Modeling and Analysis with Induction Generators, 3rd Edition

395

Appendix A: Introduction

to Fuzzy Logic

Fuzzy logic has been making a name for itself as the most successful application

of articial intelligence. It has advanced signicantly in recent years and has found

widespread applications. It has also caught the attention of the public in the past few

years. Now, people ask what it is, mathematicians study how it works, engineers

work on what it does, and marketers wonder what it can do. Engineering applications

generally use fuzzy logic for controllers in noisy, nonlinear, and time-variant sys-

tems, tuning problems, and estimation of multiple input/output relations. However,

the range of applications is amazing. Fuzzy systems can be integrated with neural

networks to extract hidden rules out of numerical data. Fuzzy reasoning can be used

to model events in politics, military planning, and appraisal processes. There are

fuzzy computers being constructed. The topic is so vast that this book can only

introduce some concepts.

The theoretical foundations of fuzzy logic were laid in 1965 when Prof. LotZadeh

published the paper “Fuzzy Sets,” in the journal Information and Control;

fuzzy set

theory was born, but no one paid much attention to it. After all, the term fuzzy had

(and still has) a sort of negative connotation in English. Before the publication of

this paper, Zadeh was already well known in the area of linear systems theory for

his contributions to the analysis of discrete systems. However, he believed that as

the complexity of a system increases, the ability to make precise and signicant

statements about its behavior diminishes. In his words, “The closer one looks at a

real-world problem, the fuzzier becomes its solution.”

Linear systems theory assumes several properties that are not actually found in

real applications. Therefore, conventional methods of control are good for simple

systems, while fuzzy systems are suitable for complex problems or in applications

that involve human descriptive or intuitive thinking. A fuzzy system can estimate

input–output functions and can be trainable for pattern recognition applications and

dynamic systems control. Unlike statistical tools and conventional (continuous or

binary) logic, it can estimate functions without a mathematical model of the system.

Therefore, fuzzy systems are model-free estimators able to learn from experience

with a linguistic description of the system’s operation.

Mamdani reported the rst application of fuzzy logic for control of a dynamic

process in a steam engine. The problem was to regulate the engine speed and boiler

steam pressure by means of the heat applied to the boiler and the throttle setting

of the engine. Since the system was nonlinear, noisy, and strongly coupled, and no

mathematical model was available, the fuzzy control was designed from the opera-

tor’s experience and performed much better than expected. Following this work,

Mamdani tried unsuccessfully to secure funding for his research from the British