Fuzzy Control and Identification

CHAPTER 1 INTRODUCTION.

1.1 Fuzzy Systems.

1.2 Expert Knowledge.

1.3 When and When Not to Use Fuzzy Control.

1.4 Control.

1.5 Interconnection of Several Subsystems.

1.6 Identification and Adaptive Control.

1.7 Summary.

Exercises.

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.

2.4 Example.

2.5 Singleton Fuzzy Sets.

2.6 Summary.

Exercises.

CHAPTER 3 MAMDANI FUZZY SYSTEMS.

3.1 If-Then Rules and Rule Base.

3.2 Fuzzy Systems.

3.3 Fuzzification.

3.4 Inference.

3.5 Defuzzification.

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.

3.7 Summary.

Exercises.

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.

4.6 Summary.

Exercises.

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.

5.4 Summary.

Exercises.

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.

6.5 Summary.

Exercises.

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.

7.5 Summary.

Exercises.

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.

8.7 Summary.

Exercises.

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.

9.4 Summary.

Exercises.

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.

10.6 Summary.

Exercises.

REFERENCES.

APPENDIX COMPUTER PROGRAMS.

INDEX.