Fuzzy Control

Contents
PREFACE vii
CHAPTER 1 / Introduction 1
1.1 Overview 1
1.2 Conventional Control System Design 3
1.2.1 Mathematical Modeling 3
1.2.2 Performance Objectives and Design Constraints 5
1.2.3 Controller Design 7
1.2.4 Performance Evaluation 8
1.3 Fuzzy Control System Design 10
1.3.1 Modeling Issues and Performance Objectives 12
1.3.2 Fuzzy Controller Design 12
1.3.3 Performance Evaluation 13
1.3.4 Application Areas 14
1.4 What This Book Is About 14
1.4.1 What the Techniques Are Good For: An Example 15
1.4.2 Objectives of This Book 17
1.5 Summary 18
1.6 For Further Study 19
1.7 Exercises 19
CHAPTER 2 / Fuzzy Control: The Basics 23
2.1 Overview 23
2.2 Fuzzy Control: A Tutorial Introduction 24
2.2.1 Choosing Fuzzy Controller Inputs and Outputs 26
2.2.2 Putting Control Knowledge into Rule-Bases 27
2.2.3 Fuzzy Quantification of Knowledge 32
2.2.4 Matching: Determining Which Rules to Use 37
2.2.5 Inference Step: Determining Conclusions 42
2.2.6 Converting Decisions into Actions 44
2.2.7 Graphical Depiction of Fuzzy Decision Making 49
2.2.8 Visualizing the Fuzzy Controller’s Dynamical Operation 50
2.3 General Fuzzy Systems 51
2.3.1 Linguistic Variables, Values, and Rules 52
2.3.2 Fuzzy Sets, Fuzzy Logic, and the Rule-Base 55
2.3.3 Fuzzification 61
2.3.4 The Inference Mechanism 62
2.3.5 Defuzzification 65
2.3.6 Mathematical Representations of Fuzzy Systems 69
2.3.7 Takagi-Sugeno Fuzzy Systems 73
2.3.8 Fuzzy Systems Are Universal Approximators 77
2.4 Simple Design Example: The Inverted Pendulum 77
2.4.1 Tuning via Scaling Universes of Discourse 78
2.4.2 Tuning Membership Functions 83
2.4.3 The Nonlinear Surface for the Fuzzy Controller 87
2.4.4 Summary: Basic Design Guidelines 89
2.5 Simulation of Fuzzy Control Systems 91
2.5.1 Simulation of Nonlinear Systems 91
2.5.2 Fuzzy Controller Arrays and Subroutines 94
2.5.3 Fuzzy Controller Pseudocode 95
2.6 Real-Time Implementation Issues 97
2.6.1 Computation Time 97
2.6.2 Memory Requirements 98
2.7 Summary 99
2.8 For Further Study 101
2.9 Exercises 101
2.10 Design Problems 110
CHAPTER 3 / Case Studies in Design and Implementation 119
3.1 Overview 119
3.2 Design Methodology 122
3.3 Vibration Damping for a Flexible Robot 124
3.3.1 The Two-Link Flexible Robot 125
3.3.2 Uncoupled Direct Fuzzy Control 129
3.3.3 Coupled Direct Fuzzy Control 134
3.4 Balancing a Rotational Inverted Pendulum 142
3.4.1 The Rotational Inverted Pendulum 142
3.4.2 A Conventional Approach to Balancing Control 144
3.4.3 Fuzzy Control for Balancing 145
3.5 Machine Scheduling 152
3.5.1 Conventional Scheduling Policies 153
3.5.2 Fuzzy Scheduler for a Single Machine 156
3.5.3 Fuzzy Versus Conventional Schedulers 158
3.6 Fuzzy Decision-Making Systems 161
3.6.1 Infectious Disease Warning System 162
3.6.2 Failure Warning System for an Aircraft 166
3.7 Summary 168
3.8 For Further Study 169
3.9 Exercises 170
3.10 Design Problems 172
CHAPTER 4 / Nonlinear Analysis 187
4.1 Overview 187
4.2 Parameterized Fuzzy Controllers 189
4.2.1 Proportional Fuzzy Controller 190
4.2.2 Proportional-Derivative Fuzzy Controller 191
4.3 Lyapunov Stability Analysis 193
4.3.1 Mathematical Preliminaries 193
4.3.2 Lyapunov’s Direct Method 195
4.3.3 Lyapunov’s Indirect Method 196
4.3.4 Example: Inverted Pendulum 197
4.3.5 Example: The Parallel Distributed Compensator 200
4.4 Absolute Stability and the Circle Criterion 204
4.4.1 Analysis of Absolute Stability 204
4.4.2 Example: Temperature Control 208
4.5 Analysis of Steady-State Tracking Error 210
4.5.1 Theory of Tracking Error for Nonlinear Systems 211
4.5.2 Example: Hydrofoil Controller Design 213
4.6 Describing Function Analysis 214
4.6.1 Predicting the Existence and Stability of Limit Cycles 214
4.6.2 SISO Example: Underwater Vehicle Control System 218
4.6.3 MISO Example: Tape Drive Servo 219
4.7 Limitations of the Theory 220
4.8 Summary 222
4.9 For Further Study 223
4.10 Exercises 225
4.11 Design Problems 228
CHAPTER 5 / Fuzzy Identification and Estimation 233
5.1 Overview 233
5.2 Fitting Functions to Data 235
5.2.1 The Function Approximation Problem 235
5.2.2 Relation to Identification, Estimation, and Prediction 238
5.2.3 Choosing the Data Set 240
5.2.4 Incorporating Linguistic Information 241
5.2.5 Case Study: Engine Failure Data Sets 243
5.3 Least Squares Methods 248
5.3.1 Batch Least Squares 248
5.3.2 Recursive Least Squares 252
5.3.3 Tuning Fuzzy Systems 255
5.3.4 Example: Batch Least Squares Training of Fuzzy Systems 257
5.3.5 Example: Recursive Least Squares Training of Fuzzy Systems 259
5.4 Gradient Methods 260
5.4.1 Training Standard Fuzzy Systems 260
5.4.2 Implementation Issues and Example 264
5.4.3 Training Takagi-Sugeno Fuzzy Systems 266
5.4.4 Momentum Term and Step Size 269
5.4.5 Newton and Gauss-Newton Methods 270
5.5 Clustering Methods 273
5.5.1 Clustering with Optimal Output Predefuzzification 274
5.5.2 Nearest Neighborhood Clustering 279
5.6 Extracting Rules from Data 282
5.6.1 Learning from Examples (LFE) 282
5.6.2 Modified Learning from Examples (MLFE) 285
5.7 Hybrid Methods 291
5.8 Case Study: FDI for an Engine 292
5.8.1 Experimental Engine and Testing Conditions 293
5.8.2 Fuzzy Estimator Construction and Results 294
5.8.3 Failure Detection and Identification (FDI) Strategy 297
5.9 Summary 301
5.10 For Further Study 302
5.11 Exercises 303
5.12 Design Problems 311
CHAPTER 6 / Adaptive Fuzzy Control 317
6.1 Overview 317
6.2 Fuzzy Model Reference Learning Control (FMRLC) 319
6.2.1 The Fuzzy Controller 320
6.2.2 The Reference Model 324
6.2.3 The Learning Mechanism 325
6.2.4 Alternative Knowledge-Base Modifiers 329
6.2.5 Design Guidelines for the Fuzzy Inverse Model 330
6.3 FMRLC: Design and Implementation Case Studies 333
6.3.1 Cargo Ship Steering 333
6.3.2 Fault-Tolerant Aircraft Control 347
6.3.3 Vibration Damping for a Flexible Robot 357
6.4 Dynamically Focused Learning (DFL) 364
6.4.1 Magnetic Ball Suspension System: Motivation for DFL 365
6.4.2 Auto-Tuning Mechanism 377
6.4.3 Auto-Attentive Mechanism 379
6.4.4 Auto-Attentive Mechanism with Memory 384
6.5 DFL: Design and Implementation Case Studies 388
6.5.1 Rotational Inverted Pendulum 388
6.5.2 Adaptive Machine Scheduling 390
6.6 Indirect Adaptive Fuzzy Control 394
6.6.1 On-Line Identification Methods 394
6.6.2 Adaptive Control for Feedback Linearizable Systems 395
6.6.3 Adaptive Parallel Distributed Compensation 397
6.6.4 Example: Level Control in a Surge Tank 398
6.7 Summary 402
6.8 For Further Study 405
6.9 Exercises 406
6.10 Design Problems 407
CHAPTER 7 / Fuzzy Supervisory Control 413
7.1 Overview 413
7.2 Supervision of Conventional Controllers 415
7.2.1 Fuzzy Tuning of PID Controllers 415
7.2.2 Fuzzy Gain Scheduling 417
7.2.3 Fuzzy Supervision of Conventional Controllers 421
7.3 Supervision of Fuzzy Controllers 422
7.3.1 Rule-Base Supervision 422
7.3.2 Case Study: Vibration Damping for a Flexible Robot 423
7.3.3 Supervised Fuzzy Learning Control 427
7.3.4 Case Study: Fault-Tolerant Aircraft Control 429
7.4 Summary 435
7.5 For Further Study 436
7.6 Design Problems 437
CHAPTER 8 / Perspectives on Fuzzy Control 439
8.1 Overview 439
8.2 Fuzzy Versus Conventional Control 440
8.2.1 Modeling Issues and Design Methodology 440
8.2.2 Stability and Performance Analysis 442
8.2.3 Implementation and General Issues 443
8.3 Neural Networks 444
8.3.1 Multilayer Perceptrons 444
8.3.2 Radial Basis Function Neural Networks 447
8.3.3 Relationships Between Fuzzy Systems and Neural Networks 449
8.4 Genetic Algorithms 451
8.4.1 Genetic Algorithms: A Tutorial 451
8.4.2 Genetic Algorithms for Fuzzy System Design and Tuning 458
8.5 Knowledge-Based Systems 461
8.5.1 Expert Control 461
8.5.2 Planning Systems for Control 462
8.6 Intelligent and Autonomous Control 463
8.6.1 What Is “Intelligent Control”? 464
8.6.2 Architecture and Characteristics 465
8.6.3 Autonomy 467
8.6.4 Example: Intelligent Vehicle and Highway Systems 468
8.7 Summary 471
8.8 For Further Study 472
8.9 Exercises 472
BIBLIOGRAPHY 477
INDEX 495

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