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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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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

• 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 tdt V RT

dT q H ET T k C tdt V C RT

C hAq t T TC V q C

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 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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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 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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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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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 PIDNonlinear PIDTime Optimal ControlDiscrete Time Optimal ControlFind 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 xx x u

x fy 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 yz z g z y uz 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 xx uy x

1 2

2

1

x xx f uy x

0 3

3

u u zz 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

0ˆu 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

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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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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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• 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://cact.csuohio.edugao@csuohio.edu

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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