Quasi-Rayleigh model for modeling hysteresis of piezoelectric actuators

Piezoelectric actuators (PEAs) have been widely used in nano-positioning applications for their high resolution of displacement. However, hysteresis, which is an inherent property of ferroelectric PEAs has been shown to significantly degrade the system performance and even system stability. In this paper, a quasi-Rayleigh model is proposed to describe the hysteresis behavior of PEAs and piezo-based systems. The microstructure of the PEAs is analyzed and the Rayleigh model is transformed into the displacement-voltage form. The Fourier series of Rayleigh model is derived and analyzed; The voltage dependence and the rate dependence of PEAs are tested and analyzed. The parameters of rate-dependent Rayleigh model are obtained and verified; To overcome the drawback of symmetric property of classical Rayleigh model, a phenomenological method is proposed. The method is based on two modified Rayleigh parameters and their corresponding coefficients, which are used to describe the ascending and descending curves of hysteresis trajectory. The experimental results demonstrate the effectiveness of the quasi-Rayleigh model.