Design and Tuning of fuzzy logic control systems

(1)

Design & Tuning

of

Fuzzy Logic Control Systems

By:

SEYED SAEEDALLAH MORTAZAVI Department of Electrical Engineering

Thesis submitted in the fulfillment of the requirements of the degree of DOCTOR OF PHILOSOPHY,

To the:

INDIAN INSTITUTE OF TECHNOLOGY-DELHI

NEW DELHI — 110016, INDIA January, 1999

(2)

(3)

Certificate

This is to certify that the thesis entitled, "Design and Tuning of Fuzzy Logic Control Systems" being submitted by S. Saeed Mortazavi for the award of the degree of the Doctor of Philosophy to the Indian Institute of Technology, Delhi is a record of the bonafide research work he has carried out under our supervision. The results contained in this thesis have not been submitted to any other University or Institute for the award of a degree or diploma.

( r. Nesar Ahmad )

Associate Professor Senior Scientific Officer - I Department of Electrical Engineering

Indian Institute of Technology, Delhi New Delhi - 110 016

(4)

ACKNOWLEGEMENTS

It is my great pleasure to be able to express my appreciation to everyone who has helped me to see this work to be completed. I am indebted to my thesis supervisors, Professor (associate) R.K.P. Bhatt and Dr. Nesar Ahmad for their unending support and invaluable guidance throughout the course of this work and corresponded papers, which have been sent for publication.

I would like to express my thanks to Professor M. Gopal lab

-

incharge for "Intelligent Control and Automation" laboratory.

I would like to express my sincere thanks to my wife and my little daughter, who encouraged and accompanied me throughout of this work. My esteemed thanks to the memory of my father and to my mother whose sacrifices made me as I am today.

(Saeecilvt-(TrtaiaVi)

II

(5)

Abstract

Fuzzy logic controllers (FLCs) have shown significant advantages in many real-world applications. They have demonstrated a good capability in controlling complex systems under wide ranges of operations. FLC can be designed with minimum system modeling information. However, so far there is no standard design procedure for FLCs. Changing of operating conditions, complexity of the process to be controlled, and plenty of input/output variables make it more difficult to design and tune a fuzzy logic controller for a particular application. In first part of this work, it is shown that it is possible to tune and adapt a fuzzy logic controller by only using nonlinear scaling factors. In this regard, all membership functions and rules are kept fixed and all nonlinearities and adaptation algorithms are shifted to nonlinear scaling factors. To show the capability of this method, a set of nonlinear scaling factors are proposed. The performance of FLC with nonlinear scaling factors in closed loop with various applications is demonstrated. Further, in this work, two qualitative adaptation techniques for applications to fuzzy logic control systems are introduced (called self- tuning and auto-tuning algorithms). Self-tuning algorithm uses overall objective variables (e.g. rise time, maximum overshoot, integral absolute error, etc) for optimization and auto-tuning algorithm uses locally available state variables (e.g.

error, change in error) as objectives for optimization. Auto-tuning method is a qualitative approximation (and generalization) for nonlinear scaling factors algorithm mentioned above. Fast tracking property of auto-tuning is an interesting specification which is demonstrated in this work.

It is envisaged that controlling higher order systems with proposed types of fuzzy logic controllers is not an easy task. To handle the control of higher order systems,

III

(6)

variable structure fuzzy logic controller is proposed. Conventionally, variable structure controller (VSC) can control nonlinear system with enough robustness.

Variable structure FLC (VS-FLC) can control nonlinear complex systems by minimum system model information and with more robustness. VSC and VS-FLC in discrete time systems applications lead to instability. In this work a nonlinear mapping is proposed which along with VS-FLC can control higher order systems in discrete time applications while preserving the closed loop stability.

Morover, in real time applications we may face in complex systems including more modules (e.g. multi-model system) and/or more contexts. In this regard this thesis proposes an alternative structure for fuzzy logic controller (FLC), called multi-storey FLC. Multi-sorey FLC takes into account multiple-model of controller (or process).

Multi-storey FLC is capable of control and modeling of more complex control systems including more contexts. Multi-storey FLC can integrate experiences coming from various disciplines extracted from various sources. Multi-storey FLC is also capable of having both known models for FLC (Mamdani and Sugeno models) in its distinct stories simultaneously. This important flexibility helps in handling more real- world problems.

The heart of the fuzzy system is the approximate reasoning. So far, various methods of approximate reasoning have been proposed for inference engine of FLC. Each of the proposed algorithms may show different performance in different applications.

Even though it is desirable to have a generalized unique reasoning algorithm. but since that is not known to us, we propose multi-reasoning FLC to handle more complex systems while getting benefit from different specifications of various approximate reasoning algorithms. In more complex control systems that FLC is supposed to handle, a full set of rules may be extracted from several operators'

IV

(7)

experiences. A single approximate reasoning algorithm out of the reported algorithms may not be able to emulate reasoning schemes of all operators. However application of multi-reasoning FLC may make this emulation closer to reality. Further, this thesis proposes a new alternative implication algorithm for fuzzy logic controller.

Comparative study shows that the proposed multi-storey and multi-reasoning FLCs present improved performance with respect to classic FLC. Moreover simulation results showed that new implication method presents much improvement in application fuzzy logic to control systems (specially for around Zero operation).

(8)

To my family

VI

(9)

1 2

5

Chapter 1 : Introduction and outline of the thesis

1-1. Introduction

1-2. A brief review of FLC design and tuning 1-2.1. Fuzzy logic control systems

1-2.2. Extracting rules from knowledge and experience.

1-2.3. Tuning of rules, membership functions and scaling factors 6 1-2.4. Approximate reasoning algorithms 8 1-2.5. Universal approximation property 11

1-2.6. Stability analysis of FLC 12

1-2.7. Variable structure FLC and stability 13 1-2.8. Neural Networks in FLC application 14 1-2.9. Genetic Algorithms in FLC application 15 1-2.10. Using Fuzzy Logic in Auto-Tuning of PID controller 17 1-2.11. Multi-model control system with FLC 18 1-3. Motivation and scope of the thesis 20 1-4. Major Contributions of this thesis 22

1-5. Outline of the thesis 25

VII

(10)

Chapter 2 : FLC with Nonlinear Scaling Factors

2-1. Introduction 27

2-2. FLC with adaptive tuning of scaling factors 31 2-2.1. Motivation for nonlinear scaling factors 32 2-3. FLC with a proposed set of nonlinear scaling factors 33 2-4. Tuning of FLC with nonlinear scaling factors using genetic algorithms 37

2-4.1. Genetic Algorithms 37

2-4.2. Genetic algorithm based tuning of FLC 40 2-5. Application of FLC with nonlinear scaling factors 43 2-5-1. Application to a liquid level rig control 43 2-5.2. Application to a thermal process 47

2-5-2-1. Effect of the number of fuzzy variables on control

performance 52 2-5.3. Application to a second order system 52

2-5-4. Application to a third order system 57

2-6. Conclusions remarks 59

Chapter 3 : Self-tuning and Auto-tuning FLC

3-2. Fuzzy logic controller with qualitative adaptation of scaling factors 63

3-2.1. Auto-tuning of FLC 66

3-2.2. Self-tuning of FLC 70

3-3. A comparative study of qualitative Self-tuning and Auto-tuning FLCs. 72

VIII

(11)

3-3.1. Self-tuning FLC implementation 72 3-3.1.1 Simulation studies for generating meta rules 73 3-3.1.2 Simulation results of application self-tuning 76 3-3.2. Auto-tuning implementation 85

3-3.2.1 Simulation studies 85

3-3.3. Some further remarks on self-tuning and auto-tuning FLC 93

3-4. Conclusions 95

Chapter 4: Variable Structure FLC

4-2. Variable structure control systems 99

4-2.1. Discrete time systems 105

4-3. Variable Structure FLC 106

4-3.1. Hierarchical VS-FLC 109

4-3.2 Hierarchical VS-FLC with nonlinear scaling factors 111

4-4. Simulation results 113

4-5. Conclusion 115

Chapter 5: Multi-Storied Fuzzy Logic control systems

5-2. A proposed Alternative Structure of a FLC 121

5-2.a. Why multi-storey FLC? 121

5-3. Genetic Algorithm in tuning multi-storey FLC 127 5-4. Multi-storey FLC applications 129 5-4.a. Application to liquid level rig 129

IX

(12)

5-4.b. Application to a second order system 132 5-4.c. Application to multi-operating points of liquid level rig 137

5-5. Conclusion 139

Chapter 6 : Multi-Reasoning FLC

6-1. Introduction 143

6-2. Fuzzy control under multi-reasoning methods: A comparative study 147 6-3. A new alternative implication method 154

6-4. Concluding remarks 159

Chapter 7 : Conclusions and suggestions for further works

7-1. A summery of conclusions 161

7-2. Some future directions 167

References

₁₇₀

Appendix I: A brief introduction to fuzzy logic controller

A-1. Fuzzy Sets and fuzzy logic 190

A-2. Fuzzy systems 192

A-3. Fuzzy Logic Controller (FLC) 193

Appendix II:

FIS file for self-tuning (Created by MATLAB fuzzy toolbox)

₁₉₆