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1 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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2 Outline Introduction Questions Research Direction Methodology Active Disturbance Rejection Advanced Technologies Take Aways Open Problems

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3 From Applied Research to Advanced Technologies Center for Advanced Control Technologies http://cact.csuohio.edu

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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

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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

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6 Sponsors NASA Rockwell Automation Kollmorgen ControlSoft Federal Mogul AlliedSignal Automotive Invacare Co. Energizer Black and Decker Nordson Co. CAMP

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7 NASA Intelligent PMAD Project

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8 Web Tension Regulation

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9 Truck Anti-lock Brake System

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10 Turbofan engine

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11 A Non-isothermal CSTR CV: product concentration C A MV: Coolant flowrate q c Difficulties: –Strong nonlinearity –Time varying parameters: c (t) h (t) (catalyst deactivation and heat transfer fouling) 11

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12 Nonlinear 3-Tank Fault Id. Problem 6 possible faults2 inputs3 outputs

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13 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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14 Outline

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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?

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16 How do we describe it? An Art of Practice? Hidden Technology? Mathematics? Engineering Science? Control Science? Natural Science?

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17 Where does control belong? Electrical Engineering Mechanical Engineering Chemical Engineering Aerospace Engineering System Engineering Mathematics Biology?

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18 Is there a theory-practice gap? Control Theory Engineering Problem Solving ?

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19 Can theory be driven by practice? New Theory ? Engineering Problem Solving

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20 Outline

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21 Theory vs. Practice A Historical Perspective

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22 Looking back PID (N. Minorsky) 1922 Nyquist1932 Bode1940 Kalman1961 … Ho1982 Han1989/1999

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23 Classical Control Era Control Practice Control Research Control Theory Mathematics

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24 Modern Control Era Control Practice Control Research Control Theory Mathematics Research Theory unobservable uncontrollable

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25 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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26 Outline

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27 Control as an Experimental Science Y.C. Ho, IEEE AC, Dec. 1982 “Control” as experimental science (the 3 rd 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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28 ExperimentDiscoverTheorize

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29 Reconnect Control Practice Control Research Control Theory Mathematics

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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

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31 The Paradox of the Robust Control Problem Making model-dependent control design independent of the model

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32 G Ö del’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

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33 Is the solution to the robust control problem outside the existing control theory?

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34 Problem Reformulation reconnect theory to practice

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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

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36 Outline

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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?

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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?

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39 Disturbance Rejection Modeling: Uncertainty Reduction Example: modeling design tuning Passive Disturbance Rejection Example: PID tuning Active Disturbance Rejection Example: Invariant Principle, ADRC (Han)

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40 A Motion Control Case Study

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41 Model-Based Method Modeling: in analytical form Design Goal: Plant: Examples: pole placement; feedback linearization Control Law:

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42 Industry Practice The PID example With unknown,

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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

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44 Getting around modeling Adding a sensor Estimating in real time

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45 Active Disturbance Rejection Augmented plant in state space: Extended State Observer (Han)

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46 Active disturbance compensation

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47 Observer Comparison Luenberge ObserverExtended State Observer

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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

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50 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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51 Bandwidth-based Tuning

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52 Hardware Test: torque disturbance

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53 Performance of the disturbance observer f(t)

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54 Motion Control Demo

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55 Outline

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56 Algorithms Nonlinear PID Discrete Time Optimal Control Active Disturbance Rejection Single Parameter Tuning Wavelet Controller/Filter

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57 Nonlinear PID Error driven, not model-based Nonlinear “proportional” term g p (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

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58 Discrete Time Optimal Control Law

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59 Comparison of switching curves Details

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60 Manufacturing (Motion, Web Tension, CNC)MotionWeb TensionCNC Power Electronics (Motor, PMAD, Converters)PMADConverters Aircraft ( Flight, Jet Engine )Jet Engine Process Control ( CSTR ) CSTR Biomedical ( Ankle) Ankle Health/fault Monitoring (A benchmark prob.)A benchmark prob. Automobile (Truck ABS)Truck ABS Technologies

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61 Take Aways Think outside “the box” Active disturbance rejection From problems to methods to methodology http://cact.csuohio.edu gao@csuohio.edu

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62 Open Problems Characteristics of ESO –Convergence, –Rate of Convergence, –Boundedness –Bound of error –Order estimation –b 0 estimation (Initial results)Initial results Practical Optimality (Initial results)Initial results Reformulation of process control problems Cybernetics

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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

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