Fuzzy Control- Phần 1

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Fuzzy Control Kevin M. Passino Department of Electrical Engineering The Ohio State University Stephen Yurkovich Department of Electrical Engineering The Ohio State University An Imprint of Addison-Wesley Longman, Inc. Menlo Park, California • Reading, Massachusetts • Harlow, England • Berkeley, California Don Mills, Ontaria • Sydney • Bonn • Amsterdam • Mexico City
ii Assistant Editor: Laura Cheu Editorial Assistant: Royden Tonomura Senior Production Editor: Teri Hyde Marketing Manager: Rob Merino Manufacturing Supervisor: Janet Weaver Art and Design Manager: Kevin Berry Cover Design: Yvo Riezebos (technical drawing by K. Passino) Text Design: Peter Vacek Design Macro Writer: William Erik Baxter Copyeditor: Brian Jones Proofreader: Holly McLean-Aldis Copyright c 1998 Addison Wesley Longman, Inc. All rights reserved. No part of this publication may be reproduced, or stored in a database or retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the pub- lisher. Printed in the United States of America. Printed simultaneously in Canada. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and Addison- Wesley was aware of a trademark claim, the designations have been printed in initial caps or in all caps. MATLAB is a registered trademark of The MathWorks, Inc. Library of Congress Cataloging-in-Publication Data Passino, Kevin M. Fuzzy control / Kevin M. Passino and Stephen Yurkovich. p. cm. Includes bibliographical references and index. ISBN 0-201-18074-X 1. Automatic control. 2. Control theory. 3. Fuzzy systems. I. Yurkovich, Stephen. II. Title. TJ213.P317 1997 97-14003 629.8’9--DC21 CIP Instructional Material Disclaimer: The programs presented in this book have been included for their instructional value. They have been tested with care but are not guaran- teed for any particular purpose. Neither the publisher or the authors oﬀer any warranties or representations, nor do they accept any liabilities with respect to the programs. About the Cover: An explanation of the technical drawing is given in Chapter 2 on page 50. ISBN 0–201–18074–X 1 2 3 4 5 6 7 8 9 10—CRW—01 00 99 98 97
iii Addison Wesley Longman, Inc., 2725 Sand Hill Road, Menlo Park, California 94025
iv To Annie and Juliana (K.M.P) To Tricia, B.J., and James (S.Y.)
v
vi
Preface Fuzzy control is a practical alternative for a variety of challenging control applica- tions since it provides a convenient method for constructing nonlinear controllers via the use of heuristic information. Such heuristic information may come from an operator who has acted as a “human-in-the-loop” controller for a process. In the fuzzy control design methodology, we ask this operator to write down a set of rules on how to control the process, then we incorporate these into a fuzzy con- troller that emulates the decision-making process of the human. In other cases, the heuristic information may come from a control engineer who has performed exten- sive mathematical modeling, analysis, and development of control algorithms for a particular process. Again, such expertise is loaded into the fuzzy controller to au- tomate the reasoning processes and actions of the expert. Regardless of where the heuristic control knowledge comes from, fuzzy control provides a user-friendly for- malism for representing and implementing the ideas we have about how to achieve high-performance control. In this book we provide a control-engineering perspective on fuzzy control. We are concerned with both the construction of nonlinear controllers for challeng- ing real-world applications and with gaining a fundamental understanding of the dynamics of fuzzy control systems so that we can mathematically verify their prop- erties (e.g., stability) before implementation. We emphasize engineering evaluations of performance and comparative analysis with conventional control methods. We introduce adaptive methods for identiﬁcation, estimation, and control. We exam- ine numerous examples, applications, and design and implementation case studies throughout the text. Moreover, we provide introductions to neural networks, ge- netic algorithms, expert and planning systems, and intelligent autonomous control, and explain how these topics relate to fuzzy control. Overall, we take a pragmatic engineering approach to the design, analysis, performance evaluation, and implementation of fuzzy control systems. We are not concerned with whether the fuzzy controller is “artiﬁcially intelligent” or with in- vestigating the mathematics of fuzzy sets (although some of the exercises do), but vii
viii rather with whether the fuzzy control methodology can help solve challenging real- world problems. Overview of the Book The book is basically broken into three parts. In Chapters 1–4 we cover the basics of “direct” fuzzy control (i.e., the nonadaptive case). In Chapters 5–7 we cover adap- tive fuzzy systems for estimation, identiﬁcation, and control. Finally, in Chapter 8 we brieﬂy cover the main areas of intelligent control and highlight how the topics covered in this book relate to these areas. Overall, we largely focus on what one could call the “heuristic approach to fuzzy control” as opposed to the more recent mathematical focus on fuzzy control where stability analysis is a major theme. In Chapter 1 we provide an overview of the general methodology for conven- tional control system design. Then we summarize the fuzzy control system design process and contrast the two. Next, we explain what this book is about via a simple motivating example. In Chapter 2 we ﬁrst provide a tutorial introduction to fuzzy control via a two-input, one-output fuzzy control design example. Following this we introduce a general mathematical characterization of fuzzy systems and study their fundamental properties. We use a simple inverted pendulum example to illus- trate some of the most widely used approaches to fuzzy control system design. We explain how to write a computer program to simulate a fuzzy control system, using either a high-level language or Matlab1 . In the web and ftp pages for the book we provide such code in C and Matlab. In Chapter 3 we use several case studies to show how to design, simulate, and implement a variety of fuzzy control systems. In these case studies we pay particular attention to comparative analysis with con- ventional approaches. In Chapter 4 we show how to perform stability analysis of fuzzy control systems using Lyapunov methods and frequency domain–based sta- bility criteria. We introduce nonlinear analysis methods that can be used to predict and eliminate steady-state tracking error and limit cycles. We then show how to use the analysis approaches in fuzzy control system design. The overall focus for these nonlinear analysis methods is on understanding fundamental problems that can be encountered in the design of fuzzy control systems and how to avoid them. In Chapter 5 we introduce the basic “function approximation problem” and show how identiﬁcation, estimation, prediction, and some control design problems are a special case of it. We show how to incorporate heuristic information into the function approximator. We show how to form rules for fuzzy systems from data pairs and show how to train fuzzy systems from input-output data with least squares, gradient, and clustering methods. And we show how one clustering method from fuzzy pattern recognition can be used in conjunction with least squares methods to construct a fuzzy model from input-output data. Moreover, we discuss hybrid ap- proaches that involve a combination of two or more of these methods. In Chapter 6 we introduce adaptive fuzzy control. First, we introduce several methods for auto- matically synthesizing and tuning a fuzzy controller, and then we illustrate their application via several design and implementation case studies. We also show how 1. MATLAB is a registered trademark of The MathWorks, Inc.
ix to tune a fuzzy model of the plant and use the parameters of such a model in the on-line design of a controller. In Chapter 7 we introduce fuzzy supervisory control. We explain how fuzzy systems can be used to automatically tune proportional- integral-derivative (PID) controllers, how fuzzy systems provide a methodology for constructing and implementing gain schedulers, and how fuzzy systems can be used to coordinate the application and tuning of conventional controllers. Follow- ing this, we show how fuzzy systems can be used to tune direct and adaptive fuzzy controllers. We provide case studies in the design and implementation of fuzzy supervisory control. In Chapter 8 we summarize our control engineering perspective on fuzzy control, provide an overview of the other areas of the ﬁeld of “intelligent control,” and explain how these other areas relate to fuzzy control. In particular, we brieﬂy cover neural networks, genetic algorithms, knowledge-based control (expert systems and planning systems), and hierarchical intelligent autonomous control. Examples, Applications, and Design and Implementation Case Studies We provide several design and implementation case studies for a variety of appli- cations, and many examples are used throughout the text. The basic goals of these case studies and examples are as follows: • To help illustrate the theory. • To show how to apply the techniques. • To help illustrate design procedures in a concrete way. • To show what practical issues are encountered in the development and implemen- tation of a fuzzy control system. Some of the more detailed applications that are studied in the chapters and their accompanying homework problems are the following: • Direct fuzzy control: Translational inverted pendulum, fuzzy decision-making sys- tems, two-link ﬂexible robot, rotational inverted pendulum, and machine schedul- ing (Chapters 2 and 3 homework problems: translational inverted pendulum, au- tomobile cruise control, magnetic ball suspension system, automated highway sys- tem, single-link ﬂexible robot, rotational inverted pendulum, machine scheduling, motor control, cargo ship steering, base braking control system, rocket velocity control, acrobot, and fuzzy decision-making systems). • Nonlinear analysis: Inverted pendulum, temperature control, hydrofoil controller, underwater vehicle control, and tape drive servo (Chapter 4 homework problems: inverted pendulum, magnetic ball suspension system, temperature control, and hydrofoil controller design).
x • Fuzzy identiﬁcation and estimation: Engine intake manifold failure estimation, and failure detection and identiﬁcation for internal combustion engine calibra- tion faults (Chapter 5 homework problems: tank identiﬁcation, engine friction estimation, and cargo ship failures estimation). • Adaptive fuzzy control: Two-link ﬂexible robot, cargo ship steering, fault toler- ant aircraft control, magnetically levitated ball, rotational inverted pendulum, machine scheduling, and level control in a tank (Chapter 6 homework problems: tanker and cargo ship steering, liquid level control in a tank, rocket velocity con- trol, base braking control system, magnetic ball suspension system, rotational inverted pendulum, and machine scheduling). • Supervisory fuzzy control: Two-link ﬂexible robot, and fault-tolerant aircraft con- trol (Chapter 7 homework problems: liquid level control, and cargo and tanker ship steering). Some of the applications and examples are dedicated to illustrating one idea from the theory or one technique. Others are used in several places throughout the text to show how techniques build on one another and compare to each other. Many of the applications show how fuzzy control techniques compare to conventional control methodologies. World Wide Web Site and FTP Site: Computer Code Available The following information is available electronically: • Various versions of C and Matlab code for simulation of fuzzy controllers, fuzzy control systems, adaptive fuzzy identiﬁcation and estimation methods, and adap- tive fuzzy control systems (e.g., for some examples and homework problems in the text). • Other special notes of interest, including an errata sheet if necessary. You can access this information via the web site: http://www.awl.com/cseng/titles/0-201-18074-X or you can access the information directly via anonymous ftp to ftp://ftp.aw.com/cseng/authors/passino/fc For anonymous ftp, log into the above machine with a username “anonymous” and use your e-mail address as a password. Organization, Prerequisites, and Usage Each chapter includes an overview, a summary, and a section “For Further Study” that explains how the reader can continue study in the topical area of the chapter. At the end of each chapter overview, we explain how the chapter is related to the
xi others. This includes an outline of what must be covered to be able to understand the later chapters and what may be skipped on a ﬁrst reading. The summaries at the end of each chapter provide a list of all major topics covered in that chapter so that it is clear what should be learned in each chapter. Each chapter also includes a set of exercises or design problems and often both. Exercises or design problems that are particularly challenging (considering how far along you are in the text) or that require you to help deﬁne part of the problem are designated with a star (“ ”) after the title of the problem. In addition to helping to solidify the concepts discussed in the chapters, the problems at the ends of the chapters are sometimes used to introduce new topics. We require the use of computer-aided design (CAD) for fuzzy controllers in many of the design problems at the ends of the chapters (e.g., via the use of Matlab or some high-level language). The necessary background for the book includes courses on diﬀerential equa- tions and classical control (root locus, Bode plots, Nyquist theory, lead-lag com- pensation, and state feedback concepts including linear quadratic regulator design). Courses on nonlinear stability theory and adaptive control would be helpful but are not necessary. Hence, much of the material can be covered in an undergraduate course. For instance, one could easily cover Chapters 1–3 in an undergraduate course as they require very little background besides a basic understanding of signals and systems including Laplace and z-transform theory (one application in Chapter 3 does, however, require a cursory knowledge of the linear quadratic regulator). Also, many parts of Chapters 5–7 can be covered once a student has taken a ﬁrst course in control (a course in nonlinear control would be helpful for Chapter 4 but is not necessary). One could cover the basics of fuzzy control by adding parts of Chapter 2 to the end of a standard undergraduate or graduate course on control. Basically, however, we view the book as appropriate for a ﬁrst-level graduate course in fuzzy control. We have used the book for a portion (six weeks) of a graduate-level course on intelligent control and for undergraduate independent studies and design projects. In addition, portions of the text have been used for short courses and workshops on fuzzy control where the focus has been directed at practicing engineers in industry. Alternatively, the text could be used for a course on intelligent control. In this case, the instructor could cover the material in Chapter 8 on neural networks and genetic algorithms after Chapter 2 or 3, then explain their role in the topics covered in Chapters 5, 6, and 7 while these chapters are covered. For instance, in Chapter 5 the instructor would explain how gradient and least squares methods can be used to train neural networks. In Chapter 6 the instructor could draw analogies between neural control via the radial basis function neural network and the fuzzy model reference learning controller. Also, for indirect adaptive control, the instructor could explain how, for instance, the multilayer perceptron or radial basis function neural networks can be used as the nonlinearity that is trained to act like the plant. In Chapter 7 the instructor could explain how neural networks can be trained to serve as gain schedulers. After Chapter 7 the instructor could then cover the material on expert control, planning systems, and intelligent autonomous control in Chapter 8. Many more details on strategies for teaching the material in a fuzzy or intelligent
xii control course are given in the instructor’s manual, which is described below. Engineers and scientists working in industry will ﬁnd that the book will serve nicely as a “handbook” for the development of fuzzy control systems, and that the design, simulation, and implementation case studies will provide very good insights into how to construct fuzzy controllers for speciﬁc applications. Researchers in academia and elsewhere will ﬁnd that this book will provide an up-to-date view of the ﬁeld, show the major approaches, provide good references for further study, and provide a nice outlook for thinking about future research directions. Instructor’s Manual An Instructor’s Manual to accompany this textbook is available (to instructors only) from Addison Wesley Longman. The Instructor’s Manual contains the following: • Strategies for teaching the material. • Solutions to end-of-chapter exercises and design problems. • A description of a laboratory course that has been taught several times at The Ohio State University which can be run in parallel with a lecture course that is taught out of this book. • An electronic appendix containing the computer code (e.g., C and Matlab code) for solving many exercises and design problems. Sales Specialists at Addison Wesley Longman will make the instructor’s manual available to qualiﬁed instructors. To ﬁnd out who your Addison Wesley Longman Sales Specialist is please see the web site: http://www.aw.com/cseng/ or send an email to: cseng@aw.com Feedback on the Book It is our hope that we will get the opportunity to correct any errors in this book; hence, we encourage you to provide a precise description of any errors you may ﬁnd. We are also open to your suggestions on how to improve the textbook. For this, please use either e-mail (passino@ee.eng.ohio-state.edu) or regular mail to the ﬁrst author: Kevin M. Passino, Dept. of Electrical Engineering, The Ohio State University, 2015 Neil Ave., Columbus, OH 43210-1272. Acknowledgments No book is written in a vacuum, and this is especially true for this one. We must emphasize that portions of the book appeared in earlier forms as conference pa- pers, journal papers, theses, or project reports with our students here at Ohio
xiii State. Due to this fact, these parts of the text are sometimes a combination of our words and those of our students (which are very diﬃcult to separate at times). In every case where we use such material, the individuals have given us permis- sion to use it, and we provide the reader with a reference to the original source since this will typically provide more details than what are covered here. While we always make it clear where the material is taken from, it is our pleasure to highlight these students’ contributions here as well. In particular, we drew heavily from work with the following students and papers written with them (in alpha- betical order): Anthony Angsana [4], Scott C. Brown [27], David L. Jenkins [83], Waihon Andrew Kwong [103, 104, 144], Eric G. Laukonen [107, 104], Jeﬀrey R. Layne [110, 113, 112, 114, 111], William K. Lennon [118], Sashonda R. Morris [143], Vivek G. Moudgal [145, 144], Jeﬀrey T. Spooner [200, 196], and Moeljono Widjaja [235, 244]. These students, and Mehmet Akar, Mustafa K. Guven, Min- Hsiung Hung, Brian Klinehoﬀer, Duane Marhefka, Matt Moore, Hazem Nounou, Jeﬀ Palte, and Jerry Troyer helped by providing solutions to several of the exer- cises and design problems and these are contained in the instructor’s manual for this book. Manfredi Maggiore helped by proofreading the manuscript. Scott C. Brown and Ra´l Ord´nez assisted in the development of the associated laboratory course u o˜ at OSU. We would like to gratefully acknowledge the following publishers for giving us permission to use ﬁgures that appeared in some of our past publications: The In- stitute of Electrical and Electronic Engineers (IEEE), John Wiley and Sons, Hemi- sphere Publishing Corp., and Kluwer Academic Publishers. In each case where we use a ﬁgure from a past publication, we give the full reference to the original pa- per, and indicate in the caption of the ﬁgure that the copyright belongs to the appropriate publisher (via, e.g., “ c IEEE”). We have beneﬁted from many technical discussions with many colleagues who work in conventional and intelligent control (too many to list here); most of these persons are mentioned by referencing their work in the bibliography at the end of the book. We would, however, especially like to thank Zhiqiang Gao and Oscar R. Gonz´lez for class-testing this book. Moreover, thanks go to the following persons a who reviewed various earlier versions of the manuscript: D. Aaronson, M.A. Abidi, S.P. Colombano, Z. Gao, O. Gonz´lez, A.S. Hodel, R. Langari, M.S. Stachowicz, a and G. Vachtsevanos. We would like to acknowledge the ﬁnancial support of National Science Foun- dation grants IRI-9210332 and EEC-9315257, the second of which was for the de- velopment of a course and laboratory for intelligent control. Moreover, we had additional ﬁnancial support from a variety of other sponsors during the course of the development of this textbook, some of whom gave us the opportunity to apply some of the methods in this text to challenging real-world applications, and others where one or both of us gave a course on the topics covered in this book. These sponsors include Air Products and Chemicals Inc., Amoco Research Center, Bat- telle Memorial Institute, Delphi Chassis Division of General Motors, Ford Motor Company, General Electric Aircraft Engines, The Center for Automotive Research (CAR) at The Ohio State University, The Center for Intelligent Transportation
xiv Research (CITR) at The Ohio State University, and The Ohio Aerospace Institute (in a teamed arrangement with Rockwell International Science Center and Wright Laboratories). We would like to thank Tim Cox, Laura Cheu, Royden Tonomura, Teri Hyde, Rob Merino, Janet Weaver, Kevin Berry, Yvo Riezebos, Peter Vacek, William Erik Baxter, Brian Jones, and Holly McLean-Aldis for all their help in the production and editing of this book. Finally, we would most like to thank our wives, who have helped set up wonderful supportive home environments that we value immensely. Kevin Passino Steve Yurkovich Columbus, Ohio July 1997
Contents PREFACE vii CHAPTER 1 / Introduction 1 1.1 Overview 1 1.2 Conventional Control System Design 3 1.2.1 Mathematical Modeling 3 1.2.2 Performance Objectives and Design Constraints 5 1.2.3 Controller Design 7 1.2.4 Performance Evaluation 8 1.3 Fuzzy Control System Design 10 1.3.1 Modeling Issues and Performance Objectives 12 1.3.2 Fuzzy Controller Design 12 1.3.3 Performance Evaluation 13 1.3.4 Application Areas 14 1.4 What This Book Is About 14 1.4.1 What the Techniques Are Good For: An Example 15 1.4.2 Objectives of This Book 17 1.5 Summary 18 1.6 For Further Study 19 1.7 Exercises 19 CHAPTER 2 / Fuzzy Control: The Basics 23 2.1 Overview 23 2.2 Fuzzy Control: A Tutorial Introduction 24 2.2.1 Choosing Fuzzy Controller Inputs and Outputs 26 2.2.2 Putting Control Knowledge into Rule-Bases 27 xv
xvi CONTENTS 2.2.3 Fuzzy Quantiﬁcation of Knowledge 32 2.2.4 Matching: Determining Which Rules to Use 37 2.2.5 Inference Step: Determining Conclusions 42 2.2.6 Converting Decisions into Actions 44 2.2.7 Graphical Depiction of Fuzzy Decision Making 49 2.2.8 Visualizing the Fuzzy Controller’s Dynamical Operation 50 2.3 General Fuzzy Systems 51 2.3.1 Linguistic Variables, Values, and Rules 52 2.3.2 Fuzzy Sets, Fuzzy Logic, and the Rule-Base 55 2.3.3 Fuzziﬁcation 61 2.3.4 The Inference Mechanism 62 2.3.5 Defuzziﬁcation 65 2.3.6 Mathematical Representations of Fuzzy Systems 69 2.3.7 Takagi-Sugeno Fuzzy Systems 73 2.3.8 Fuzzy Systems Are Universal Approximators 77 2.4 Simple Design Example: The Inverted Pendulum 77 2.4.1 Tuning via Scaling Universes of Discourse 78 2.4.2 Tuning Membership Functions 83 2.4.3 The Nonlinear Surface for the Fuzzy Controller 87 2.4.4 Summary: Basic Design Guidelines 89 2.5 Simulation of Fuzzy Control Systems 91 2.5.1 Simulation of Nonlinear Systems 91 2.5.2 Fuzzy Controller Arrays and Subroutines 94 2.5.3 Fuzzy Controller Pseudocode 95 2.6 Real-Time Implementation Issues 97 2.6.1 Computation Time 97 2.6.2 Memory Requirements 98 2.7 Summary 99 2.8 For Further Study 101 2.9 Exercises 101 2.10 Design Problems 110 CHAPTER 3 / Case Studies in Design and Implementation 119 3.1 Overview 119 3.2 Design Methodology 122 3.3 Vibration Damping for a Flexible Robot 124 3.3.1 The Two-Link Flexible Robot 125 3.3.2 Uncoupled Direct Fuzzy Control 129 3.3.3 Coupled Direct Fuzzy Control 134 3.4 Balancing a Rotational Inverted Pendulum 142 3.4.1 The Rotational Inverted Pendulum 142
CONTENTS xvii 3.4.2 A Conventional Approach to Balancing Control 144 3.4.3 Fuzzy Control for Balancing 145 3.5 Machine Scheduling 152 3.5.1 Conventional Scheduling Policies 153 3.5.2 Fuzzy Scheduler for a Single Machine 156 3.5.3 Fuzzy Versus Conventional Schedulers 158 3.6 Fuzzy Decision-Making Systems 161 3.6.1 Infectious Disease Warning System 162 3.6.2 Failure Warning System for an Aircraft 166 3.7 Summary 168 3.8 For Further Study 169 3.9 Exercises 170 3.10 Design Problems 172 CHAPTER 4 / Nonlinear Analysis 187 4.1 Overview 187 4.2 Parameterized Fuzzy Controllers 189 4.2.1 Proportional Fuzzy Controller 190 4.2.2 Proportional-Derivative Fuzzy Controller 191 4.3 Lyapunov Stability Analysis 193 4.3.1 Mathematical Preliminaries 193 4.3.2 Lyapunov’s Direct Method 195 4.3.3 Lyapunov’s Indirect Method 196 4.3.4 Example: Inverted Pendulum 197 4.3.5 Example: The Parallel Distributed Compensator 200 4.4 Absolute Stability and the Circle Criterion 204 4.4.1 Analysis of Absolute Stability 204 4.4.2 Example: Temperature Control 208 4.5 Analysis of Steady-State Tracking Error 210 4.5.1 Theory of Tracking Error for Nonlinear Systems 211 4.5.2 Example: Hydrofoil Controller Design 213 4.6 Describing Function Analysis 214 4.6.1 Predicting the Existence and Stability of Limit Cycles 214 4.6.2 SISO Example: Underwater Vehicle Control System 218 4.6.3 MISO Example: Tape Drive Servo 219 4.7 Limitations of the Theory 220 4.8 Summary 222 4.9 For Further Study 223 4.10 Exercises 225
xviii CONTENTS 4.11 Design Problems 228 CHAPTER 5 / Fuzzy Identiﬁcation and Estimation 233 5.1 Overview 233 5.2 Fitting Functions to Data 235 5.2.1 The Function Approximation Problem 235 5.2.2 Relation to Identiﬁcation, Estimation, and Prediction 238 5.2.3 Choosing the Data Set 240 5.2.4 Incorporating Linguistic Information 241 5.2.5 Case Study: Engine Failure Data Sets 243 5.3 Least Squares Methods 248 5.3.1 Batch Least Squares 248 5.3.2 Recursive Least Squares 252 5.3.3 Tuning Fuzzy Systems 255 5.3.4 Example: Batch Least Squares Training of Fuzzy Systems 257 5.3.5 Example: Recursive Least Squares Training of Fuzzy Systems 259 5.4 Gradient Methods 260 5.4.1 Training Standard Fuzzy Systems 260 5.4.2 Implementation Issues and Example 264 5.4.3 Training Takagi-Sugeno Fuzzy Systems 266 5.4.4 Momentum Term and Step Size 269 5.4.5 Newton and Gauss-Newton Methods 270 5.5 Clustering Methods 273 5.5.1 Clustering with Optimal Output Predefuzziﬁcation 274 5.5.2 Nearest Neighborhood Clustering 279 5.6 Extracting Rules from Data 282 5.6.1 Learning from Examples (LFE) 282 5.6.2 Modiﬁed Learning from Examples (MLFE) 285 5.7 Hybrid Methods 291 5.8 Case Study: FDI for an Engine 292 5.8.1 Experimental Engine and Testing Conditions 293 5.8.2 Fuzzy Estimator Construction and Results 294 5.8.3 Failure Detection and Identiﬁcation (FDI) Strategy 297 5.9 Summary 301 5.10 For Further Study 302 5.11 Exercises 303 5.12 Design Problems 311
CONTENTS xix CHAPTER 6 / Adaptive Fuzzy Control 317 6.1 Overview 317 6.2 Fuzzy Model Reference Learning Control (FMRLC) 319 6.2.1 The Fuzzy Controller 320 6.2.2 The Reference Model 324 6.2.3 The Learning Mechanism 325 6.2.4 Alternative Knowledge-Base Modiﬁers 329 6.2.5 Design Guidelines for the Fuzzy Inverse Model 330 6.3 FMRLC: Design and Implementation Case Studies 333 6.3.1 Cargo Ship Steering 333 6.3.2 Fault-Tolerant Aircraft Control 347 6.3.3 Vibration Damping for a Flexible Robot 357 6.4 Dynamically Focused Learning (DFL) 364 6.4.1 Magnetic Ball Suspension System: Motivation for DFL 365 6.4.2 Auto-Tuning Mechanism 377 6.4.3 Auto-Attentive Mechanism 379 6.4.4 Auto-Attentive Mechanism with Memory 384 6.5 DFL: Design and Implementation Case Studies 388 6.5.1 Rotational Inverted Pendulum 388 6.5.2 Adaptive Machine Scheduling 390 6.6 Indirect Adaptive Fuzzy Control 394 6.6.1 On-Line Identiﬁcation Methods 394 6.6.2 Adaptive Control for Feedback Linearizable Systems 395 6.6.3 Adaptive Parallel Distributed Compensation 397 6.6.4 Example: Level Control in a Surge Tank 398 6.7 Summary 402 6.8 For Further Study 405 6.9 Exercises 406 6.10 Design Problems 407 CHAPTER 7 / Fuzzy Supervisory Control 413 7.1 Overview 413 7.2 Supervision of Conventional Controllers 415 7.2.1 Fuzzy Tuning of PID Controllers 415 7.2.2 Fuzzy Gain Scheduling 417 7.2.3 Fuzzy Supervision of Conventional Controllers 421 7.3 Supervision of Fuzzy Controllers 422 7.3.1 Rule-Base Supervision 422 7.3.2 Case Study: Vibration Damping for a Flexible Robot 423 7.3.3 Supervised Fuzzy Learning Control 427
xx CONTENTS 7.3.4 Case Study: Fault-Tolerant Aircraft Control 429 7.4 Summary 435 7.5 For Further Study 436 7.6 Design Problems 437 CHAPTER 8 / Perspectives on Fuzzy Control 439 8.1 Overview 439 8.2 Fuzzy Versus Conventional Control 440 8.2.1 Modeling Issues and Design Methodology 440 8.2.2 Stability and Performance Analysis 442 8.2.3 Implementation and General Issues 443 8.3 Neural Networks 444 8.3.1 Multilayer Perceptrons 444 8.3.2 Radial Basis Function Neural Networks 447 8.3.3 Relationships Between Fuzzy Systems and Neural Networks 449 8.4 Genetic Algorithms 451 8.4.1 Genetic Algorithms: A Tutorial 451 8.4.2 Genetic Algorithms for Fuzzy System Design and Tuning 458 8.5 Knowledge-Based Systems 461 8.5.1 Expert Control 461 8.5.2 Planning Systems for Control 462 8.6 Intelligent and Autonomous Control 463 8.6.1 What Is “Intelligent Control”? 464 8.6.2 Architecture and Characteristics 465 8.6.3 Autonomy 467 8.6.4 Example: Intelligent Vehicle and Highway Systems 468 8.7 Summary 471 8.8 For Further Study 472 8.9 Exercises 472 BIBLIOGRAPHY 477 INDEX 495