Modeling Piezoelectric Tube Scanner With Hysteresis and Creep by Finite Element Method

Abstract

An accurate finite element (FE) model of piezoelectric tube actuator with nonlinearities is proposed in this paper. Both of the hysteresis and the creep are the first to be implemented together into the model in order that the simulation is more precise to account for the dynamic behavior of the piezoelectric tube actuator in the reality. Prandtl-Ishlinskii (PI) operators and creep operators are adopted to formulate the nonlinear constitutive equations. As a result, nonlinear ordinary differential equations can be derived through the energy approach and Hamilton’s Principle. It is observed that the simulation results exhibit nonlinearly with either step or triangular input. They, moreover, agree quite well with the experimental results. The effect on the output response due to the different dimensions of electrode is also investigated. Finally, a proportional controller is implemented to reveal the controllability of this nonlinear FE model. Simulation results also demonstrate that the nonlinear FE model can be used for controller design.