Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems

by Chen; Guanrong

• ISBN13: 9780849316586
• ISBN10: 0849316588
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-11-27
• Publisher: CRC Press

Summary

In the early 1970s, fuzzy systems and fuzzy control theories added a new dimension to control systems engineering. From its beginnings as mostly heuristic and somewhat ad hoc, more recent and rigorous approaches to fuzzy control theory have helped make it an integral part of modern control theory and produced many exciting results. Yesterday's "art" of building a working fuzzy controller has turned into today's "science" of systematic design. To keep pace with and further advance the rapidly developing field of applied control technologies, engineers, both present and future, need some systematic training in the analytic theory and rigorous design of fuzzy control systems. Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems provides that training by introducing a rigorous and complete fundamental theory of fuzzy sets and fuzzy logic, and then building a practical theory for automatic control of uncertain and ill-modeled systems encountered in many engineering applications. The authors proceed through basic fuzzy mathematics and fuzzy systems theory and conclude with an exploration of some industrial application examples. Almost entirely self-contained, Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems establishes a strong foundation for designing and analyzing fuzzy control systems under uncertain and irregular conditions. Mastering its contents gives students a clear understanding of fuzzy control systems theory that prepares them for deeper and broader studies and for many practical challenges faced in modern industry.

Table of Contents

Fuzzy Set Theory	1	(56)
Classical Set Theory	1	(4)
Fundamental Concepts	1	(2)
Elementary Measure Theory of Sets	3	(2)
Fuzzy Set Theory	5	(4)
Interval Arithmetic	9	(28)
Fundamental Concepts	9	(3)
Interval Arithmetic	12	(1)
Algebraic Properties of Interval Arithmetic	13	(4)
Measure Theory of Intervals	17	(3)
Properties of the Width of an Interval	20	(2)
Interval Evaluation	22	(3)
Interval Matrix Operations	25	(5)
Interval Matrix Equations and Interval Matrix Inversion	30	(7)
Operations on Fuzzy Sets	37	(20)
Fuzzy Subsets	37	(5)
Fuzzy Numbers and Their Arithmetic	42	(12)
Problems	54	(2)
References	56	(1)
Fuzzy Logic Theory	57	(32)
Classical Logic Theory	58	(4)
Fundamental Concepts	58	(3)
Logical Functions of the Two-Valued Logic	61	(1)
The Boolean Algebra	62	(3)
Basic Operations of the Boolean Algebra	62	(1)
Basic Properties of the Boolean Algebra	63	(2)
Multi-Valued Logic	65	(1)
Three-Valued Logic	65	(1)
n-Valued Logic	65	(1)
Fuzzy Logic and Approximate Reasoning	66	(3)
Fuzzy Relations	69	(6)
Fuzzy Logic Rule Base	75	(14)
Fuzzy IF-THEN Rules	75	(2)
Fuzzy Logic Rule Base	77	(3)
Interpretation of Fuzzy IF-THEN Rules	80	(2)
Evaluation of Fuzzy IF-THEN Rules	82	(2)
Problems	84	(3)
References	87	(2)
Fuzzy System Modeling	89	(50)
Modeling of Static Fuzzy Systems	90	(12)
Fuzzy Logic Description of Input-Output Relations	90	(6)
Parameters Identification in Static Fuzzy Modeling	96	(6)
Discrete-Time Dynamic Fuzzy Systems and Their Stability Analysis	102	(12)
Dynamic Fuzzy Systems without Control	103	(6)
Dynamic Fuzzy Systems with Control	109	(5)
Modeling of Continuous-Time Dynamic Fuzzy Control Systems	114	(10)
Fuzzy Interval Partitioning	115	(4)
Dynamic Fuzzy System Modeling	119	(5)
Stability Analysis of Continuous-Time Dynamic Fuzzy Systems	124	(5)
Controllability Analysis of Continuous-Time Dynamic Fuzzy Systems	129	(4)
Analysis of Nonlinear Continuous-Time Dynamic Fuzzy Systems	133	(6)
Problems	136	(2)
References	138	(1)
Fuzzy Control Systems	139	(44)
Classical Programmable Logic Control	140	(5)
Fuzzy Logic Control (I): A General Model-Free Approach	145	(25)
A Closed-Loop Set-Point Tracking System	147	(3)
Design Principle of Fuzzy Logic Controllers	150	(10)
Examples of Model-Free Fuzzy Controller Design	160	(10)
Fuzzy Logic Control (II): A General Model-Based Approach	170	(13)
Problems	178	(4)
References	182	(1)
Fuzzy PID Controllers	183	(56)
Conventional PID Controllers: Design	183	(9)
Fuzzy PID Controllers Design	192	(31)
Fuzzy PD Controller	193	(14)
Fuzzy PI Controller	207	(2)
Fuzzy PI+D Controller	209	(14)
Fuzzy PID Controllers: Stability Analysis	223	(16)
BIBO Stability and the Small Gain Theorem	223	(3)
BIBO Stability of Fuzzy PD Control Systems	226	(3)
BIBO Stability of Fuzzy PI Control Systems	229	(2)
BIBO Stability of Fuzzy PI+D Control Systems	231	(1)
Graphical Stability Analysis of Fuzzy PID Control Systems	232	(4)
Problems	236	(1)
References	237	(2)
Adaptive Fuzzy Control	239	(32)
Fundamental Adaptive Fuzzy Control Concept	240	(6)
Operational Concepts	240	(2)
System Parameterization	242	(1)
Adjusting Mechanism	243	(2)
Guidelines for Selecting an Adaptive Fuzzy Controller	245	(1)
Gain Scheduling	246	(6)
Fuzzy Self-Tuning Regulator	252	(3)
Model Reference Adaptive Fuzzy Systems	255	(2)
Dual Control	257	(1)
Sub-Optimal Fuzzy Control	258	(13)
SISO Control Systems	259	(1)
MIMO Control Systems	260	(6)
Problems	266	(3)
References	269	(2)
Some Applications of Fuzzy Control	271	(44)
Health Monitoring Fuzzy Diagnostic Systems	271	(10)
Fuzzy Rule-Based Health Monitoring Expert Systems	272	(4)
Computer Simulations	276	(1)
Numerical Results	277	(4)
Fuzzy Control of Image Sharpness for Autofocus Cameras	281	(10)
Basic Image Processing Techniques	282	(1)
Fuzzy Control Model	283	(3)
Computer Simulation Results	286	(5)
Fuzzy Control for Servo Mechanic Systems	291	(9)
Fuzzy Modeling of a Servo Mechanic System	292	(2)
Fuzzy Controller of a Servo Mechanic System	294	(1)
Computer Simulations and Numerical Results	295	(5)
Fuzzy PID Controllers for Servo Mechanic Systems	300	(2)
Fuzzy PID Controller of a Servo Mechanic System	300	(1)
Adaptive Fuzzy Controller of a Servo Mechanic System	301	(1)
Fuzzy Controller for Robotic Manipulator	302	(13)
Fuzzy Modeling of a 2-Link Planar Manipulator	304	(3)
Fuzzy Controller of a 2-Link Planar Manipulator	307	(1)
Numerical Simulations	307	(4)
Problems	311	(2)
References	313	(2)
Index	315