Tracking control design for a wave equation with dynamic boundary conditions modeling a piezoelectric stack actuator

This paper is concerned with the design of an asymptotically stabilizing tracking controller for an undamped wave equation modeling a piezoelectric stack actuator. For this, flatness‐based methods for trajectory planning and feedforward control are combined with dynamic feedback control involving a Luenberger‐type observer within the two degrees‐of‐freedom control concept. The asymptotic stability of the closed‐loop system is verified using Lyapunov's stability theory and LaSalle's invariance principle. Thereby, a separation theorem is introduced for bounded perturbations of infinitesimal generators of asymptotically stable C₀‐semigroups. Finally, the tracking performance is illustrated in simulation scenarios. Copyright © 2010 John Wiley & Sons, Ltd.