A nonlinear finite element model of a piezoelectric tube actuator with hysteresis andcreep

Abstract

Piezoelectric tube actuators are commonly used for nanopositioning in atomic forcemicroscopes (AFMs). However, piezoelectric tube actuators exhibit hysteresis and creepwhich significantly limit the accuracy of nanopositioning. A finite element model of apiezoelectric tube actuator with hysteresis and creep is important for control purposes, butso far one has not been developed. The purpose of this paper is to present a nonlinear finiteelement (FE) model with hysteresis and creep for design purposes. Prandtl–Ishlinskii (PI)hysteresis operators and creep operators are adopted into constitutive equations.The nonlinear FE model is formulated using energy approach and Hamilton’sprinciple. The parameters of the PI hysteresis operators and the creep operatorsare identified by comparing the simulation results and experimental results ofother researchers. The working operation of the piezoelectric tube actuator issimulated by the reduced order FE model, and the displacement error due tohysteresis, creep and coupling effect is investigated. An output feedback controller isimplemented into the reduced order FE model to show that this model is controllable.