Rejection of disturbance with nonlinear dynamics

Abstract

Linear feedback control based on internal model principle achieves asymptotic tracking for linear system with known linear exogenous signal dynamics. This paper investigates the case of rejecting exogenous chaotic signals with known nonlinear dynamics for linear systems in the discrete time domain. Feedback controllers based on the internal model principle and predictive internal model control respectively are proposed and investigated in this paper. Both control algorithms are based on inversion of the linear system. It is shown that asymptotic tracking performance is achieved when perfect plant inversion is possible and it cannot be achieved with either algorithm when inversion errors from unmodeled dynamics or plant nonminimum phase zeros exist. The closed loop stability and performance rely on the relative size of the linear system inversion errors to the exogenous signal's local growth rate.