Introduction To Type-2 Fuzzy Logic Control E-Book

Jerry Mendel

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: IEEE Press Series on Computational Intelligence
• Sprache: Englisch

Seitenzahl: 508

Veröffentlichungsjahr: 2014

Beschreibung

An introductory book that provides theoretical, practical, and application coverage of the emerging field of type-2 fuzzy logic control Until recently, little was known about type-2 fuzzy controllers due to the lack of basic calculation methods available for type-2 fuzzy sets and logic--and many different aspects of type-2 fuzzy control still needed to be investigated in order to advance this new and powerful technology. This self-contained reference covers everything readers need to know about the growing field. Written with an educational focus in mind, Introduction to Type-2 Fuzzy Logic Control: Theory and Applications uses a coherent structure and uniform mathematical notations to link chapters that are closely related, reflecting the book's central themes: analysis and design of type-2 fuzzy control systems. The book includes worked examples, experiment and simulation results, and comprehensive reference materials. The book also offers downloadable computer programs from an associated website. Presented by world-class leaders in type-2 fuzzy logic control, Introduction to Type-2 Fuzzy Logic Control: * Is useful for any technical person interested in learning type-2 fuzzy control theory and its applications * Offers experiment and simulation results via downloadable computer programs * Features type-2 fuzzy logic background chapters to make the book self-contained * Provides an extensive literature survey on both fuzzy logic and related type-2 fuzzy control Introduction to Type-2 Fuzzy Logic Control is an easy-to-read reference book suitable for engineers, researchers, and graduate students who want to gain deep insight into type-2 fuzzy logic control.

Leseprobe

Table of Contents

Cover

Series

Title Page

Copyright

Dedication

Preface

Contributors

Chapter 1: Introduction

1.1 Early History of Fuzzy Control

1.2 What Is a Type-1 Fuzzy Set?

1.3 What Is a Type-1 Fuzzy Logic Controller?

1.4 What Is a Type-2 Fuzzy Set?

1.5 What Is a Type-2 Fuzzy Logic Controller?

1.6 Distinguishing an FLC from Other Nonlinear Controllers

1.7 T2 FLCs Versus T1 FLCs

1.8 Real-World Applications of IT2 Mamdani FLCs

1.9 Book Rationale

1.10 Software and How It Can Be Accessed

1.11 Coverage of the Other Chapters

Chapter 2: Introduction to Type-2 Fuzzy Sets

2.1 Introduction

2.2 Brief Review of Type-1 Fuzzy Sets

1

2.3 Interval Type-2 Fuzzy Sets

2.5 Wrapup

2.4 General Type-2 Fuzzy Sets

2.6 Moving On

Chapter 3: Interval Type-2 Fuzzy Logic Controllers

3.1 Introduction

3.2 Type-1 Fuzzy Logic Controllers

3.3 Interval Type-2 Fuzzy Logic Controllers

3.4 Wu–Mendel Uncertainty Bounds

3.5 Control Analyses of IT2 FLC

3.6 Determining the fou Parameters of IT2 FLC

3.7 Moving on

Appendix 3A. Proof of Theorem 3.4

Chapter 4: Analytical Structure of Various Interval Type-2 Fuzzy PI and PD Controllers

4.1 Introduction

4.2 PID, PI, and PD Controllers and Their Relationships

4.3 Components of the Interval T2 Fuzzy PI and PD Controllers

4.4 Mamdani Fuzzy PI and PD Controllers—Configuration

1

4.5 Mamdani Fuzzy PI and PD Controllers—Configuration

2

4.6 Mamdani Fuzzy PI and PD Controllers—Configuration

3

4.7 Mamdani Fuzzy PI and PD Controllers—Configuration

4

4.8 TSK Fuzzy PI and PD Controllers—Configuration

5

4.9 Analyzing the Derived Analytical Structures

6

4.10 Design Guidelines for the T2 Fuzzy PI and PD Controllers

7

4.11 Summary

Appendix 4A

Chapter 5: Analysis of Simplified Interval Type-2 Fuzzy PI and PD Controllers

5.1 Introduction

5.2 Simplified Type-2 FLCs: Design, Computation, and Performance

1

5.3 Analytical Structure of Interval T2 Fuzzy PD and PI Controller

5.4 Conclusions

Chapter 6: On the Design of IT2 TSK FLCs

6.1 Introduction

6.2 Preliminaries

2

6.3 Novel Inference Engine for Control Design

3

6.4 Stability of IT2 TSK FLCs

6.5 Design of Adaptive IT2 TSK FLC

5

6.6 Adaptive Control Design with Application to Robot Manipulators

6

6.7 Robust Control Design

8

6.8 Summary

Appendix

9

Chapter 7: Looking into the Future

7.1 Introduction

7.2 William Melek and Hao Ying Look into The Future

7.3 Hani Hagras Looks into the Future

1

7.4 Woei Wan Tan Looks Into the Future

7.5 Jerry Mendel Looks into The Future

Appendix A: T2 FLC Software: From Type-1 to zSlices-Based General Type-2 FLCs

A.1 Introduction

A.2 FLC for Right-Edge Following

A.3 Type-1 FLC Software

A.4 Interval T2 FLC Software

A.5 zSlices-Based General Type-2 FLC Software

References

Index

Series

End User License Agreement

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Guide

Cover

Table of Contents

Preface

Chapter 1: Introduction

List of Illustrations

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 1.6

Figure 1.7

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Figure 1.10

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List of Tables

Table 2.1

Table 2.2

Table 2.3

Table 2.4

Table 2.5

Table 2.6

Table 3.1

Table 3.2

Table 3.3

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Table 4.1

Table 4.2

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Table 5.2

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Table 5.6

Table 5.7

Table 5.8

Table 5.9

Table 6.1

Table 6.2

Table 6.3

Table 6.4

Table 6.5

Introduction to Type-2 Fuzzy Logic Control

Theory and Applications

Jerry M. Mendel

Hani Hagras

Woei-Wan Tan

William W. Melek

Hao Ying

Copyright © 2014 by The Institute of Electrical and Electronics Engineers, Inc.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:}

Mendel, Jerry M., 1938–

Introduction to type-2 fuzzy logic control : theory and applications / Jerry M. Mendel,

Hani Hagras, Woei-Wan Tan, William W. Melek, Hao Ying.

pages cm

Includes bibliographical references and index.

ISBN 978-1-118-27839-0 (cloth)

1. Automatic control. 2. Fuzzy systems. I. Hagras, Hani. II. Tan, Woei-Wan. III. Melek,

William W. IV. Ying, Hao, 1958- V. Title.

TJ217.5.M46 2014

629.8′95633–dc23

2014000084

To

the memory of

Ebrahim Mamdani (1943–2010)

Founder of Fuzzy Logic Control

Preface

When Lotfi Zadeh invented fuzzy sets in 1965, he never dreamt that the field in which they would be most widely used would arguably be the one that became the most hostile to the concept of fuzziness, namely control. Perhaps this was because the word “fuzzy” in Western civilization does not have a positive connotation and suggests an abandonment of mathematical rigor, one of the cornerstones of control. Perhaps it was because some famous mathematical probabilists (incorrectly) claimed that there was no difference between a fuzzy set and subjective probability. Perhaps it was because for almost a decade, until the 1974 seminal paper by Prof. Ebrahim Mamdani, who founded the field of fuzzy logic control and to whose memory our book is dedicated, there were no substantial real-world applications for fuzzy sets. Or, perhaps, it was because after the founding of this field many exaggerated claims were made by the fuzzy logic control community that flew in the face of mathematical rigor and did not pay attention to the same metrics that were and still are the cornerstones for control and cannot be ignored.

Now, 40 years after Mamdani's seminal paper, fuzzy logic control using regular (i.e., type-1) fuzzy sets and logic has been extensively studied, applied to practical problems, and is very widely used in many real-world applications. It can and has been studied with the same level of mathematical rigor that control theorists are accustomed to, and is now considered a matured field; however, it still has some shortcomings. Its major shortcoming (in the opinions of the authors of this book) goes back to one of the earliest criticisms made about a type-1 fuzzy set, namely the unfuzziness of its membership function, that is, the word “fuzzy” has the connotation of being uncertain. But how can this connotation be captured by a membership function that is completely certain?

Importantly, in 1975 Zadeh introduced more general kinds of fuzzy sets in which their membership function grades are themselves fuzzy. The two most widely studied of these are interval-valued fuzzy sets and type-2 fuzzy sets. For the former, the membership grade is a uniformly weighted interval of values, whereas for the latter the membership grade is a nonuniformly weighted interval of values. Obviously, interval-valued fuzzy sets are a special case of type-2 fuzzy sets and are therefore called by many (as we do in this book) interval type-2 fuzzy sets.

Why should using type-2 fuzzy sets be of interest to the fuzzy logic control community? This question is answered in great detail in this book, but two short answers are: (1) they are more robust to system uncertainties and can provide better control system performance than type-1 fuzzy sets; and (2) there is now more than a critical mass of papers that have been published that demonstrate these improvements for many real-world applications.

Because of the lack of basic calculation methods for type-2 fuzzy sets in their early days, type-2 fuzzy logic controllers (T2 FLCs) did not emerge until fairly recently. Things have changed a lot during the past decade, so that type-2 fuzzy logic control (which is still an emerging field) now has the attention of the fuzzy systems community, and, as a result of this, the number of publications on it is growing quickly.

Recall that the central themes of any control methodology, fuzzy or conventional, are (1) to analyze various aspects of a control system and (2) to design a control system to achieve given user specifications. This book focuses on both topics for T2 FLCs and type-2 fuzzy logic control systems. The analysis includes (1) the mathematical structure of some T2 FLCs, (2) stability of type-2 fuzzy logic control systems, and (3) robustness of the type-2 fuzzy logic control systems.

This book, the first one entirely on T2 FLC, shows how to design type-2 fuzzy logic control systems based on a variety of choices for the T2 FLC components and also demonstrates how to apply type-2 fuzzy logic control theory to applications. It has been written by five of the leading experts on type-2 fuzzy sets, systems, and control, with the help of six contributors. It will be useful to any technical person interested in learning type-2 fuzzy logic control theory and its applications, from students to practicing engineers.

This is an introductory book that provides theoretical, practical, and application coverage of type-2 fuzzy logic control, and uses a coherent structure and uniform mathematical notations to link chapters, which are closely related, reflecting the book's central themes—analysis and design of type-2 fuzzy logic control systems. It has been written with an educational focus rather than a pure research focus. Each chapter includes worked examples, and most refer to their computer codes (programs) accessible through the book's common website, and outline how to use them at some high level. It is a self-contained reference book suitable for engineers, researchers, and college graduate students who want to gain deep insights about type-2 fuzzy logic control.

The book begins with an easy-to-read chapter meant to whet the reader's appetite so that he or she will read on; it explains what the differences are between a type-1 fuzzy set and a type-2 fuzzy set, and a T2 FLC and a T1 FLC, and, it provides many real-world applications in which T2 FLCs have shown marked improvements in performance over T1 FLCs. Chapter 2 provides all of the background material that is needed about type-2 fuzzy sets so that you can read the rest of the book; its main emphasis is on interval type-2 fuzzy sets because at present they are the most widely used type-2 fuzzy sets in type-2 fuzzy logic control. Chapter 3 is about Mamdani and TSK interval T2 FLCs. Chapter 4 examines the analytical structure of various interval type-2 fuzzy PI and PD controllers. Chapter 5 is about ways to simplify interval type-2 fuzzy PI and PD controllers. Chapter 6 is about the rigorous design of interval type-2 TSK fuzzy controllers. Chapter 7 provides each of the five authors with an opportunity to look into the future of type-2 fuzzy logic control. The book's appendix describes Java-based software that will let the reader examine type-1, interval type-2, and even general type-2 FLCs. All references (which are very extensive) have been integrated into one list that is at the end of the book.

The book's software can be downloaded by means of the following procedure: Software for Examples 4.1 and 4.6 and the examples in Chapter 6 can be accessed at http://booksupport.wiley.com, and software for Appendix A, that supports T1, IT2 and GT2 FLCs, is available at http://juzzy.wagnerweb.net.

In addition to the five authors, six of their (former) graduate students contributed to this book, to whom the authors are greatly appreciative. Their names are listed in the Contributors List. More specifically, Christian Wagner contributed to Chapters 2, 3 and 7, and prepared the entire Appendix; Xinyu Du and Haibo Zhou contributed to Chapter 4; Maowen Nie and Dongrui Wu contributed to Chapter 5; and Mohammad Biglarbegian contributed to Chapter 6.

The authors gratefully acknowledge material quoted from books or journals published by Elsevier, IEEE, John Wiley & Sons, Mancy Publishing (www.maney.co.uk/journals/irs and www.ingentaconnect.com/content/maney/ias) and Pearsons Education, Inc. For a complete listing of quoted books or articles, please see the References.

Jerry M. Mendel

Los Angeles, California

Hani Hagras

Colchester, UK

Woei-Wan Tan

Singapore

William W. Melek

Waterloo, Canada

Hao Ying

Detroit, Michigan

Contributors

Mohammad Biglarbegian

, University of Guelph, Guelph Ontario, Canada

Xinyu Du

, Wayne State University, Detroit, Michigan

Maowen Nie

, A*Star Institute of Infocomm Research, Singapore

Christian Wagner

, University of Nottingham, Nottingham, United Kingdom

Dongrui Wu

, GE Global Research, New York

Haibo Zhou

, Central South University, Changsha, China

Chapter 1Introduction

1.1 Early History of Fuzzy Control

Fuzzy control (also known as fuzzy logic control) is regarded as the most widely used application of fuzzy logic and is credited with being a well-accepted methodology for designing controllers that are able to deliver satisfactory performance in the face of uncertainty and imprecision (Lee, 1990; Sugeno, 1985); Feng, 2006). In addition, fuzzy logic theory provides a method for less skilled personnel to develop practical control algorithms in a user-friendly way that is close to human thinking and perception, and to do this in a short amount of time. Fuzzy logic controllers (FLCs) can sometimes outperform traditional control systems [like proportional–integral–derivative (PID) controllers] and have often performed either similarly or even better than human operators. This is partially because most FLCs are nonlinear controllers that are capable of controlling real-world systems (the vast majority of such systems are nonlinear) better than a linear controller can, and with minimal to no knowledge about the mathematical model of the plant or process being controlled.

Fuzzy logic controllers have been applied with great success to many real-world applications. The first FLC was developed by Mamdani and Assilian (1975), in the United Kingdom, for controlling a steam generator in a laboratory setting. In 1976, Blue Circle Cement and SIRA in Denmark developed a cement kiln controller (the first industrial application of fuzzy logic), which went into operation in 1982 (Holmblad and Ostergaard, 1982). In the 1980s, several important industrial applications of fuzzy logic control were launched successfully in Japan, including a water treatment system developed by Fuji Electric. In 1987, Hitachi put a fuzzy logic based automatic train operation control system into the Sendai city's subway system (Yasunobu and Miyamoto, 1985). These and other applications of FLCs motivated many Japanese engineers to investigate a wide range of novel applications for fuzzy logic. This led to a “fuzzy boom” in Japan, a result of close collaboration and technology transfer between universities and industry.