A hysteresis model based on ellipse polar coordinate and microscopic polarization theory

In this paper, the underlying anhysteretic polarization is derived based on Boltzmann statictics and Langevin model. The remnant polarization and the irreversible polarization are analyzed. A thermodynamic description of ferroelectric phenomena is proposed to address the coupling relationship between electrical field and mechanical field by considering the series expansion of the elastic Gibbs energy function. A simple linear mapping hysteresis model based on theory of microscopic polarization and ellipse polar coordinate is derived. In order to evaluate the effectiveness of the proposed model, a nano-positioning stage driven by the PZT in open-loop operation is used to test. The experimental results show that the proposed hysteresis model could precisely describe hysteresis phenomena. The model max relative error of full span range is about 0.5 %. The proposed model simplifies the identification procedure of its inverse model. It is experimentally demonstrated that the tracking precision is significantly improved.