Error Based Periodic Output Tracking for a Wave System with Kelvin-Voigt Damping

In this paper, we are concerned with the output tracking problem for a wave system with Kelvin-Voigt damping. The control force acts on the system and the output is at one end which needs to track an unknown periodic signal. By constituting an auxiliary approximation system and infinite dimensional internal model dynamic, a novel error-based dynamic compensator is proposed to achieve output tracking. The well-posedness and stability of the closed-loop system are proved by employing the semigroup theory.