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325 Pages·1996·5.166 MB·English
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Fuzzy Logic Fuzzy Logic Implementation and Applications Edited by M J Patyra University of Minnesota, USA OM Mlynek Swiss Federal Institute of Lausanne Switzerland ~W1LEYmTEUBNER A Partnership between John Wiley & Sons and B. G. Teubner Publishers Chichester . New York . Brisbane . Toronto . Singapore . Stuttgart . Leipzig Copyright © 1996 jointly by John Wiley & Sons Ltd. and B.G. Teubner Softcover reprint of the hardcover I st edition 1996 John Wiley & Sons Ltd B.G. Teubner Baffins Lane IndustriestraBe 15 Chichester 70565 Stuttgart (Vaihingen) West Sussex Postfach 80 10 69 P019IUD 70510 Stuttgart England Germany National Chichester 01243779777 National Stuttgart (0711) 789010 International (+44) 1243779777 International +49711 789010 All rights reserved. No part of this book may be reproduced by any means, or transmitted, or translated into a machine language without the written permission of the publisher. Other Wiley Editorial OffICes John Wiley & Sons, Inc., 605 Third Avenue New York, NY 10158-0012, USA Brisbane· Toronto· Singapore Other Teubner Editorial Offices B.G. Teubner, Verlagsgesellschaft mbH, JohannisgaBe 16 D-04103 Leipzig, Germany Die Deutsche Bibliotheck -CIP-Einheitsaufnahme Fuzzy logic: implementation and applications 1 ed. by M. J. Patyra : D. M. Mlynek. -Stuttgart; Leipzig; Teubner; Chichester; New York; Brisbane; Toronto; Singapore: Wiley, 1996 ISBN-13: 978-3-322-88957-7 e-ISBN-13: 978-3-322-88955-3 DOl: 10.1007/978-3-322-88955-3 NE: Patyra, Marek J. (Hrsg.) WG:37 DBN 94.719152.6 96.03.26 2790 nh V: Teubner Library of Congress Cataloging in Publication Data Fuzzy logic: implementation and applications 1 edited by M. J. Patyra, D. M. Mlynek. p. cm. Includes bibliographical references and index. ISBN 0 471 95059 9 1. Automatic control. 2. Fuzzy logic. I. Patyra, M. J. (Marek 1.) U. Mlynek, D. M. TJ213.F881996 629.8- dc20 95-45241 CIP British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Typeset in I 0/12pt Times by Thomson Press (India) Ltd, New Ddhi This book is printed on acid-free paper responsibly manufactured from sustainable forestation for which at least two trees are planted' for each one used for paper production. Contents Editor's Preface xi List of Contributors xvii Acknowledgments xix THEORY 1 1 Fuzzy Sets in Approximate Reasoning: a Personal View 3 1.1 Introduction 3 1.2 Graduality-and Similarity-based Approximate Reasoning 4 1.2.1 Comparison of Fuzzy Relations, Extension Principle and Similarity 4 1.2.2 Interpolative Reasoning 6 1.2.3 Qualitative Reasoning 9 1.3 Uncertainty Management 11 1.3.1 Background 12 1.3.2 Uncertain Fuzzy Rules 15 1.3.3 Approximate Reasoning with Fuzzy Rules 18 1.3.4 Possibilistic Logic 21 1.3.5 Default Reasoning 24 1.3.6 Abductive Reasoning 26 1.4 Concluding Remarks 32 References 32 FUZZY LOGIC CONTROL 37 2 Fuzzy Logic Control: a Systematic Design and Performance Assessment Methodology 39 2.1 Introduction 39 2.2 The Phase Portrait Assignment Algorithm 41 2.2.1 Fuzzy Logic control 41 2.2.2 The Automatic Rule-Generation Method 42 2.3 Performance Assessment 49 2.3.1 Stability Analysis 50 2.3.2 Robustness Analysis 51 2.4 Application Examples 53 2.4.1 The Engine Model 53 2.4.2 The Fuzzy Controller 55 2.4.3 Simulation Results 59 vi CONTENTS 2.5 Stability and Robustness Results 59 2.6 Conclusions 61 Acknowledgment 61 References 62 3 On the Compatibility of Fuzzy Control and Conventional Control Techniques 63 3.1 Introduction 63 3.2 Sliding Mode Fuzzy Control 65 3.2.1 The Principle of Sliding Mode Control 65 3.2.2 The Similarity Between SMC and FC 67 3.2.3 The Sliding Mode FC (SMFC) as a State-dependent Filter 68 3.2.4 Normalization and Denormalization 69 3.2.5 FC with Boundary Layer 70 3.2.6 FC of Higher Order 71 3.2.7 Numerical Example 73 3.3 Scaling of Fuzzy Controllers Using the Cross-correlation 78 3.3.1 Input-Output Correlation for an FC 81 3.3.2 Application to a Redundant Manipulator Arm 87 3.4 Fuzzy inputs 90 3.4.1 Some Useful Operations on Fuzzy Sets 91 3.4.2 The sgn-function 97 3.4.3 Sliding Mode Control and Related Control Strategies 99 3.4.4 Simulation Results 107 References 113 4 On the Crisp-type Fuzzy Controller: Behaviour Analysis and Improvement 117 4.1 Introduction 117 4.2 The Crisp-Type Fuzzy Logic Controller 118 4.3 The Dynamic Analysis of the Crisp-Type Fuzzy Controller 119 4.4 The Static Analysis of the Crisp-Type Fuzzy Control System 127 4.5 An Improvement: Pid-Type Fuzzy Controller Structure 130 4.6 Further Improvement: The Parameter Adaptive Fuzzy Controller 134 4;7 Conclusions 137 References 138 FUZZY LOGIC HARDWARE IMPLEMENTATIONS 141 5 Design Considerations of Digital Fuzzy Logic Controllers 143 5.1 Introduction 143 5.2 Digital-based Fuzzy Logic Hardware 144 5.2.1 Digital Fuzzification 144 5.2.2 Digital Fuzzy Inferencing 146 5.2.3 Digital Defuzzification 149 5.3 Fuzzy Logic Based Controllers 151 5.3.1 Digital FLC Characteristics 151 5.3.2 Single-Input Single-Output Fuzzy Logic Controllers 153 5.3.3 Double-Input Single-Output Fuzzy Logic Controller 155 5.3.4 Multiple-Input Single-Output Fuzzy Logic Controller 157 5.3.5 Multiple-Input Multiple-Output Fuzzy Logic Controller 159 CONTENTS vii 5.4 Hardware Implementation: Comparative Study 163 5.4.1 Hardware Mapping of FLC Models 164 5.4.2 Hardware Implementation Issues 171 5.4.3 Summary 172 5.5 Final Remarks 172 References 173 6 Parallel Algorithm for Fuzzy Logic Controller 177 6.1 Introduction 177 6.2 Mathematical Models for Fuzzy Model Building and Inference Computations 177 6.2.1 Single-Input Single-Output System 177 6.2.2 Multiple-Input Single-Output System 179 6.2.3 Multiple-Input Multiple-Output System 180 6.3 Parallel Algorithm 181 6.4 Conceptual Hardware Implementation 187 6.4.1 SISO System 187 6.4.2 Hardware Architectures for MISO and MIMO Systems 190 6.4.3 Fuzzy Controller Hardware Accelerator 191 6.5 Performance Characteristics 192 6.5.1 Maximum Sustainable Processing Rate 192 6.5.2 Improvements 193 6.6 Conclusions 194 References 194 7 Fuzzy Flip-flop 197 7.1 Introduction 197 7.2 Outline of Binary Flip-flop and Fundamental Fuzzy Operations 198 7.2.1 A Binary Logic J-K Flip-flop 198 7.2.2 Definition of Fuzzy Negation, t-norm and s-norm 199 7.3 Definition of Fuzzy Flip-flop 201 7.4 Fuzzy Flip-flop using Complementation, Min and Max Operations 203 7.5 Fuzzy Flip-flop using Complementation, Algebraic Product and Algebraic Sum 207 7.6 Fundamentals of Implementation of the Min Max Fuzzy Flip-flop 207 7.7 Discrete and Voltage Mode Min Max Fuzzy Flip-flop Circuits 210 7.8 Fundamentals of Implementation of the Algebraic Fuzzy Flip-flop 217 7.9 Discrete and Voltage Mode Algebraic Fuzzy Flip-flop Circuits 219 7.10 Comparison of the Performance of Min Max Type Versus Algebraic Type Fuzzy Flip-flop circuit 221 7.11 Fuzzy register circuit 222 7.12 VLSI design of the Fuzzy Register Circuit 224 7.12.1 VLSI Design ofthe Min Max Type Fuzzy Flip-flop Circuit 224 7.12.2 VLSI Design of the Fuzzy Register 230 7.13 Conclusion 235 References 235 8 Design Automation of Fuzzy Logic Circuits 237 8.1 Introduction 237 8.2 Basic Fuzzy Operators 238 8.2.1 Terminology and Resolution Principle 238 8.2.2 Fuzzy Inclusion as the Natural Extension of Boolean Inclusion 239 8.2.3 Symbolic Implementation of Fuzzy Operators 242 viii CONTENTS 8.3 CMOS Implementation 243 8.3.1 CMOS Implementation of Fuzzy Operators 243 8.3.2 Current Mirror-based Approach 244 8.3.3 Case Study: Implementation of the Min Unit 247 8.4 Fuzzy Development System 247 8.4.1 Basic Framework of the Fuzzy Logic Development Environment 248 8.4.2 Graphical Simulation Interface 249 8.4.3 Design Automation System 250 8.4.4 Netlist 252 8.4.5 Placement 256 8.4.6 Route 256 8.4.7 Superphenix 256 8.5 CMOS Fuzzy Logic-based Controller 259 8.6 Conclusion 260 8.6.1 Features of the VLSI technique taken for the Integration of Fuzzy Circuits 260 8.6.2 Improvement of the Structure of the Fuzzy Logic Development Environment 261 Acknowledgments 262 References 262 HYBRID SYSTEMS AND APPLICATIONS 265 9 Neuro-fuzzy Systems: Hybrid Configurations 267 9.1 Preliminaries 267 9.2 Main Classes of Fuzzy Systems 269 9.3 Fuzzy Systems 270 9.3.1 Linguistic Systems and Fuzzy Systems 270 9.3.2 Fuzzy Systems and Memory Processes 271 9.3.3 Classic Neurons 272 9.3.4 Linear Combiners as Neurons 274 9.3.5 Elementary Recurrent Systems 275 9.4 Fuzzy Neurons 276 9.4.1 Elementary Fuzzy Neurons 276 9.4.2 Neurons with Fuzzy Weights 277 9.4.3 Inclusion of Fuzzy Weights into the Conventional Neuron Model 277 9.5 Neural Networks 283 9.6 Discrete Systems and Generalizations to Neuro-fuzzy Systems 285 9.7 Invariant Neuro-fuzzy Systems 287 9.7.1 Main Configurations 287 9.7.2 Series Neuro-fuzzy Systems and their Interpretation 290 9.8 Several Recurrent Neuro-fuzzy System Configurations 292 9.8.1 Elementary Loops: Models of Memory Effects (Output Memory) 292 9.8.2 Implementation of Complex Equations and Connections with Chaos in Classic Systems 294 9.9 Final Remarks 296 References 296 10 A Fuzzy Logic Approach to Handwriting Recognition 299 10.1 Introduction 299 10.2 Human reading 300 10.3 Handwriting Recognition: Current Approaches 302 10.4 A Fuzzy Processor for Handwriting Recognition 304 10.4.1 Data Extraction and Preprocessing 304 CONTENTS ix 10.4.2 The Feature Measures 305 10.4.3 The Fuzzy Recognition Process 307 10.5 Training 308 10.5.1 Fuzziness and Statistics 308 10.6 Rulebase quality 309 10.6.1 Discriminability 309 10.6.2 Usefulness of Measures and Rulebase Reduction 310 10.6.3 Completeness 310 10.6.4 Overall Quality and Self-tuning 312 10.7 Results 312 10.8 Conclusions 313 Acknowledgments 313 References 313 Index 315 Editor's Preface This edited volume contains ten papers on the subject of fuzzy technology. Fuzzy technology emerged as a combination of fuzzy sets theory, fuzzy logic and fuzzy-based reasoning. As a technology it gained a very practical meaning through thousands of applications in different theoretical as well as practical disciplines, covering mathematics, physics, chemistry, biology, life science, social science, economy, computer science, and (foremost) electrical, electronic, mechanical, nuclear, chemical, textile, aeronautic, ocean, and many other engineering disciplines. The goal of this book is to create an interest in fuzzy technology among researchers, engineers, professionals and students involved in the research and development in the broad area of artificial intelligence. This book is also intended to bring the reader up-to-date in the area of implementations and applications of fuzzy technology, as well as to generate and stimulate new research ideas in this area. It may inspire and motivate the researcher in new directions, as well as creating a force for new efforts to make a fuzzy technology commonly known and used in science and engineering. This volume appears at a time of unprecedented research interest in the field of fuzzy technology. I intentionally wrote research due to the events that have occurred during the last couple of years. To be more specific, I should describe this interest geographically. Without any doubts, it means industrial and scientific interest in Asia and Europe, but it is still 'only' a scientific interest in America. This paradox has been discussed on many occasions and is a subject of unofficial talks at almost all conferences covering fuzzy sets and fuzzy logic topics. According to industrial sources, the US market for fuzzy logic based products 'isn't there yet'. A similar source admitted that most of the developments for fuzzy logic are going on in Asia (Japan) and Europe (Germany), mainly because 'US companies only look at the short term return', whereas Japanese and Europeans 'tend to look farther down the road'. One positive aspect of this situation is that the top management in US companies recognize tremendous opportunities for fuzzy technology, and it predicts an 'enormous market in the US within five years'. The home and popular electronic goods will mostly contribute to the success to come. On the other hand, in the area of research fuzzy technology has gained great attention due to its ability to cope with many ill-defined and/or artificial intelligence problems. Fuzzy technology has been recognized as one of the tools of so-called 'soft computing'. Neural network methods and genetic algorithms are among other tools that help in efficient problem-solving. Theory, application and implementation of fuzzy control is an arena where fuzzy technology has been most successful. This phenomenon also motivated the creation of this volume. xii EDITOR'S PREFACE Henceforth we expect that this volume will be of great benefit to researchers, scientists and professionals developing fuzzy logic applications and working on the enhancements ofthe theory; within the five years it may still be a source of information and inspiration to managers and engineers helping them define features for their new products. Many authors from around the world contributed to this volume. They are currently doing research, development and implementation at the cutting edge of fuzzy technology. All the authors deserve special recognition for making this volume possible and for providing such high-quality contributions. The material is organized in four thematic sections. The first is an introduction to the theory of fuzzy sets; the second is devoted to fuzzy logic control; the third section covers unique examples of fuzzy logic implementation; finally, the fourth presents examples of neuro-fuzzy hybrid systems and their applications. The introductory section contains the paper by top world experts in the theory of fuzzy sets and approximate reasoning, Didier Dubois and Henri Prade from Universite Paul Sabatier, Toulouse, France. Their contribution, entitled Fuzzy Sets in Approximate Reasoning: a Personal View, is absolutely unique because it presents an extraordinarily peron sal view inside the applications of fuzzy sets in approximate reasoning. Due to their inherent abilities, fuzzy sets are capable of modelling uncertain situations and can be instrumental in the formalization of interpolative reasoning. There are at least two major advantages that can immediately be indicated in such an approach. First, similarity-based reasoning can benefit from fuzzy sets, since similarity is usually a matter of degree. Second, fuzzy sets can represent incomplete information; hence, they can be viewed as possibility distributions and can be used to generate possibility and necessity measures to assess the degree of possibility in various statements. This paper provides a personal overview throughout the last decade resulting from the research performed jointly by both authors. In this research they have explored two interpretations of fuzziness as either the description of a gradual property or as a model of incomplete state of information. The paper is an excellent introduction and a thorough guide to possibility theory serving as a convenient framework for modelling uncertainty in a qualitative way. It provides an overview through the methods where fuzzy sets serve reasoning purposes as well as the background necessary to understand basic methodological issues. The second section of this volume is devoted to various aspects of fuzzy logic control. The first paper in this section, Fuzzy Logic Control: a Systematic Design and Per formance Assessment Methodology, is written by a noble scientist and researcher G. Vachtsevanos, from Georgia Institute of Technology, Atlanta, Georgia, and is co authored by S. Farinvata, from Ford Electronics Division, Melvindale, MI. This paper sets a milestone in the systematic analysis and design approach to fuzzy dynamic systems. The lack of mathematical rigour in the analysil> and design of fuzzy logic controllers motivated the presented research. As a result, an analytical background is laid out to avoid intuitive and ad hoc implementations offuzzy logic in control. In the design area, the proposed approach combines the approximate system modelling and heuristic approach to develop a fuzzy logic controller that is complete and robust. Three measures of performance assessment are proposed: fuzzy stability, robustness, and optimality. Fur thermore, the main objective in these areas is to formalize the analysis and design tools and to demonstrate their effectiveness in dealing with real-world applications. Usually, when the plant dynamics are ill-defined, such a system is subject to large disturbances. The proposed methodology provides an alternative solution to the available ones.

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Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.