A Lumped Parameter Electromechanical Model for Describing the Nonlinear Behavior of Piezoelectric Actuators

A lumped-parameter model of a piezoelectric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and in particular for control applications requiring accurate position tracking performance. In addition to describing the input-output dynamic behavior, the proposed model explains aspects of nonintuitive behavioral phenomena evinced by piezoelectric actuators, such as the input-output rate-independent hysteresis and the change in mechanical stiffness that results from altering electrical load. Bond graph terminology is incorporated to facilitate the energy-based formulation of the actuator model. The authors propose a new bond graph element, the generalized Maxwell resistive capacitor, as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data.