Output Feedback Direct Adaptive Fuzzy Controller Based on Frequency-Domain Methods

Abstract

This paper describes a design method that guarantees the stability of an adaptive fuzzy control system. The system consists of an unstable plant with an irrational transfer function, a Takagi–Sugeno fuzzy adaptive controller, a nonlinear reference model, and an adaptation mechanism. The gradient-based adaptation mechanism changes the consequents of the controller rules in such a way that the closed-loop system behaves like the reference model. The proposed design procedure utilizes frequency-domain methods in the forms of the Nyquist and circle criteria. It is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition. This condition means that the controller function lies between two lines passing through the origin. In this method, the function of the fuzzy controller is verified during online adaptation; therefore, it stays in the allowed sector. This method is illustrated by an example of a control system containing an unstable plant with a transport delay. The main contribution of this paper is to use frequency methods combined with adaptive fuzzy control. These methods have previously been used for nonadaptive fuzzy control, but in this paper, they are used for the first time for adaptive fuzzy control.