Robust control of processes subject to saturation nonlinearities

Abstract

Motivated by current practice, a two-step design technique for saturating systems is studied. First an “optimal” (for example in the H∞ sense) linear controller is designed neglecting saturation. Then a saturation compensation scheme (anti-windup) is designed which provides graceful degradation of closed-loop performance in the face of saturation. The focus in this paper is on the second step, and obtaining general results and insights applicable to any (linear) system subject to saturation. A design technique is developed which results in effective saturation compensation for a given multivariable plant and linear compensation design. For particular controller choices the resulting saturation compensator is shown to be equivalent to proven techniques includin g anti-rest windup and internal model control (IMC). Tools are developed for robust stability and performance analysis of nonlinear systems. Well-known structured singular value robustness tests for linear systems are extended to a class of nonlinear systems. Sufficient conditions are developed which guarantee closed-loop stability for all plants in a structured uncertainty set and for all nonlinearities of a specified form. These tests result in simple conditions on the initial linear controller design which must be satisfied in order to guarantee robust stability of the saturating plant. In some instances this requires that the original linear design be detuned. A procedure for performing this detuning is outlined. A promising single-step procedure for the synthesis of optimal robust linear controllers for saturating systems is also outlined. While this approach lacks the simplicity of the two-level decomposition, it appears to have promise for situations where the impact of the saturation on the closed loop is severe.