Dual Control Design: TS fuzzy model transformation based approach

The paper would like introduce the key steps of the Dual Control Design that is based on the fact that if the controller and the observer are derived from different TS fuzzy models of the given model the resulting control solution yield a better control performance. The motivation is based on the fact that finding the best controller and observer requires different features of the TS fuzzy model.

I. Introduction

The TS (Takagi Sugeno) fuzzy model transformation also termed as TP (Tensor Product) model transformation is a very effective tool to variate the antecedent and conseuqent fuzzy sets of a given TS fuzzy model. Hence it is capable of derive alternative TS fuzzy models with different antecedents and consequents. The controller and observer design need different features of the TS fuzzy model. A rule of thumb is demonstrated in [1] that the effectiveness of the controller design is increasing when we are tightening the convex hull defined by the consequent vertices of the TS fuzzy model. In contrast the effectiveness of the resulting observer increase when the TS fuzzy model is based on a more loose convex hull where upon the design is executed. Therefore it is reasonable to derive two different TS fuzzy model alternatives to derive controller and observer. As a matter of fact finally a stability analysis is needed to check if stability of the whole systems is guaranteed. The paper suggests a control design framework termed as Dual Control Design.