LMI Based design approach for the Stabilization and Tracking of a 3-DOF Remote Controlled Helicopter, Modeled in TP form *

摘要

The Tensor Product (TP) transformation is a technique for modifying Linear Parameter Varying (LPV) state-space models into parameter varying convex combination of Linear Time Invariant (LTI) systems. The method is computationally fast and Linear Matrix Inequality (LMI) - based control design framework can immediately be applied to the resulting models to give controllers with guaranteed tractable performance. The main focus of this paper is to study the effectiveness of the TP modeling technique i.e. how it can be readily executed without many analytical derivations. The transformation is based on Higher Order Singular Value Decomposition (HOSVD) to transform an N-dimensional polytope to 2-D polytope and to obtain dynamics of the system in terms of weighting functions and then different convexities are incorporated to the TP form to analyze the characteristics of the system. To study the effectiveness of the technique, a benchmark system the Three Degree of Freedom (3DOF) remote controlled (RC) helicopter, is selected and then the analysis is done on this system. The system is transformed to TP form by retaining the dominant singular values and the controller is designed to stabilize the system. Then to validate the control design, simulations results of the resulting closed-loop system is presented. Apart from the stabilization analysis which was already made, an additional tracking analysis is done in this paper.