Compensation of Simultaneous Input/Output Delay and Unknown Sinusoidal Disturbances for Known LTI Systems

This paper focuses on estimation and cancellation of unknown sinusoidal disturbances in a known LTI system with the presence of simultaneous known input-output delay. Parametrizing the disturbance and representing the delays 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 $t\rightarrow\infty$ is achieved in the closed loop system. The effectiveness of the controller is demonstrated in a numerical simulation.