9781584885313

Introduction to Fuzzy Systems

by ;
  • ISBN13:

    9781584885313

  • ISBN10:

    1584885319

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

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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

Prefacep. v
Table of Contentsp. ix
Fuzzy Set Theoryp. 1
Classical Set Theoryp. 1
Fuzzy Set Theoryp. 5
Interval Arithmeticp. 9
Some Fundamental Conceptsp. 10
Interval Arithmeticp. 11
Algebraic Properties of Interval Arithmeticp. 14
Interval Evaluationp. 17
Operations on Fuzzy Setsp. 21
Fuzzy Sets and [alpha] Cutsp. 21
Arithmetic of Fuzzy Setsp. 22
Problemsp. 37
Fuzzy Logic Theoryp. 39
Classical Logic Theoryp. 40
Fundamental Conceptsp. 40
Logical Functions of the Two-Valued Logicp. 41
The Boolean Algebrap. 43
Basic Operations of the Boolean Algebrap. 43
Basic Properties of the Boolean Algebrap. 43
Multi-Valued Logicp. 46
The Three-Valued Logicp. 46
The n-Valued Logicp. 46
Fuzzy Logic and Approximate Reasoningp. 47
Fuzzy Relationsp. 51
Problemsp. 58
Some Applications of Fuzzy Logicp. 61
Product Quality Evaluationp. 61
Decision Making for Investmentp. 64
Performance Evaluationp. 66
Problem Formulationp. 66
Performance Evaluation Formulap. 69
Miscellaneous Examplesp. 73
Problemsp. 88
Fuzzy Rule Base and Fuzzy Modelingp. 89
Fuzzy Rule Basep. 89
Fuzzy IF-THEN Rulesp. 89
Fuzzy Logic Rule Basep. 91
Fuzzy IF-THEN Rule Base as a Mathematical Modelp. 96
Evaluation of Fuzzy IF-THEN Rulesp. 98
Fuzzy Modelingp. 99
Basic Concept of System Modelingp. 100
Modeling of Static Fuzzy Systemsp. 101
Parameters Identification in Static Fuzzy Modelingp. 108
Discrete-Time Dynamic Fuzzy Systems Stabilityp. 115
Dynamic Fuzzy Systems without Controlp. 116
Dynamic Fuzzy Systems with Controlp. 119
Problemsp. 124
Fuzzy Control Systemsp. 125
Classical Programmable Logic Controlp. 126
Fuzzy Logic Control: A General Model-Free Approachp. 138
Closed-Loop Set-Point Tracking Systemp. 138
Design Principle of Fuzzy Logic Controllersp. 141
Examples of Model-Free Fuzzy Controller Designp. 155
Problemsp. 168
Fuzzy PID Control Systemsp. 171
Conventional PID Controllersp. 171
Fuzzy PID Controllers (Type 1)p. 179
Discretization of PID Controllersp. 179
Designing Type-1 Fuzzy PID Controllersp. 183
Two Examplesp. 184
Fuzzy PID Controllers (Type 2)p. 190
Designing Type-2 Fuzzy PD Controllerp. 192
Designing Type-2 Fuzzy PI Controllerp. 207
Designing Type-2 Fuzzy PI+D Controllerp. 209
Fuzzy PID Controllers: Stability Analysisp. 225
BIBO Stability and the Small Gain Theoremp. 226
BIBO Stability of Fuzzy PD Control Systemsp. 230
BIBO Stability of Fuzzy PI Control Systemsp. 233
BIBO Stability of Fuzzy PI+D Control Systemsp. 236
Graphical Stability Analysis of Fuzzy PID Control Systemsp. 237
Problemsp. 242
Computational Verb Fuzzy Controllersp. 245
Computational Verbs and Verb Numbersp. 245
Fundamental Conceptsp. 246
Computational Verb Numbersp. 248
Verb Similarityp. 249
Verb Rules and Verb Inferencep. 250
Verb Inference with a Single Verb Rulep. 250
Verb Inference with a Verb Algorithmp. 253
Deverbification: Reconstruct Computational Verbs from Similarity Functionsp. 255
Computational Verb-Based Fuzzy PID Controllersp. 255
Fuzzy Gain Schedulersp. 257
From Fuzzy Control Rules to Verb-Based Control Rulesp. 259
Constructing Verb Rules for Tuning the Gain K[subscript p] from Phase Plotsp. 262
Constructing Verb Rules for Tuning the Gain K[subscript d] from Phase Plotsp. 266
Constructing Verb Rules for Tuning the Gain [gamma] from Phase Plotsp. 268
Implementing the Verb-based P-controllerp. 268
Implementing the Verb-based P-controller for a Second-Order Plantp. 272
Problemsp. 286
Referencesp. 289
Solutionsp. 291
Indexp. 313
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