Compensation Method for the Nonlinear Characteristics with Starting Error of a Piezoelectric Actuator in Open-Loop Controls Based on the DSPI Model

Nanopositioning stages with piezoelectric actuators have been widely used in fields such as precision mechanical engineering, but the nonlinear start-up accuracy problem under open-loop control has still not been solved, and more errors will accumulate, especially under open-loop control. This paper first analyzes the causes of the starting errors from both the physical properties of materials and voltages: the starting errors are affected by the material properties of piezoelectric ceramics, and the magnitude of the voltage determines the magnitude of the starting errors. Then, this paper adopts an image-only model of the data separated by a Prandtl-Ishlinskii model (DSPI) based on the classical Prandtl-Ishlinskii model (CPI), which can improve the positioning accuracy of the nanopositioning platform after separating the data based on the start-up error characteristics. This model can improve the positioning accuracy of the nanopositioning platform while solving the problem of nonlinear start-up errors under open-loop control. Finally, the DSPI inverse model is used for the feedforward compensation control of the platform, and the experimental results show that the DSPI model can solve the nonlinear start-up error problem existing under open-loop control. The DSPI model not only has higher modeling accuracy than the CPI model but also has better performance in terms of compensation results. The DSPI model improves the localization accuracy by 99.427% compared to the CPI model. When compared with another improved model, the localization accuracy is improved by 92.763%.