ROBUST OPTIMAL STABILIZATION OF LINEAR SYSTEMS WITH PARAMETRIC VARIATIONS

Abstract

This paper proposes a novel controller for guaranteeing robust performance in SISO linear systems affected by parametric variations. Synthesis of the proposed variable-gain controller is carried out in Linear Quadratic framework through a two-stage procedure. This procedure firstly designs a linear quadratic regulator for nominal values of parametric variations and secondly determines the variable gains using an automated formulation. These variable gains are found out to be functions of constant gains of linear quadratic regulator and instantaneous values of parametric variations. The proposed formulation also makes it possible to scale-up the controller for an infinite-dimensional parametrically varying linear system. Since the controller is obtainable only for linear systems with scalar control input, a coordinate transformation is proposed to convert linear systems with vector control inputs into systems with scalar control inputs. Furthermore, it is shown that the proposed control law can be modified to have a switching capability so as to meet different performance indexes during operation. Such a capability can be used to determine boundaries of safe operation with respect to parametric variations. A fourth-order linearized model of an inverted pendulum on a cart system is used for simulations to show the efficacy of the proposition.