TP Model Transformation as a Way to LMI-Based Controller Design

Abstract

The main objective of this paper is to propose a numerical controller design methodology. This methodology has two steps. In the first step, tensor product (TP) model transformation is applied, which is capable of transforming a dynamic system model, given over a bounded domain, into TP model form, including polytopic or Takagi-Sugeno model forms. Then, in the second step, Lyapunov's controller design theorems are utilized in the form of linear matrix inequalities (LMIs). The main novelty of this paper is the development of the TP model transformation of the first step. It does not merely transform to TP model form, but it automatically prepares the transformed model to all the specific conditions required by the LMI design. The LMI design can, hence, be immediately executed on the result of the TP model transformation. The secondary objective of this paper is to discuss that representing a dynamic model in TP model form needs to consider the tradeoff between the modeling accuracy and computational complexity. Having a controller with low computational cost is highly desired in many cases of real implementations. The proposed TP model transformation is developed and specialized for finding a complexity minimized model according to a given modeling accuracy. Detailed control design examples are given.