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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 A ssistant: 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 Desig n Macro Writer: William Erik B axter Copyeditor: Brian Jones Proofreader: Holly McLean-Aldis Copyright c  1998 Addison Wesley Longman, Inc. All rights reserved. No part of this publicationmaybereproduced, 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 Congres s 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, nordotheyaccept 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 12345678910—CRW—0100999897 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. Suchheuristic 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 expertiseisloaded 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- ingreal-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- neticalgorithms, expert and planning systems, and intelligent autonomous control, and explain how these topics relate to fuzzy control. Overall, we take a pragmatic engineering approach tothedesign, analysis, performance evaluation, and implementation of fuzzy control systems. We are not concernedwith 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-levellanguage or Matlab 1 .Inthewebandftppages 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 andshow 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 acombination 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,howfuzzy 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 supervisorycontrol. In Chapter 8 we summarize our control engineeringperspective 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 toapply 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- antaircraftcontrol, 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: liquidlevel 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. Youcan access this information via the web site: http://www.awl.com/cseng/titles/0-201-18074-X or youcan 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 thechapter is related to the [...]... 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 Supervision of Fuzzy Controllers 422 7.3.1 Rule-Base Supervision 422 7.3.2 Case Study: Vibration Damping for a Flexible Robot 7.3.3 Supervised Fuzzy Learning Control 427 423 xix xx CONTENTS 7.4 7.3.4 Case Study: Fault-Tolerant Aircraft Control Summary... then, the role of modeling in fuzzy control design is quite similar to its role in conventional control system design In fuzzy control there is a more significant emphasis on the use of heuristics, but in many control approaches (e.g., PID control for process control) there is a similar emphasis Basically, in fuzzy control there is a focus on the use of rules to represent how to control the plant rather... achieve high-performance control, and these are still present just as they were for conventional control (e.g., nonminimum phase or unstable behavior still presents challenges for fuzzy control) 1.3.2 Fuzzy Controller Design Fuzzy control system design essentially amounts to (1) choosing the fuzzy controller inputs and outputs, (2) choosing the preprocessing that is needed for the controller inputs and... knowledge about how to control a system In this section we seek to provide a philosophy of how to approach the design of fuzzy controllers This will lead us to provide a motivation for, and overview of, the entire book The fuzzy controller block diagram is given in Figure 1.2, where we show a fuzzy controller embedded in a closed-loop control system The plant outputs are 1.3 Fuzzy Control System Design... tune a fuzzy controller using data from the plant Such an adaptive fuzzy controller can be quite useful for plants where it is difficult to generate detailed a priori knowledge on how to control a plant, or for plants where there will be significant changes in its dynamics that result in inadequate performance if only a fixed fuzzy controller were used For the cruise control example, an adaptive fuzzy controller... Depiction of Fuzzy Decision Making 49 2.2.8 Visualizing the Fuzzy Controller’s Dynamical Operation 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. .. Uncoupled Direct Fuzzy Control 129 3.3.3 Coupled Direct Fuzzy Control 134 3.4 Balancing a Rotational Inverted Pendulum 3.4.1 The Rotational Inverted Pendulum 142 142 119 50 CONTENTS 3.7 3.4.2 A Conventional Approach to Balancing Control 3.4.3 Fuzzy Control for Balancing 145 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... inputs are denoted by u(t), and the reference input to the fuzzy controller is denoted by r(t) FIGURE 1.2 Fuzzy Inference Inference mechanism Mechanis m Rule-Base Rule-base Defuzzification Defuzzification Reference input r(t) Fuzzification Fuzzification Fuzzy controller Inputs u(t) Process Outputs y(t) Fuzzy controller architecture The fuzzy controller has four main components: (1) The “rule-base” holds... adaptive fuzzy control and provide several case studies that help explain how to design, simulate, and implement adaptive fuzzy control systems In Chapter 7 we study another approach to specifying adaptive fuzzy controllers for the case where there is a priori heuristic knowledge available about how a fuzzy or conventional controller should be tuned We will load such knowledge about how to supervise the fuzzy. .. 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 2.1 Overview 23 2.2 23 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 2.7 2.2.3 Fuzzy Quantification of Knowledge 32 2.2.4 Matching: Determining Which Rules to Use 37 2.2.5 . nventional Controllers 415 7.2.1 Fuzzy Tuning of PID Controllers 415 7.2. 2Fuzzy Gain Scheduling 417 7.2.3 Fuzzy Supervision of Conventional Controllers 421 7.3 Supervision of Fuzzy Controllers. 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. Exercises 19 CHAPTER 2 / Fuzzy Control: The Basics 23 2.1 Overview 23 2. 2Fuzzy Control: A Tut orial Introduction 24 2.2.1Choosing F uzzy Controller Inputs and Outputs 26 2.2.2 Putting Control Knowledge