STABILITY ANALYSIS OF FUZZY CONTROL SYSTEMS USING DESCRIBING FUNCTION

Abstract

Fuzzy logic as a part of new concept of soft computing has been successfully applied to various fields, varying from controlling operation in servomechanism to highly demanding highly reliable operation such as missile control and nuclear reactor control. Fuzzy logic basically performs the mapping process which maps any variable from input space to the output space. This process embodies high level of complexity consequently the dynamical behavior of systems consisting fuzzy logic control may be much richer and complex than that of linear systems. In control systems, the problem at hand is to stabilize the system at the operating point. An area that is receiving an increasing amount of attention is in the area of stability analysis offuzzy control systems. The control systems community is paying increasing attention to the complexity and richness of behavior that fuzzy control systems can display. It is important to perform mathematical analysis offuzzy control systems prior to its implementation, to give insight to the expert, on how to modify the fizzy controller to guarantee that stable behavior and performance specifications are achieved. The present dissertation work is a detailed study of stability analysis offuzzy control systems with describing function analysis, commonly used for nonlinear control. The great practical value of this method lies in its simplicity and clarity, due mainly to its•graphical nature. The work provides an introduction to the use of the describing function technique for the prediction of the existence of limit cycles, their frequency, amplitude, and nature. The study is supported with two examples of Fuzzy PD and Fuzzy P control. Further the describing function method is extended for the gain-phase margin analysis offuzzy control systems. The various simulations during the course of study are performed using MA TLAB 6.5 release 13 and Simulink 5.0 release 13 software packages.