Fuzzy Adaptive Control Based on MRAS for SISO Nonlinear Systems with Uncertainty

In this paper, a fuzzy adaptive control for SISO nonlinear systems is presented. The nonlinear system is modeled using Takagi-Sugeno (T-S) model. Then, a fuzzy adaptive control based on reference model (MRAS) is designed to track reference signal. The parameters of the controller are calculated on-line at each instant. For each bounded input reference signal, the states of the system follow the states of the reference model. In this paper, first a lemma called extended estimation lemma is introduced and proved. Then, to select the control law, adaptation law and to prove the overall system stability, this lemma is used. The stability proof of the adaptation algorithm with system parametric uncertainty is presented fully. Moreover, for two very popular linear systems, using the extended estimation lemma, adaptive controls are designed. The proposed controller is designed for inverse pendulum nonlinear system and the performance of the controller is verified with MATLAB software.