Rejection of sinusoidal disturbances for known LTI systems in the presence of output delay

Abstract

This paper focuses on estimation and cancellation of unknown sinusoidal disturbances in a known LTI system with the presence of a known output delay. Parametrizing the disturbance and representing the delay as a transport PDE, the problem is converted to an adaptive control problem for ODE–PDE cascade. An existing state observer is used to estimate the ODE system states. The exponential stability of the equilibrium of the closed-loop and error system is proved. The perfect estimation of the disturbance and state is shown. Moreover, the convergence of the state to zero as t→∞ is achieved in the closed loop system. The effectiveness of the controller is demonstrated in a numerical simulation.