Model-Reference Fuzzy Adaptive Control as a Framework for Nonlinear System Control

Abstract

The paper presents a general methodology of adaptive control based on fuzzy model to deal with unknown plants. The problem of parameter estimation is solved using a direct approach, i.e. the controller parameters are adapted without explicitly estimating plant parameters. Thus, very simple adaptive and control laws are obtained using Lyapunov stability criterion. The generality of the approach is substantiated by Stone-Weierstrass theorem, which indicates that any continuous function can be approximated by fuzzy basis function expansion. In the sense of adaptive control, this implies the adaptive law with fuzzified adaptive control parameters. The proposed control algorithm may be viewed as an extension of classical adaptive control for linear plants, but compared to the latter it provides higher adaptation ability and consequently better performance if the plant is nonlinear. The global stability of the control system is assured and the tracking error converges to the residual set that depends on fuzzification properties. The main advantage of the approach is simplicity that suits control engineers since wide range of industrial processes can be controlled by the proposed method. In the paper, the control of heat exchanger is performed.