Adaptive Harmonic Disturbance Cancellation for LTI Systems with Heat PDE Actuator Dynamics

The focus of this paper is cancellation of unknown unmatched harmonic disturbances in a known LTI system with diffusion PDE actuator dynamics. Firstly, the disturbance is parametrized and written as a boundary of heat PDE. From there on, the problem can be treated as an adaptive controller design for an uncertain ODE-PDE couple. To cancel the disturbance and compensate the input dynamics, an infinite dimensional backstepping procedure is applied. Finally, an adaptive control algorithm is designed and stability of the closed loop system equilibrium is confirmed. The convergence of the system states to zero as time goes to infinity and the perfect estimation of the disturbance are proven. The performance of the controller is validated with a numerical simulation.