Polytopic Decomposition of the Linear Parameter-varying Model of the Parallel-type Double inverted Pendulum

Most of the formal controller synthesis approaches require conditions like controllability, observability of the systems, however it is still difficult to verify these properties in general. In case of polytopic models these conditions and the feasibility of the linear matrix inequalities (LMI) based design strongly depends on the weighting of the LTI vertex components of the polytopic model. With tensor product (TP) model transformation it is possible to decompose linear parameter-varying (LPV) models into polytopic forms in various ways and also provides the appropriate weighting functions. The objective of this paper is to use this decomposition on the the parallel-type double inverted pendulum control problem.

I. Introduction

The Tensor Product TP model transformation is a recently proposed automatically executable numerical method. It was originally developed for controller design involving linear parameter varying model representation and linear matrix inequality based control design. It is capable of numerically reconstructing the HOSVD based canonical and different convex polytopic forms of LPV dynamic models, whereupon LMI based design is immediately be executable [1]–[5]. It is important to emphasize that in many cases, the analytical derivation of these polytopic models can be really troublesome, time consuming or even impossible even.