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Contents
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Foreword ix
Preface xi
Acknowledgements xiii
Introduction xv
Part I How Does it Work? or The Theory of
Fuzzy Control 1
1 Fuzzy sets, logic and control 3
1.1 Why do we need this new theory, what
are the advantages of fuzzy control? 3
1.2 Where does fuzzy logic come from? 5
1.3 What are the main areas of fuzzy
logic applications? 9
2 Basic mathematical concepts of fuzzy sets 19
2.1 Fuzzy sets versus crisp sets 19
2.2 Operations on fuzzy sets 30
2.3 Extension principle and fuzzy algebra 34
2.3.1 Extension principle 34
2.3.2 Fuzzy numbers 37
2.3.3 Arithmetic operations with
intervals of confidence 38
2.3.4 Arithmetic operations with
fuzzy numbers 41
2.4 Linguistic variables and hedges 44
2.5 Fuzzy relations 51
3 The structure and operation of a fuzzy controller 59
3.1 The reasons to apply fuzzy controllers 59
3.2 Fuzzy rules processing 61
3.2.1 Mamdani-type fuzzy processing 61
3.2.2 Linguistic variables 63
3.2.3 Fuzzy rules firing 65
3.2.4 Calculating the applicability degree 67
3.2.5 Clipping and scaling a fuzzy output 68
3.2.6 Sugeno-type fuzzy processing 70
3.3 Fuzzy controllers operation 73
3.4 Structure of a simple open-loop fuzzy controller 74
3.5 Structure of a feedback PID-like fuzzy controller 78
3.5.1 Fuzzy controllers as a part of a feedback
system 78
3.5.2 PD-like fuzzy controller 79
3.5.3 Rules table notation 81
3.5.4 PI-like fuzzy controller 83
3.5.5 PID-like fuzzy controller 86
3.5.6 Combination of fuzzy and conventional
PID controllers 90
3.6 Stability and performance problems for a fuzzy
control system 93
3.6.1 Stability and performance evaluation
by observing the response 93
3.6.2 Stability and performance indicators 96
3.6.3 Stability evaluation by observing the
trajectory 98
3.6.4 Hierarchical fuzzy controllers 99
Part II How to Make it Work or The Design
and Implementation of Fuzzy Controllers 105
4 Fuzzy controller parameter choice 107
4.1 Practical examples 107
4.1.1 Fuzzy autopilot for a small marine vessel 107
4.1.2 Smart heater control 112
4.1.3 Active noise control 117
4.2 Iterative nature of a fuzzy controller design process 121
4.3 Scaling factor choice 124
4.3.1 What is a scaling factor? 124
4.3.2 Where should the tuning start? 126
4.3.3 Application example 129
4.4 Membership function choice 131
4.4.1 Distributing membership functions
on the universe of discourse? 131
4.4.2 An evaluation of the membership
function width 132
4.4.3 Application example 135
4.5 Fuzzy rule formulation 136
4.5.1 Where do rules come from? 136
4.5.2 How do we get rules? 138
4.5.3 How do we check if the rules are OK? 139
4.5.4 Application examples 141
4.6. Choice of the defuzzification procedure 147
4.6.1 Centre-of area/gravity 147
4.6.2 Centre-of-largest-area 148
4.6.3 First-of-maxima/last-of-maxima 149
4.6.4 Middle-of-maxima 150
4.6.5 Mean-of-maxima 150
4.6.6 Height 151
4.6.7 Compare different defuzzification
procedures 151
5 Fuzzy controller parameter adjustment 153
5.1 Self-organising, adaptive, and learning fuzzy
controllers: main principles and methods 153
5.1.1 What do we need adjustments for? 153
5.1.2 Self-organising fuzzy controllers 154
5.1.3 Performance/robustness problem
and solutions 154
5.1.4 Adaptive fuzzy controllers 156
5.1.5 Features of different controller types 158
5.1.6 Learning fuzzy controllers 159
5.2 Tuning of the fuzzy controller scaling factors 160
5.2.1 On-line and off-line tuning 160
5.2.2 Off-line tuning of the output
scaling factors 160
5.2.3 On-line tuning of the input and output
scaling factors 161
5.2.4 Application example 163
5.3 Artificial neural networks and
neuro-fuzzy controllers 166
5.3.1 What is a neural network? 166
5.3.2 ANN structure 167
5.3.3 ANN types 171
5.3.4 ANN application in fuzzy controller design 174
5.3.5 ANFIS architecture 175
5.3.6 Adaptive neuro-fuzzy controller 176
5.3.7 Application examples 177
5.4 Adjustment procedures with genetic/evolutionary
algorithms 180
5.4.1 How does it work? 180
5.4.2 GA and EA application in fuzzy
controller design 182
5.4.3 Application example 184
6 Fuzzy system design software tools 187
6.1 Fuzzy technology products classification 187
6.2 Main features of the fuzzy software tools 190
6.3 Realisation examples 191
7 Fuzzy controller implementation 201
7.1 How do we implement a fuzzy controller? 201
7.2 Implementation of a digital general purpose
processor 202
7.3 Implementation of a digital specialised
processor 205
7.4 Specialised processor development system 209
7.5 Implementation on analog devices 211
7.6 Integration of fuzzy and conventional
control hardware 214
Part III What Else Can I Use? or Supplementary
Information 219
8 A brief manual to fuzzy controller design 219
8.1 When to apply fuzzy controllers 219
8.2. When not to apply fuzzy controllers 219
8.3 Fuzzy controller operation 220
8.4 Which fuzzy controller type to choose? 223
8.5 Fuzzy controller structure and
parameter choice 223
8.6 How to find membership functions 225
8.7 How to find rules? 226
8.8 How to implement a fuzzy controller 226
8.9 How to test a fuzzy controller 227
8.10 How to fix a fuzzy controller 228
8.11 How to choose a design package 229
9 Problems and assignment topics 239
10 Design projects 253
11 Glossary 267
12 Bibliography 273
List of examples 283
Index 285

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