Modelling and control using Takagi-Sugeno fuzzy models

Fuzzy models have received particular attention in the area of nonlinear modeling, especially the Takagi-Sugeno (TS) fuzzy models, due to their capability to approximate any nonlinear behavior. The performances of a TS fuzzy model depend on its complexity (Number of fuzzy rules), on the type of membership functions and also on antecedent variables and consequent regressors. In the first part of this paper we describe an algorithm for TS fuzzy modeling. The main idea is to select antecedent variables independently of consequent regressors in order to identify a “best” TS fuzzy model. In the second part we discuss the use of TS fuzzy models to design a fuzzy predictive controller. Predictive control has been first developed to control Linear Time Invariant (LTI) plants, described by Auto Regressive Moving Average with eXternal inputs (ARIMAX) models. The extension of this control strategy in the case when the behavior of the plant is non linear and modeled by a Takagi-Sugeno fuzzy model is considered here. This kind of nonlinear model is locally linear and the GPC technique can be extended as a parallel distributed controller.