Modellierung und Regelung eines piezoelektrischen Balkens

The use of smart structures in combination with modern control strategies offers new ways for the actor design. A good mathematical model and the determination of special mathematical structures are very important for the controller design. For a cantilever beam with two piezoelectric layers the equations of motion are derived by means of the Hamilton formalism. This system is a so-called Hamilton-AI-system and it possesses a special symplectic structure. The mathematical model of the investigated beam may be approximated by a transfer function of low order for the controller design. An optimal linear controller is designed and experimental results show the feasibility of the proposed approach.