A control scheme for a class of uncertain linear plants

Abstract

An observer-based controller for a class of uncertain minimum-phase linear systems is presented. The main idea is to lump the uncertainties into a term, which is interpreted as a new uncertain state. In this way, the original system is posed in an extended state space where the dynamics of the new uncertain state can be reconstructed from measurements of the output. The design is simple. If the order of the system is n, first we assume that the output, its first n time derivatives and the uncertainties (new state) are available for feedback and design a state feedback controller in appropriate coordinates. Then we use a high-gain observer to estimate the derivatives of the output and the new uncertain state. On the contrary to traditional adaptive schemes, it results in a linear closed-loop system. Besides, a persistence of excitation condition is not necessary to assure closed-loop stability. Under signal tracking conditions, the controller yields global practical tracking, such that the tracking error can be made as small as desired by adjusting certain observer and controller parameters. The performance of the controller is evaluated by means of a simulation example.