Tracking Control of a Wave Equation with Boundary Disturbance: Combining ADRC and Differential Flatness

In this paper, we study the tracking control problem of a wave equation with boundary disturbance. Applying the active disturbance rejection control (ADRC) method, the unknown disturbance is estimated by the extended state observer (ESO). The flatness-based method for trajectory planning is applied to derive the feedforward controller, which allows us to realize the tracking of suitably prescribed trajectories for the system output. Combining the disturbance estimation and the feedforward controller, a feedback controller is designed to stabilize the tracking error system. The closed-loop system of the tracing error is proved to be asymptotically stable and the tracking performance is illustrated by numerical simulation.