Output Feedback Controller Design for LTI Systems with Heat PDE Actuator Dynamics and Periodic Disturbances

This paper focuses on rejection of unknown periodic disturbances in a known LTI system with diffusion PDE actuator dynamics by using output feedback. Firstly, the disturbance is parametrized and written as a boundary of heat PDE. Then, the problem is reformulated as an adaptive controller design for an uncertain ODE-PDE couple. Thirdly, an adaptive observer is designed to estimate the ODE system states and unknown disturbance. After that, to cancel the disturbance and compensate the input dynamics, an infinite dimensional backstepping procedure is applied. Finally, an observer based adaptive control algorithm is proposed and stability of the closed loop system equilibrium is confirmed. It is proven that the system states and observer error states converge to zero exponentially. The performance of the controller is validated with a numerical simulation.