An asymmetric PI hysteresis model for piezoceramics in nanoscale AFM imaging

A modified Prandtl-Ishlinskii (PI) model, referred to as an asymmetric PI model, is implemented to reduce the displacement error between the model and the actual trajectory of a piezoceramic actuator used for AFM-based nanoscale imaging. The fact that the standard PI model is symmetric, while the actual hysteresis loop of a piezoceramic actuator is asymmetric, assures scanning errors if the standard PI operator is used. In order to improve the accuracy of the model, instead of using the same slope values in the entire PI model, different slope values to describe the forward loop (voltage increase) and the backward loop (voltage decrease) is proposed. The accuracy of the asymmetric PI model is validated on a custom-built AFM by comparing the experimental results derived from it with the results for the standard PI model.