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Fuzzy Control and Identification

ISBN: 978-0-470-54277-4
231 pages
December 2010
Fuzzy Control and Identification (0470542772) cover image
This book gives an introduction to basic fuzzy logic and Mamdani and Takagi-Sugeno fuzzy systems. The text shows how these can be used to control complex nonlinear engineering systems, while also also suggesting several approaches to modeling of complex engineering systems with unknown models.

Finally, fuzzy modeling and control methods are combined in the book, to create adaptive fuzzy controllers, ending with an example of an obstacle-avoidance controller for an autonomous vehicle using modus ponendo tollens logic.

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PREFACE.

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.

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John H. Lilly, PhD, is a professor in the Speed School of Engineering at the University of Louisville. His research interests are nonlinear and adaptive control, fuzzy identification and control, positive/negative fuzzy systems, pneumatic muscle actuators, and robotics. In addition to his twenty-eight years of teaching experience, Dr. Lilly has written more than fifty refereed journal and conference articles, book chapters, invited scholarly lectures, and seminars.
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“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)

 

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