Influence of the Manipulation of the Polytopic Tensor Product Model Representation on the Control Performance of LMI Based Design

Abstract

The paper studies the effect of the manipulation of the polytopic TP model representation of a given quasi Linear Parameter Varying (qLPV) state-space model on the control performance results. The investigated model in the case study consists of the extended, Stribeck friction included three degrees of-freedom version of the aero elastic wing section of the Nonlinear Aero elastic Test Apparatus (NATA) model. The investigation is carried out through the Tensor Product (TP) model transformation based Control Design Framework, which bridges the manipulation of the polytopic representation and Linear Matrix Inequality (LMI) based control design methods. Different TP model representations of the given qLPV model are derived: a TP model representation with a sum-normalized non-negative (SNNN) convex hull, a TP model representation with a close to-normal (CNO) convex hull and interpolated TP model representations. Upon these representations Linear Matrix Inequality based design methods are applied to attain the controller and observer system components. The resulting control systems are tested through numerical simulation and their performance are compared and evaluated. The paper presents results, where the interpolated representations lead to better control performance results, which indicates, that the manipulation of the polytopic TP model representation may lead to further potential optimization possibilities. Also, this shows, that in order to find the optimal solution the manipulation is a necessary and important step.