A Multi-conditional Prandtl-Ishlinskii model for nonlinearity compensation on the longitudinal-shear piezoelectric

The longitudinal-shear piezoelectric nanopositioning stage (LSPNS) is a novel type of object positioning platform. It employs multi-degree-of-freedom piezoelectric stack actuators (PSAs), with LSPNS's displacement driven by shear PSA and preload force adjusted by longitudinal PSA, rendering it highly valuable in real applications. However, during the motion of the LSPNS, the PSAs are continuously affected by various conditions such as frequency adjustment in speed regulation, preload force determined by loads, and temperature changes, which cause alteration in the dynamic nonlinear characteristics. The previous phenomenological models lack the ability to track the uncertainty of changing conditions, resulting in damage to the control accuracy of the LSPNS. In this paper, a Multi-conditional Prandtl-Ishlinskii (McPI) modeling method is proposed. It takes the advantage from material analysis to various impact factors, to build a model that combines both physics and phenomenology based on the PI model. An inverse model is then derived, and open-loop compensation for the LSPNS is ultimately achieved through feedforward control. Model fitting results demonstrate that the McPI model can accurately describe the alteration of piezoelectric nonlinear characteristics in changing conditions. Compensation results show that the average mean square error of the McPI model is decreased by 18.60% to 59.68%. Compared with other PI models, McPI model is proved to have the tracking ability to multiple conditions.