State space models of piezomechanical systems as method for coupling of finite element simulation and control design

An application area of piezoelectric sensors and actuators is active vibration control of mechanical structures. For the design of controllers for such mechatronic systems it is common practice to use reduced models of the mechanical subsystem. Often state space models of the systems concerned are applied during design of control units [1]. On the other hand finite element models are used to characterise system behavior of continua. Therefore it is at least desirable if not necessary to map detailed finite element models to state space representations during the design process of piezomechanical systems. Two methods of making the state space representation of the piezomechanical system will be presented. The first method is based on superelement matrices obtained by substructure analysis of the finite element model. A procedure for the export of the superelement matrices from the finite-element code ANSYS suggested in [2] is used. The second method of making the state space representation of the piezomechanical system uses a modal approach. To obtain a correct representation of the piezo-mechanical system both for the mechanical subsystem and the electrical one the electrical stiffness has to be considered as direct transmission matrix of the state space model. Both approaches are demonstrated and compared on an example.