Infinite-dimensional decoupling control of the tip position and the tip angle of a composite piezoelectric beam with tip mass

This contribution is devoted to the infinite-dimensional control of a multi-layered piezoelectric cantilever with a tip mass. Thereby, the design of the layer structure, in particular of the piezoelectric actuator and sensor layers, is considered as a part of the controller design. The control objective is to provide two independently controllable degrees-of-freedom for the tip mass in form of the tip position and the tip angle. The control concept being proposed consists of an open-loop flatness-based tracking controller and a linear dynamic feedback controller in order to asymptotically stabilize the closed-loop error system. A rigorous stability proof based on the C 0 -semigroup theory and on LaSalle's invariance principle for infinite-dimensional systems will be given. Finally, simulation results demonstrate the potential of this smart actuator.