Nazmul Siddique Intelligent Control A Hybrid Approach Based on Fuzzy Logic, Neural Networks and Genetic Algorithms Foreword by Bernard Widrow 4^ Springer
Contents 1 Introduction 1 1.1 Intelligent Control 1 1.2 Intelligent Control Architecture 4 1.3 Approaches to Intelligent Control 5 1.4 Experimental Rig of Flexible Arm 6 1.5 Overview of the Book 7 References 8 2 Dynamical Systems 11 2.1 Introduction 11 2.2 Dynamics of Robot Manipulator 12 2.3 Dynamics of Flexible-Arm 13 2.3.1 Strength and Stiffness 14 2.3.2 Safety Factor 16 2.3.3 Experimental Flexible Arm 17 2.3.4 Printed Armature Motor 18 2.3.5 Motor Drive Amplifier 20 2.3.6 Accelerometer 21 2.3.7 Computer Interfacing 22 2.3.8 Operating Characteristics 22 2.4 Previous Research and Developments 23 2.5 Dynamic Equations of Flexible Robotic Ann 26 2.5.1 Development of the Simulation Algorithm 28 2.5.2 Hub Displacement 29 2.5.3 End-Point Displacement 30 2.5.4 Matrix Formulation 31 2.5.5 State-Space Formulation 32 2.6 Some Simulation Results 33 2.6.1 Bang-Bang Signal 34 2.7 Summary 36 References 36 xiii
x v Contents 3 Control Systems 39 3.1 Introduction 39 3.2 Control Systems 41 3.3 Control of Flexible Arm 44 3.4 Open-Loop Control 47 3.5 Closed-Loop Control 47 3.5.1 Joint Based Collocated Controller 49 3.5.2 Hybrid Collocated and Non-Collocated Controller 50... 3.6 Alternative Control Approaches 51 3.6.1 Intelligent Control Approaches 52 3.7 Summary 53 References 53 4 Mathematics of Fuzzy Control 57 4.1 Fuzzy Logic 57 4.2 Fuzzy Sets 57 4.3 Membership Functions 58 4.3.1 Piecewise Linear MF 59 4.3.2 Nonlinear Smooth MF 60 4.3.3 Sigmoidal MF 61 4.3.4 Polynomial or Spline-Based Functions 63 4.3.5 Irregular Shaped MF 65 4.4 Linguistic Variables 67 4.5 Features of Linguistic Variables 68 4.6 Linguistic Hedges 70 4.7 Fuzzy If-then Rules 72 4.7.1 Fuzzy Proposition 72 4.7.2 Methods for Construction of Rule-Base 73 4.7.3 Properties of Fuzzy Rules 76 4.8 Fuzzification 77 4.9 Inference Mechanism 78 4.9.1 Mamdani Fuzzy Inference 79 4.9.2 Sugeno Fuzzy Inference 80 4.9.3 Tsukamoto Fuzzy Inference 81 4.10 Defuzzification 82 4.10.1 Defuzzification Methods 82 4.10.2 Properties of Defuzzification 88 4.10.3 Analysis of Defuzzification Methods 89 4.11 Summary 90 References 90 5 Fuzzy Control 95 5.1 Introduction 95 5.1.1 Fuzzification for Control 96
Contents xv 5.1.2 Inference Mechanism for Control 97 5.1.3 Rule-Base for Control 98 5.1.4 Defuzzification for Control 100 5.2 Theoretical Analysis of Fuzzy Controllers 101 5.2.1 Consideration of Process Variables 102 5.2.2 Types of Fuzzy Controllers 104 5.3 Fuzzy Controller for Flexible Arm 108 Ill 115. 5.3.1 Input-Output Selection 110 5.4 PD-Like Fuzzy Logic Controller Ill 5.4.1 PD-Like Fuzzy Controller with Error and Change of Error 5.4.2 PD-Like Fuzzy Controller with Error and. Velocity. 5.5 Pi-Like Fuzzy Controller 118 5.6 Integral Windup Action 122 5.7 PID-Like Fuzzy Controller 123 5.8 PD-PI-Type-like Fuzzy Controller 125 5.9 Some Experimental Results on PD-PI FLC 129 5.10 Choice of Scaling Factors 131 5.11 Summary 132 References 133 6 Evolutionary-Fuzzy Control 137 6.1 Introduction 137 6.2 Overview of Evolutionary Algorithms 142 6.2.1 Evolutionary Programming 143 6.2.2 Evolution Strategies 143 6.2.3 Genetic Programming 144 6.2.4 Differential Evolution 144 6.2.5 Cultural Algorithm 145 6.2.6 Genetic Algorithm 145 6.3 Evolutionary Fuzzy Control 147 6.4 Merging MFs and Rule-Bases of PD-PI FLC 150 6.5 Optimising FLC Parameters Using GA 155 6.5.1 Encoding 6.5.2 Chromosome Representation for MFs 157 6.5.3 Chromosome Representation Scheme 157 for Rule-Base 159 6.5.4 Objective Function 159 6.5.5 Dynamic Crossover 161 6.5.6 Dynamic Mutation 162 6.5.7 Selection 165 6.5.8 Initialisation 166 6.5.9 Evaluation 166
xvi Contents 6.6 Some Experimental Results 167 6.7 Summary 173 References 173... 7 Neuro-Fuzzy Control 179 7.1 Introduction 179 7.2 Neural Networks and Architectures 180 7.3 Combinations of Neural Networks and Fuzzy Controllers 183 7.3.1 NN for Correcting FLC 185 7.3.2 NN for Learning Rules 185 7.3.3 NN for Determining MFs 186 7.3.4 NN for Learning/Tuning Scaling Parameters 188 7.4 Scaling Parameters of PD-PI Fuzzy Controller 189 7.5 Reducing the Number of Scaling Parameters 191 7.6 Neural Network for Tuning Scaling Factors 192 7.6.1 Backpropagation Learning with LinearActivation Function 193 7.6.2 Learning with Non-Linear Activation Function 196 7.7 Multi-Resolution Learning 198 7.7.1 Adaptive Neural Activation Functions 200 7.8 Some Experimental Results 202 7.9 Summary 212 References 213 8 Evolutionary-Neuro-Fuzzy Control 217 8.1 Introduction 217 8.2 Integration of Fuzzy Systems, Neural Networks and Evolutionary Algorithms 219 8.3 EA-NN Cooperative Combination 226 8.3.1 EA for Weight Learning 226 8.3.2 EA for Weights and Activation Functions Learning 229 8.4 Optimal Sigmoid Function Shape Learning 232 8.5 Evolutionary-Neuro-Fuzzy PD-PI-like Controller 233 8.5.1 GA-Based Neuro-Fuzzy Controller 234 8.6 Some Experimental Results 236 8.7 Summary 240 References 240 9 Stability Analysis of Intelligent Controllers 243 9.1 Introduction 243 9.2 Mathematical Preliminaries 244 9.3 Qualitative Stability Analysis of Fuzzy Controllers 252
Contents xvii 9.4 Passivity Approach to Stability Analysis of Fuzzy Controllers 258 9.5 Stability Analysis of PD-PI-like Fuzzy Controller 260 9.6 Summary References 264 262 10 Future Work 269 10.1 Epilogue 269 10.2 Future Research Directions 270 10.3 Adaptive Neural Network Control 271 10.3.1 Adaptive Neuro-Fuzzy Controller 271 10.3.2 B-Spline Neural Network 274 10.3.3 CMAC Network 274 10.3.4 Binary Neural Network-Based Fuzzy Controller 276 10.4 Summary 279 References 279 Index 281