Output feedback control of a class of nonlinear systems

Abstract

The problems of observation and control of nonlinear systems have received a particular attention throughout the last four decades. Considerable efforts were dedicated to the analysis of the structural properties to understand better the concepts of controllability and of observability of nonlinear systems. Several control and observer design methods were developed thanks to the available techniques, namely feedback linearisation, flatness, high gain, variable structure, sliding modes and backstepping. The main difference between these contributions consist in the design model, and and henceforth the considered class of systems, and the nature of stability and performance results. A particular attention has been devoted to the design of state feedback control laws incorporating an observer satisfying the the separation principle requirements as in the case of linear systems. The motivation of this talk consists in providing an output feedback controller for a class of nonlinear controllable and uniformly observable systems. The output feedback controller is obtained by simply combining an appropriate high gain state feedback control with a standard high gain observer. The high gain concept is particulary appropriate to take off the separation principle challenge inherent for nonlinear systems. The state feedback control design was particularly suggested from the the high gain observer design bearing in mind the control and observation duality. Of particular interest, the controller gain involves a well defined design function which provides a unified framework for the high gain control design, namely several versions of sliding mode controllers are obtained by considering particular expressions of the design function. Furthermore, it is shown that a filtered integral action can be simply incorporated into the control design to carry out a robust compensation of step like disturbances while reducing appropriately the noise control system sensitivity. The effectiveness of the proposed output feedback control method is emphasized throughout simulation results involving useful process control problems, namely chemical rector temperature tracking and induction motor sensorless control.