A fuzzy control system is a control system based on fuzzy logic, which is a mathematical system that makes decisions using human reasoning processes. This book presents an introductory–level exposure to two of the principal uses for fuzzy logic identification and control. Drawn from the author′s lectures presented in a graduate–level course over the past decade, this volume serves as a holistically suitable single text for a fuzzy control course, compiling the information often found in several different books on the subject into one.
Starting with explanations of fuzzy logic, fuzzy control, and adaptive fuzzy control, the book introduces the concept of expert knowledge, which is the basis for much of fuzzy control. From there, the author covers:
Basic concepts of fuzzy sets such as membership functions, universe of discourse, linguistic variables, linguistic values, support, a–cut, and convexity
Both Mamdani and Takagi–Sugeno fuzzy systems, showing how an effective controller can be designed for many complex nonlinear systems without mathematical models or knowledge of control theory while also suggesting several approaches to modeling of complex engineering systems with unknown models
How PID controllers can be made fuzzy and why this is useful
Position–form and incremental–form fuzzy controllers
How nonlinear systems can be modeled as fuzzy systems in several forms
How fuzzy tracking control and model reference control can be realized for nonlinear systems using parallel distributed techniques
The estimation of nonlinear systems using the batch least squares, recursive least squares, and gradient methods
The creation of direct and indirect adaptive fuzzy controllers
Also included are many examples, exercises, and computer program listings, all class–tested. Fuzzy Control and Identification is intended for seniors and first–year graduate students, and is suitable for any engineering department. No knowledge specific to any particular branch of engineering is required, and no knowledge of electrical, chemical, or mechanical systems is necessary to read and understand the material.
CHAPTER 1 INTRODUCTION.
1.1 Fuzzy Systems.
1.2 Expert Knowledge.
1.3 When and When Not to Use Fuzzy Control.
1.5 Interconnection of Several Subsystems.
1.6 Identification and Adaptive Control.
CHAPTER 2 BASIC CONCEPTS OF FUZZY SETS.
2.1 Fuzzy Sets.
2.2 Useful Concepts for Fuzzy Sets.
2.3 Some Set Theoretic and Logical Operations on Fuzzy Sets.
2.5 Singleton Fuzzy Sets.
CHAPTER 3 MAMDANI FUZZY SYSTEMS.
3.1 If–Then Rules and Rule Base.
3.2 Fuzzy Systems.
3.5.1 Center of Gravity (COG) Defuzzification.
3.5.2 Center Average (CA) Defuzzification.
3.6 Example: Fuzzy System for Wind Chill.
3.6.1 Wind Chill Calculation, Minimum T–Norm, COG Defuzzification.
3.6.2 Wind Chill Calculation, Minimum T–Norm, CA Defuzzification.
3.6.3 Wind Chill Calculation, Product T–Norm, COG Defuzzification.
3.6.4 Wind Chill Calculation, Product T–Norm, CA Defuzzification.
3.6.5 Wind Chill Calculation, Singleton Output Fuzzy Sets, Product T–Norm, CA Defuzzification.
CHAPTER 4 FUZZY CONTROL WITH MAMDANI SYSTEMS.
4.1 Tracking Control with a Mamdani Fuzzy Cascade Compensator.
4.1.1 Initial Fuzzy Compensator Design: Ball and Beam Plant.
4.1.2 Rule Base Determination: Ball and Beam Plant.
4.1.3 Inference: Ball and Beam Plant.
4.1.4 Defuzzification: Ball and Beam Plant.
4.2 Tuning for Improved Performance by Adjusting Scaling Gains.
4.3 Effect of Input Membership Function Shapes.
4.4 Conversion of PID Controllers into Fuzzy Controllers.
4.4.1 Redesign for Increased Robustness.
4.5 Incremental Fuzzy Control.
CHAPTER 5 MODELING AND CONTROL METHODS USEFUL FOR FUZZY CONTROL.
5.1 Continuous–Time Model Forms.
5.1.1 Nonlinear Time–Invariant Continuous–Time State–Space Models.
5.1.2 Linear Time–Invariant Continuous–Time State–Space Models.
5.2 Model Forms for Discrete–Time Systems.
5.2.1 Input Output Difference Equation Model for Linear Discrete–Time Systems.
5.2.2 Linear Time–Invariant Discrete–Time State–Space Models.
5.3 Some Conventional Control Methods Useful in Fuzzy Control.
5.3.1 Pole Placement Control.
5.3.2 Tracking Control.
5.3.3 Model Reference Control.
5.3.4 Feedback Linearization.
CHAPTER 6 TAKAGI SUGENO FUZZY SYSTEMS.
6.1 Takagi Sugeno Fuzzy Systems as Interpolators between Memoryless Functions.
6.2 Takagi Sugeno Fuzzy Systems as Interpolators between Continuous–Time Linear State–Space Dynamic Systems.
6.3 Takagi Sugeno Fuzzy Systems as Interpolators between Discrete–Time Linear State–Space Dynamic Systems.
6.4 Takagi Sugeno Fuzzy Systems as Interpolators between Discrete–Time Dynamic Systems described by Input Output Difference Equations.
CHAPTER 7 PARALLEL DISTRIBUTED CONTROL WITH TAKAGI SUGENO FUZZY SYSTEMS.
7.1 Continuous–Time Systems.
7.2 Discrete–Time Systems.
7.3 Parallel Distributed Tracking Control.
7.4 Parallel Distributed Model Reference Control.
CHAPTER 8 ESTIMATION OF STATIC NONLINEAR FUNCTIONS FROM DATA.
8.1 Least–Squares Estimation.
8.1.1 Batch Least Squares.
8.1.2 Recursive Least Squares.
8.2 Batch Least–Squares Fuzzy Estimation in Mamdani Form.
8.3 Recursive Least–Squares Fuzzy Estimation in Mamdani Form.
8.4 Least–Squares Fuzzy Estimation in Takagi Sugeno Form.
8.5 Gradient Fuzzy Estimation in Mamdani Form.
8.6 Gradient Fuzzy Estimation in Takagi Sugeno Form.
CHAPTER 9 MODELING OF DYNAMIC PLANTS AS FUZZY SYSTEMS.
9.1 Modeling Known Plants as Takagi Sugeno Fuzzy Systems.
9.2 Identification in Input Output Difference Equation Form.
9.2.1 Batch Least–Squares Identification in Difference Equation Form.
9.2.2 Recursive Least–Squares Identification in Input Output Difference Equation Form.
9.2.3 Gradient Identification in Input Output Difference Equation Form.
9.3 Identification in Companion Form.
9.3.1 Least–Squares Identification in Companion Form.
9.3.2 Gradient Identification in Companion Form.
CHAPTER 10 ADAPTIVE FUZZY CONTROL.
10.1 Direct Adaptive Fuzzy Tracking Control.
10.2 Direct Adaptive Fuzzy Model Reference Control.
10.3 Indirect Adaptive Fuzzy Tracking Control.
10.4 Indirect Adaptive Fuzzy Model Reference Control.
10.5 Adaptive Feedback Linearization Control.
APPENDIX COMPUTER PROGRAMS.
This is a very useful and attractive material on fuzzy sets in control engineering–accessible to large categories of readers The book is equally recommended to students (who want to become familiar with the fuzzy logic approach), educators (who are looking for a reliable course and / or application support) and practitioners (who are interested in enlarging their professional horizon). (Zentralblatt MATH, 2012)