Introduction to Fuzzy Systems

by Chen; Guanrong

• ISBN13: 9781584885313
• ISBN10: 1584885319
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-11-16
• Publisher: Chapman & Hall/

Summary

Introduction to Fuzzy Systems provides students with a self-contained introduction that requires no preliminary knowledge of fuzzy mathematics and fuzzy control systems theory. Simplified and readily accessible, it encourages both classroom and self-directed learners to build a solid foundation in fuzzy systems.After introducing the subject, the authors move directly into presenting real-world applications of fuzzy logic, revealing its practical flavor. This practicality is then followed by basic fuzzy systems theory. The book also offers a tutorial on fuzzy control theory, based mainly on the well-known classical Proportional-Integral-Derivative (PID) controllers theory and design methods. In particular, the text discusses fuzzy PID controllers in detail, including a description of the new notion of generalized verb-based fuzzy-logic control theory.Introduction to Fuzzy Systems is primarily designed to provide training for systems and control majors, both senior undergraduate and first year graduate students, to acquaint them with the fundamental mathematical theory and design methodology required to understand and utilize fuzzy control systems.

Author Biography

Trung Tat Pham is ISA Robotics and Expert System Division Director Elect, Chief Technology Officer, Dicentral Corporation, Houston, Texas, USA.

Table of Contents

Preface	p. v
Table of Contents	p. ix
Fuzzy Set Theory	p. 1
Classical Set Theory	p. 1
Fuzzy Set Theory	p. 5
Interval Arithmetic	p. 9
Some Fundamental Concepts	p. 10
Interval Arithmetic	p. 11
Algebraic Properties of Interval Arithmetic	p. 14
Interval Evaluation	p. 17
Operations on Fuzzy Sets	p. 21
Fuzzy Sets and [alpha] Cuts	p. 21
Arithmetic of Fuzzy Sets	p. 22
Problems	p. 37
Fuzzy Logic Theory	p. 39
Classical Logic Theory	p. 40
Fundamental Concepts	p. 40
Logical Functions of the Two-Valued Logic	p. 41
The Boolean Algebra	p. 43
Basic Operations of the Boolean Algebra	p. 43
Basic Properties of the Boolean Algebra	p. 43
Multi-Valued Logic	p. 46
The Three-Valued Logic	p. 46
The n-Valued Logic	p. 46
Fuzzy Logic and Approximate Reasoning	p. 47
Fuzzy Relations	p. 51
Problems	p. 58
Some Applications of Fuzzy Logic	p. 61
Product Quality Evaluation	p. 61
Decision Making for Investment	p. 64
Performance Evaluation	p. 66
Problem Formulation	p. 66
Performance Evaluation Formula	p. 69
Miscellaneous Examples	p. 73
Problems	p. 88
Fuzzy Rule Base and Fuzzy Modeling	p. 89
Fuzzy Rule Base	p. 89
Fuzzy IF-THEN Rules	p. 89
Fuzzy Logic Rule Base	p. 91
Fuzzy IF-THEN Rule Base as a Mathematical Model	p. 96
Evaluation of Fuzzy IF-THEN Rules	p. 98
Fuzzy Modeling	p. 99
Basic Concept of System Modeling	p. 100
Modeling of Static Fuzzy Systems	p. 101
Parameters Identification in Static Fuzzy Modeling	p. 108
Discrete-Time Dynamic Fuzzy Systems Stability	p. 115
Dynamic Fuzzy Systems without Control	p. 116
Dynamic Fuzzy Systems with Control	p. 119
Problems	p. 124
Fuzzy Control Systems	p. 125
Classical Programmable Logic Control	p. 126
Fuzzy Logic Control: A General Model-Free Approach	p. 138
Closed-Loop Set-Point Tracking System	p. 138
Design Principle of Fuzzy Logic Controllers	p. 141
Examples of Model-Free Fuzzy Controller Design	p. 155
Problems	p. 168
Fuzzy PID Control Systems	p. 171
Conventional PID Controllers	p. 171
Fuzzy PID Controllers (Type 1)	p. 179
Discretization of PID Controllers	p. 179
Designing Type-1 Fuzzy PID Controllers	p. 183
Two Examples	p. 184
Fuzzy PID Controllers (Type 2)	p. 190
Designing Type-2 Fuzzy PD Controller	p. 192
Designing Type-2 Fuzzy PI Controller	p. 207
Designing Type-2 Fuzzy PI+D Controller	p. 209
Fuzzy PID Controllers: Stability Analysis	p. 225
BIBO Stability and the Small Gain Theorem	p. 226
BIBO Stability of Fuzzy PD Control Systems	p. 230
BIBO Stability of Fuzzy PI Control Systems	p. 233
BIBO Stability of Fuzzy PI+D Control Systems	p. 236
Graphical Stability Analysis of Fuzzy PID Control Systems	p. 237
Problems	p. 242
Computational Verb Fuzzy Controllers	p. 245
Computational Verbs and Verb Numbers	p. 245
Fundamental Concepts	p. 246
Computational Verb Numbers	p. 248
Verb Similarity	p. 249
Verb Rules and Verb Inference	p. 250
Verb Inference with a Single Verb Rule	p. 250
Verb Inference with a Verb Algorithm	p. 253
Deverbification: Reconstruct Computational Verbs from Similarity Functions	p. 255
Computational Verb-Based Fuzzy PID Controllers	p. 255
Fuzzy Gain Schedulers	p. 257
From Fuzzy Control Rules to Verb-Based Control Rules	p. 259
Constructing Verb Rules for Tuning the Gain K[subscript p] from Phase Plots	p. 262
Constructing Verb Rules for Tuning the Gain K[subscript d] from Phase Plots	p. 266
Constructing Verb Rules for Tuning the Gain [gamma] from Phase Plots	p. 268
Implementing the Verb-based P-controller	p. 268
Implementing the Verb-based P-controller for a Second-Order Plant	p. 272
Problems	p. 286
References	p. 289
Solutions	p. 291
Index	p. 313
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