Disturbance rejection for nonlinear systems

Tracking or rejection of unknown exogenous signals with known generating dynamics is of major concern in feedback control design. Linear feedback control based on the internal model principle achieves asymptotic performance for linear systems with linear exogenous signal dynamics. This paper presents a control design based on the internal model principle to track or reject nonlinear exogenous signal dynamics for nonlinear systems. Necessary condition to achieve asymptotic disturbance rejection based on the proposed control structure is first derived. It is shown that the necessary condition becomes sufficient for linear systems with linear disturbance dynamics. Inspired by the unique structure of the necessary condition, sufficient conditions are then proposed. Simulations of a nonlinear plant with chaotic disturbance show the effectiveness of the proposed scheme.