Hysteresis compensation of piezoelectric actuators: The modified Rayleigh model

In this study, we develop a novel modified Rayleigh model for hysteresis compensation in piezoelectric actuators. Piezoelectric actuators suffer from hysteresis, in large drive fields of more than 100 V, which can result in serious displacement errors. The typical phenomenological approach is to use the Rayleigh model; however, this model gives more than 10% difference with experiments at the large electric fields of more than 1 kV/mm. Furthermore, there are no studies that apply the Rayleigh model to the compensation of precision actuators, such as stack actuators; it has only been applied in the study of the physical properties of piezoelectric materials. Therefore, we propose a modified Rayleigh model, in which each coefficient is defined differently according to whether the field is increasing or decreasing to account for asymmetry at the high fields. By applying a computer-based control from an inverse form of this modified Rayleigh model, we show that we can compensate for hysteresis to reduce the position error to less than five percent. This model has the merits of reducing complicated fitting procedures and of saving computation time compared to the Preisach model. Specifically, this model cannot only predict the hysteresis curves in all local fields using only one fitting procedure, but also make it possible to control the displacement of various piezo-based actuators without expensive sensors, based on the charge-based model.