Controller Synthesis of an Uncertain Three Tank System Using Polytypic System Approach

Abstract

Many of the systems in process and aerospace industry can be modeled as a three tank system. LMI and NLMI based controller design methods have been applied to three tank system in literature. Nonlinear methods suffer from lack of ease for implementation, on the other hand, LMI based methods have to be unduly robust to cater for significant uncertainties arising from linearization around an equilibrium point. This paper presents an LMI based controller design method, which specifically uses second or higher order terms of nonlinear three tank model, thus resulting in a robust controller with no compromise on performance. A second degree error model is derived using small signal linearization method about an arbitrary operating point. A set of LMI's are formulated for each polytopic region and solved to obtain the corresponding state feedback controller gains for that particular polytopic region. The series of designed controllers drives the system states from starting point to the desired state through a series of connected polytopic regions. The controller is robust with respect to parameter variations due to the combined polytopic-LMI problem formulation. The effects of parametric variations and disturbances are accounted for in such a formulation via appropriate bounds. The performance of the designed controller is also compared with LMI based H∞ controller.