Hysteresis Characteristics and MPI Compensation of Two-Dimensional Piezoelectric Positioning Stage

Abstract

Piezoelectric positioning stage is the core component of precision positioning system and advanced instrument. Its hysteresis characteristics, especially rate-dependent characteristics, are the main factors affecting the positioning or control accuracy. The multi-slope Prandtl–Ishlinskii (MPI) based hysteresis modeling and compensation experiments of two-dimensional piezoelectric positioning stage are discussed. The impact of the driving voltage amplitude and frequency on the hysteresis characteristics of uniaxial piezoelectric actuator in the piezoelectric positioning stage are studied, especially the influence of variable-frequency voltages on the output displacement of a piezoelectric actuator. The MPI compensation control of two-dimensional piezoelectric positioning stage is carried out, and the fitting coefficient R2 is proposed to evaluate the hysteresis compensation accuracy of MPI model. Under the full range driving voltage of 20~120 V, the fitting coefficient reaches more than 99.6%. The experiments of feedforward compensation and feedback compensation are implemented. Having applied the composite triangular-wave signal, the average absolute displacement error of the piezoelectric actuator is 0.1192 μm, as well as the mean square error 0.2949 μm. It demonstrates that the MPI model is effective against hysteresis for two-dimensional piezoelectric positioning stage.

Application of adaptive inverse compensation feedforward - MPC feedback control to AFM piezoelectric micro-positioning platform

“…Because of its simple structure, PID controller is widely used in PMP of commercial AFM [24]. The inverse P-I model is used as a feedforward controller and PID feedback controller to eliminate the hysteresis of PMP [25]. However, because of the small bandwidth of PID control, the performance is limited when tracking high frequency signals.…”

Design and disturbance rejection control of a piezoelectric nanopositioning stage

“…23,24 Different control methods have been developed to eliminate hysteresis, such as feedforward compensation and feedback control. 24 Feedforward compensation can reduce the hysteresis by inversely using the established hysteresis model, for example, the Preisach model, Maxwell model, and Prandtl-Ishlinskii (PI) model. [23][24][25][26][27][28][29] Rakotondrabe 28 proposed a feedforward compensation method to reduce nonlinear piezoelectric hysteresis significantly.…”

“…24 Feedforward compensation can reduce the hysteresis by inversely using the established hysteresis model, for example, the Preisach model, Maxwell model, and Prandtl-Ishlinskii (PI) model. [23][24][25][26][27][28][29] Rakotondrabe 28 proposed a feedforward compensation method to reduce nonlinear piezoelectric hysteresis significantly. Feedforward compensation can achieve satisfactory performance when the system can be modeled accurately.…”

“…While the piezoelectric actuator brings high actuation resolution to nanopositioning stages, it also exhibits nonlinear hysteresis. 23,24 Different control methods have been developed to eliminate hysteresis, such as feedforward compensation and feedback control. 24 Feedforward compensation can reduce the hysteresis by inversely using the established hysteresis model, for example, the Preisach model, Maxwell model, and Prandtl-Ishlinskii (PI) model.…”