Making of state space models of piezo-mechanical systems with exact impedance mapping and strain output signals

The paper presents two methods to develop state space models of piezo-mechanical systems based on finite element discretisation. Both methods deliver state space representations, which reproduce correct frequency response functions of the full finite element model for the mechanical and the electrical DOF of the system as well as the coupling of both. The electrical stiffness matrix is an essential part of the direct transmission matrix for both methods. The usage of it is necessary for the correct reproduction of electrical impedance. One of the presented methods uses superelement matrices of the finite element model. The other one is based on a modal description of the piezomechanical system. For both approaches it is possible to incorporate strain parameters as output signals. The model approaches are demonstrated on an actuator-sensor-unit for uniaxial vibration reduction of machine tools.