Sensorless control for hysteresis compensation of AFM scanner by modified Rayleigh model

Abstract

A novel modified Rayleigh model was developed for compensating hysteresis problem of an atomic force microscope (AFM) scanner. In high driving fields, piezoelectric actuators that integrated a scanner have severe hysteresis, which can cause serious displacement errors. Piezoelectric hysteresis is from various origins including movement of defects, grain boundary effects, and displacement of interfaces. Furthermore, because its characteristic is stochastic, it is almost impossible to predict the piezoelectric hysteresis analytically. Therefore, it was predicted phenomenologically, which means that the relationship between inputs and outputs is formulated. The typical phenomenological approach is the Rayleigh model. However, the model has the discrepancy with experiment result as the fields increase. To overcome the demerit of the Rayleigh model, a modified Rayleigh model was proposed. In the modified Rayleigh model, each coefficient should be defined differently according to the field direction due to the increase of the asymmetry in the high fields. By applying an inverse form of this modified Rayleigh model to an AFM scanner, it is proved that hysteresis can be compensated to a position error of less than 5%. This model has the merits of reducing complicated fitting procedures and saving computation time compared with the Preisach model.