EVALUATION OF THE ROBUSTNESS OF RULE REGULATION OF INDIRECT ADAPTIVE FUZZY CONTROLLER DESIGN

Abstract

The evaluation of the robustness (effectiveness) of rule regulation of an indirect adaptive fuzzy controller based on the Lyapunov theory is discussed. Adaptive fuzzy controller is synthesized from a collection of fuzzy IF-THEN rules. The parameters of the membership functions characterizing the linguistic terms in the fuzzy IF-THEN rules change according to two adaptive laws for the purpose of controlling a plant to track a desired trajectory. These fuzzy IF-THEN rules are generated automatically during the adaptation procedure .Two sets of fuzzy systems are used to represent the controlled system. The fuzzy controller based on the discussed adaptive laws has the ability to generate rules during real time operation. In particular, the rules are represented in analytic equation form, so that the scheme of adaptive control can be applied successfully. The stability of the indirect adaptive fuzzy controller is checked with the help of Lyapunov theory. Design approach is synthesized through the following steps. Firstly, we construct fuzzy systems, and define the fuzzy sets whose membership functions cover the state space .IF part of the membership functions of the fuzzy sets are distributed equally in the individual universe of discourse. Secondly, two adaptive laws are derived to adjust the constructed rules, which are used to approximate an optimum control tracking error I converges to zero automatically. Finally, a second order nonlinear inverted pendulum system is used to check the robustness of rule regulation of an indirect adaptive fuzzy controller.