Fuzzy Controllers Handbook (eBook)

Cover 1
Contents 5
Foreword 9
Preface 11
Acknowledgements 13
Introduction 15
PART I: HOW DOES IT WORK? OR THE THEORY OF FUZZY CONTROL 22
1. Fuzzy sets, logic and control 24
Why do we need this new theory, what are the advantages of fuzzy control? 24
Where does fuzzy logic come from? 26
What are the main areas of fuzzy logic applications? 30
2. Basic mathematical concepts of fuzzy sets 40
Fuzzy sets versus crisp sets 40
Operations on fuzzy sets 51
Extension principle and fuzzy algebra 55
Extension principle 55
Fuzzy numbers 58
Arithmetic operations with intervals of confidence 59
Arithmetic operations with fuzzy numbers 62
Linguistic variables and hedges 65
Fuzzy relations 72
3. The structure and operation of a fuzzy controller 80
The reasons to apply fuzzy controllers 80
Fuzzy rules processing 82
Mamdani-type fuzzy processing 82
Linguistic variables 84
Fuzzy rules firing 86
Calculating the applicability degree 88
Clipping and scaling a fuzzy output 89
Sugeno-type fuzzy processing 91
Fuzzy controller operation 94
Structure of a simple open-loop fuzzy controller 95
Structure of a feedback PID-like fuzzy controller 99
Fuzzy controllers as a part of a feedback system 99
PD-like fuzzy controller 100
Rules table notation 102
PI-like fuzzy controller 104
PID-like fuzzy controller 107
Combination of fuzzy and conventional PID controllers 111
Stability and performance problems for a fuzzy control system 114
Stability and performance evaluation by observing the response 114
Stability and performance indicators 117
Stability evaluation by observing the trajectory 119
Hierarchical fuzzy controllers 120
PART II: HOW TO MAKE IT WORK OR DESIGN AND IMPLEMENTATION OF FUZZY CONTROLLERS 126
4. Fuzzy controller parameter choice 128
Practical examples 128
Fuzzy autopilot for a small marine vessel 128
Smart heater control 133
Active noise control 138
Iterative nature of a fuzzy controller design process 142
Scaling factor choice 145
What is a scaling factor? 145
Where should the tuning start? 147
Application example 150
Membership function choice 152
Distributing membership functions on the universe of discourse 152
An evaluation of the membership function width 153
Application example 156
Fuzzy rule formulation 157
Where do rules come from? 157
How do we get rules? 159
How do we check if the rules are OK? 160
Application examples 162
Choice of the defuzzification procedure 168
Centre-of-area/gravity 168
Centre-of-largest-area 169
First-of-maxima/last-of-maxima 170
Middle-of-maxima 171
Mean-of-maxima 171
Height 172
Compare different defuzzification procedures 172
5. Fuzzy controller parameter adjustment 174
Self-organising, adaptive and learning fuzzy controllers: the main principles and methods 174
What do we need adjustments for? 174
Self-organising fuzzy controllers 175
Performance/robustness problem and solutions 175
Adaptive fuzzy controllers 177
Features of different controller types 179
Learning fuzzy controllers 180
Tuning of the fuzzy controller scaling factors 181
On-line and off-line tuning 181
Off-line tuning of the output scaling factors 181
On-line tuning of the input and output scaling factors 182
Application example 184
Artificial neural networks and neuro-fuzzy controllers 187
What is a neural network? 187
ANN structure 188
ANN types 192
ANN application in fuzzy controller design 195
ANFIS architecture 196
Adaptive neuro-fuzzy controller 197
Application examples 198
Adjustment procedures with genetic/evolutionary algorithms 201
How does it work? 201
GA and EA application in fuzzy controller design 203
Application example 205
6. Fuzzy system design software tools 208
Fuzzy technology products classification 208
Main features of the fuzzy software tools 211
Realisation examples 212
7. Fuzzy controller implementation 222
How do we implement a fuzzy controller? 222
Implementation on a digital general purpose processor 223
Implementation on a digital specialised processor 226
Specialised processor development system 230
Implementation on analog devices 232
Integration of fuzzy and conventional control hardware 235
PART III: WHAT ELSE CAN I USE? OR SUPPLEMENTARY INFORMATION FOR TEACHING AND LEARNING 238
8. A brief manual to fuzzy controller design 240
When to apply fuzzy controllers 240
When not to apply fuzzy controllers 240
Fuzzy controller operation 241
Which fuzzy controller type to choose 244
Fuzzy controller structure and parameter choice 244
How to find membership functions 246
How to find rules 247
How to implement a fuzzy controller 247
How to test a fuzzy controller 248
How to fix a fuzzy controller 249
How to choose a design package 250
9. Problems and assignment topics 260
10. Design projects 274
Glossary 288
Bibliography 294
Index 304