TIME DOMAIN ROBUST CONTROL DESIGN FOR LINEAR QUADRATIC REGULATORS BY PERTURBATION BOUND ANALYSIS

Abstract

This paper addresses the aspect of designing robust controllers for Linear Quadratic (LQ) Regulators in time domain. Upper bounds, available in the literature, on the linear perturbation of an asymptotically stable optimal linear regulator for robust stability and robust regulation are unified into a single framework, both for ‘structured’ and ‘unstructured’ perturbations. Introducing a quantitative measure called ‘Performance (Regulation) Robustness Index’, a design algorithm in the standard optimal linear regulator format is presented by which one can achieve a trade off between nominal performance and regulation robustness. The proposed design using this ‘Perturbation Bound Analysis’ is illustrated with the help of a simple example and results are discussed. The extensions of this methodology to dynamic compensator design and Linear Quadratic Gaussian (LQG) regulators are explored.