itself; it
must be properly identified and
optimized through proper action…”
AACC Theory and Applications
Committee meeting, 3/24/1964
“Bridging the Gap Between Theory
and Practice”
26
4/1965 IEEE Trans. Automatic Control
Guest Editorial by Harold Chestnut
Proposed Solutions:
• Company sponsored
Education
• Component Study by
Universities
• Promotion of Economic
Incentives
• Publication Policies
• Definition of characteristics of
systems and subsystems
27
8/1967 IEEE Trans. Automatic Control
Editorial by J.C. Lozier
On panel discussions:
“These panels, staffed with leading
theoreticians, have automatically
assumed that theory is ahead of
practice, and they conclude that the
solution lies in reeducating the
designers. The establishment has
spoken.”
Suggestion in bridging the gap:
stimulate
– papers on general practice
– papers on advanced engineering
practice
– a more hospital atmosphere where
results are as important as
methods
28
2/1968 IEEE Trans. Automatic Control
Announcement by John. B. Lewis
• Special two day conference
preceding JACC meeting
• Responding to 65 and 67 editorials
• Each session is “a complete case
history necessarily brings together
theory and practice”
• “Demonstration of what can be
achieved by applying control
theory to major problems”
29
12/1982 IEEE Trans. Automatic Control
Editorial by Y.C. Ho
• “Control” as experimental science
(the 3rd dimension w.r.t. the gap)
• Experiment vs. Application
(detective vs. craftsman)
• The “observation-conjectureexperiment-theory-validation”
paradigm
• Carried out by BOTH theorists and
experimentalists
30
The debate continues
• “On Control Theory and Practice”, G. John, AC, June 1970
• “Editorial: Some Thoughts on Research”, J. Mereditch, AC, Feb.
1980
• “Editorial: Theory and application: A common ground?” M. Sain,
June 1980.
• “An Industrial Point of View on Control Teaching and Theory”, E. H.
Bristol, CSM, Feb. 1986
• Special Issue on Theory and Practice Gap, CSM December 1999.
• Theory vs. Practice Forum, ACC 2004
31
The ISA Initiative
• ISA (Instrument, systems, and automation)
is the largest organization of instrument
and control engineers in the world
• ISA is organizing a Theory vs. Practice
Forum at ACC2004 (by Z. Gao and R. Rhinehart)
32
Reflection on Control Research
What and Why?
33
What is controls?
r
e
u
y
Controls: An instrument
or a setPlant
of
Controller
Reference
Gas Pedal
Vehicle
Error
Speedinstruments used to operate,
Position
regulate,Speed
or
guide a machine or vehicle
Sensor
-the American Heritage Dictionary
Is it a branch of engineering, science, or
mathematics?
34
Control Engineering?
Engineering: The application of scientific
principles to practical ends as the design,
construction, and operation of efficient and
economical structures, equipment, and
systems.
-the American Heritage Dictionary
If control is a branch of engineering, what
are the scientific principles behind it?
35
Control Science?
Science: The observation, identification,
description, experimental investigation,
and theoretical explanation of natural
phenomena. -the American Heritage Dictionary
36
The Theory-Practice Divide
• Practitioners practice, improvise,
experiment (experience counts in industry)
• Theorists theorize
Modern Control Theory is often viewed as a
branch of Applied Mathematics
• Why the divide?
37
Experimental Controls Research
Discover vs. Apply
38
Experiment
Discover
Theorize
39
• Observation:
95% of controllers used in Industry is PID
u  K p e  K I  edt  K D e
• Conjectures:
• Error based design must have merits;
• Solution to robust control is outside the realm of
modern control theory;
• Better controllers can be found experimentally
40
Experiment #1: A design not strictly
based on the math model
y  f (t , y, y, w)  bu
f (t , y, y, w)  f (t )
u  ( f (t )  u0 ) / b
y  u0
41
A unique disturbance estimator
Augmented plant in state space: x1  y, x2  y, x3  f (t , y, y, w)
y  f (t , y, y, w)  bu

 x1  x2
 x  x  bu,
3
 2

 x3  f
y  x

1
Extended State Observer
 z1  z2  1 g1 ( z1  y )

 z2  z3   2 g 2 ( z1  y )  bu
 z   g ( z  y)
3 3 1
 3
z1  x1 z2  x2 z3  x3
42
Active disturbance compensation
 x1  x2

 x2  f  bu
y  x
1

u  (u0  z3 ) / b
z3  f
f (t ) or f (t , x1 , x2 , w)?
 x1  x2

 x2  u0
y  x
1

43
Active Disturbance Rejection Control
w(t)
v2(t)
r(t)
u0(t)
+_
Profile
Generator
+_
Nonlinear
PD
u(t)
y(t)
+_
Plant
1/b0
b0
v1(t)
z3(t)
z2(t)
Extended
State Observer
(ESO)
z1(t)
44
A Breakthrough in Motion Control
y  f (t , y, y, w)  bu (t )
transient profile and output
2
bandwidth: 4 rad/sec
bandwidth: 20 rad/sec
transient profile
1
0
position
2
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
y
z1
1
0
0.5
0
1
2
3
velocity
4
5
6
2
dy/dt
z2
1
0
0
-1
2
0
1
2
3
4
disturbance
and unknown
dyanmics
5
6
50
f
z3
1
0
0
-1
-50
0
1
2
3
time second
4
5
6
45
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
46
Performance of the disturbance observer
Total disturbance and its estimation
30
20
a(t)
f(t)
z3(t)
10
0
-10
-20
-30
0
1
2
3
4
5
Time (sec.)
47
Extension to Higher Order MIMO Plants
, Y ( n1) , d (t ))  U , Y  Rl ,U  Rl , d  R m
Y ( n)  F (Y , Y ,
Model of F(.) in the state space→ in the time domain：
W (t )  F (Y , Y ,
, Y ( n 1) , d (t ))
U  W (t )  V
Y (n)  V
How to reconstruct the extended state
W (t )F (Y (t ), Y (t ),
From U and Y ?
, Y ( n1) (t ), d (t ))
48
Y ( n)  F (Y , Y ,
, Y ( n1) , d (t ))  U
W (t )  F (Y , Y ,
Y
(n)
 W (t )  U
U  W (t )  U 0
, Y ( n1) , d (t ))
Extended state
Dynamic linearization and decoupling
Y (n)  U 0
 z1i  z2i   01 g1 ( z1i  yi )

 z2i  z3   02 g 2 ( z1i  yi )


z  z
ni
n 1,i   0 n g n ( z1i  yi )  ui


 zn 1,i    0 n 1 g n 1 ( z1i  yi )
Extended state observer (ESO)
Z1  Y
Z2  Y
Z n  Y ( n 1)
Z n 1  W (t )
U   Z n 1  U 0
49
Successful Applications
•
•
•
•
•
•
•
Motion Control (All manufacturing Industries)
Web Tension Regulation (paper, steel, printing..)
Machine Tools
Power Electronics (Motor, Converters …)
Aircraft Control (MIMO)
Process Control (with long transport delay)
Active Magnetic Bearing
50
New Control Technologies “Discovered”
•
•
•
•
•
Nonlinear PID
Discrete Time Optimal Control
Active Disturbance Rejection
Single Parameter Auto-Tuning
Wavelet Controller/Filter
51
A Paradigm Shift
• Gao, Huang, Han, CDC2001
• Existing Paradigm: Model Based Design
• New Paradigm: Error (e=r-y) Based
• Same Objective: Desired error behavior
52
The Paradox of the
Robust Control Problem
Making the performance of the modeldependent control design independent
of the model
53
GÖdel’s Incompleteness Theorem
“Within any formal system of axioms,
such as present day mathematics,
questions always persist that can
neither be proved or disproved on the
basis of the axioms that define the
system.” --paraphrased by S. Hawking
54
Is the solution to the robust control problem
outside the existing control theory?
55
Problem Reformulation
reconnect theory to practice
56
Reconnect
Control
Practice
Control
Research
Mathematics
Control
Theory
57
Components of Problem Definition
• 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
58
A Motion Control Case Study
y  f (t , y, y, w)  bu
f (t , y, y, w) : continuous and differentiable
f (t , y, y, w)  F
| f (t , y, y, w) | k1,| f (t , y, y, w) | k2
b, k1, and k2 are given
59
A Common Design Objective
Make y follow a reference signal, v,
within a specified accuracy:
|v - y| < g(v,t), g(v,t) > 0 is given
a special case: g(v,t) is a constant
V  {v :| v | v 0 ,| v | v1,| v | v 2 }
60
Common Design Constraints
Hard constraints
| u | umax ,| u | umax
Soft constraints
u is “smooth”
t2
 | u (t ) | dt is “small”
t1
61
Controller C(p)
• A dynamic system represented in s.s. as
z  p( z, u, v, v, y)
u  q( z, v, v, y)
• p is the parameter vector to be selected (tuned)
62
Problem Formulation
f (t , y, y, w)  F
v V
• Does a controller C(p) exist that meets the
design objective subject to the constraints?
• If so, how to find it?
• If there is more than one solutions, what is the
optimal solution in practical sense?
• How to find such an optimal solution?
63
Where are we?
Observations
Conjectures
Experiments
• Theory?
– formulate the problem
• Validation?
64
Build A New Research Infrastructure
• Practitioners/Researchers/Mathematicians
• Discover (both practitioners and theoreticians)
• Theorize
– Prove stability and convergence
– Generalized
– Establish a new kind of theory
• Validate
– Verify the new theory against other problems
– Define the range of applicability
65
Conclusions
• Think out of box:
controls as an experimental science
• Experiments lead to new methods
• From problems to methods to
theory
66
A Nonlinear PID Application
NPID CONTROLLER
Transient
Profile
PWM
Kp
Ki
1
s
Kd
s
( s  1)2
DC-DC
Converter
Output
Voltage
Signal
Conditioning
67
Load Disturbance Rejection
Load decreasing(36->3A)
Load increasing(3->36A)
PI
PI
NPID
NPID
68
PI
NPID
Output Voltage
1.0V/div
ADRC
TOADRC
Time: 2.0ms.div
69
Discrete Time Optimal Control Law
u  fst (( x1 , x2 , r , h)
x ( k  1)  Ax ( k )  Bu ( k )
d  rh; d 0  hd
| u ( k ) | r
y  x1  hx2
x 
1
x
,A
 x 
 0
x (0)  x0
a0  d 2  8r | y |
1
2
0
xf   
0
h
0
,B 
 h 
1 
a0  d

sign( y ), | y | d 0
 x2 
a
2
 x2  y / h,
| y | d 0

r sign(a ), | a | d

fst    a
| a | d
 r d ,
70
Comparison of switching curves
71
72
73
Other Nonlinear Feedbacks
(not based on Lyapunov methods)
• Explore the use of nonlinear mechanisms
– Nonlinear feedback
– Nonlinear differentiation
– Nonlinear PID
– Discrete Time Optimal Control
74
Nonlinear PID
u  K p g p (e)  K I  gi (e)dt  K D g d (e)
• 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
75
Non-smooth feedback
y  w  u, w  0, u  10  e  sign(e), e  r  y
a
26
76
Non-smooth feedback
y  w  u, w  2  sin(10t ), u  10  e  sign(e)
a
27
77
Further gain experimentation
u
u=e
u = fal(e)
-d
d
1
e
| e |a sign(e), | e | d ,
fal (e)  
d 0
1 a
| e | d ,
 e/d ,
78
A special case of NPD
• Time Optimal Control (TOC) of a double
integral plant
• Solution obtained in the 60s for continuous
plants
• Chattering problem
• Recent solution (DTOC) for discrete plant
fundamentally resolved the chattering
• Used as a controller or a differentiator
79