# Foundations of Fuzzy Control

ISBN: 978-0-470-06117-6 August 2007 230 Pages

## Description

Fuzzy logic is key to the efficient working of many consumer, industrial and financial applications. Providing a brief history of the subject as well as analysing the system architecture of a fuzzy controller, this book gives a full and clearly set out introduction to the topic.

As an essential guide to this subject for many engineering disciplines, Foundations of Fuzzy Control successfully exploits established results in linear and non-linear control theory.  It presents a full coverage of fuzzy control, from basic mathematics to feedback control, all in a tutorial style.

In particular this book:

• Systematically analyses several fuzzy PID (Proportional-Integral-Derivative) control systems and state space control, and also self-learning control mechanisms
• Sets out practical worked through problems, examples and case studies to illustrate each type of control system
• Provides an accompanying Web site that contains downloadable Matlab programs.

This book is an invaluable resource for a broad spectrum of researchers, practitioners, and students in engineering.  In particular it is especially relevant for those in mechanical and electrical engineering, as well as those in artificial intelligence, machine learning, bio-informatics, and operational research.  It is also a useful reference for practising engineers, working on the development of fuzzy control applications and system architectures.

Foreword.

Preface.

List of Figures.

1 Introduction.

1.1 What Is Fuzzy Control?

1.2 Why Fuzzy Control?

1.3 Controller Design.

1.4 Introductory Example: Stopping a Car.

1.5 Summary.

1.6 Notes and references.

2 Fuzzy Reasoning.

2.1 Fuzzy Sets.

2.2 Fuzzy Set Operations.

2.3 Fuzzy Logic.

2.4 Fuzzy Implication.

2.5 Rules of Inference.

2.6 Generalized Modus Ponens.

2.7 Triangular Norms.

2.8 Formal Derivation of the Mamdani Inference*.

2.9 Summary.

2.10 Notes and References.

3 Fuzzy Control.

3.1 Controller Components.

3.2 Rule-Based Controllers.

3.3 Table-Based Controller.

3.4 Linear Controller.

3.5 Analytical Simplification of the Inference*.

3.6 Summary.

3.7 Notes and References.

4 Linear Fuzzy PID Control.

4.1 Fuzzy P Controller.

4.2 Fuzzy PD Controller.

4.3 Fuzzy PD+I Controller.

4.4 Fuzzy Incremental Controller.

4.5 Tuning.

4.6 Scaling.

4.7 Simulation Study: Higher-Order Process.

4.8 Practical Considerations*.

4.9 Summary.

4.10 Notes and References.

5 Nonlinear Fuzzy PID Control.

5.1 Phase Plane Analysis.

5.2 Fuzzy PD Control.

5.3 Fuzzy PD+I Control.

5.4 Fine-tuning.

5.5 Higher-Order Systems.

5.6 Practical Considerations.

5.7 Summary.

5.8 Notes and References.

6 The Self-Organizing Controller.

6.1 Model Reference Adaptive Systems.

6.2 The Original SOC.

6.3 A Linear PerformanceMeasure.

6.4 Example with a Long Deadtime.

6.5 Tuning and Time Lock.

6.6 Analytical Derivation of the Adaptation Law*.

6.7 Summary.

6.8 Notes and References.

7 Stability Analysis by Describing Functions.

7.1 Describing Functions.

7.2 Fuzzy PD Controller.

7.3 Fuzzy PD+I Controller.

7.4 The Nyquist Criterion for Stability.

7.5 Closed-Loop Simulation Examples.

7.6 Analytical Derivation of the Describing Function*.

7.7 Summary.

7.8 Notes and References.

8 Simulation Study: Cart–Ball Balancer.

8.1 Laboratory Rig.

8.2 Mathematical Model.

8.3 Step 1: Design a Crisp PID Controller.

8.4 Step 2: Replace It with a Linear Fuzzy.

8.5 Step 3:Make It Nonlinear.

8.6 Step 4: Fine-tune It.

8.7 Further State-Space Analysis*.

8.8 Summary.

8.9 Notes and References.

9 Supervisory Control*.

9.1 Process Control.

9.2 High-Level Fuzzy Control .

9.3 Summary.

9.4 Notes and References.

Bibliography.

Index.

"Its key strengths are the use of a very structured framework to introduce fuzzy control…" (Artificial Intelligence 171, October 2008)

"…a compact reference source for anybody interested in fuzzy control." (Computing Reviews.com, September 25, 2007)