Robust Tracking of Linear Systems for Matched Uncertainty using LQR Approach

Abstract

Robust control is derived for general linear uncertain systems with scalar control. In this paper we have shown way to solve a robust control problem of a uncertain system (matched uncertainty) by transforming it into an optimal control problem which becomes Linear Quadratic Regulator problem (LQR) for linear systems and can be solved by using algebraic Riccati equation. We assume that the control objective is not only to drive the states to zero but also to track a non-zero reference signal which is to be assumed as polynomial function of time. We also emphasized on finding the largest value of uncertain parameter for which given system is on the verge of instability, which has not been mentioned in the previous work. The control is derived by using LQR method and has state negative feedback form. The performance of proposed controller is examined by simulating linear system model in MATLAB environment.