Coupling Modeling and Adaptive Control for Piezoelectric-Actuated Positioning Stage

Abstract

In this paper, a nonlinear coupling model with hysteresis, dynamics, and creep is proposed to describe accurately the complex characteristics of piezoelectric-actuated positioning stage, where a classic Hammerstein model in series with a fractional-order model is given. The fractional-order model is presented to express the nonlinear creep characteristics. Firstly, the Hammerstein structure model is composed of two blocks, where the former block is the classical PI model to describe the static hysteresis effects, and the latter block is the second-order discrete transfer function model to characterize the dynamic characteristics. In addition, the parameters of the coupling model are identified. Secondly, based on the built model, the inverse of fractional-order model and the inverse of PI model are implemented as the feedforward compensations, and an adaptive control is designed to adjust the tracking performance of the whole system. Finally, the effectiveness of the proposed coupling model and controllers are verified by the piezoelectric-actuated positioning experiment stage. Experimental results show that the established coupling model can accurately characterize the hysteresis, dynamics, and creep properties of the stage. Also, the results show that the tracking error is less than 0.8% at low frequency and mixed frequency.

Research on the mechanism and control methods of mechanical drift in linear ultrasonic motors

“…Observations indicate that mechanical drift in LUMs manifests as a slow-evolving, nonlinear dynamic process. It exhibits a gradual change in output displacement over time, resembling the creep phenomenon observed in piezoelectric actuators [9][10][11].…”

Review on the Nonlinear Modeling of Hysteresis in Piezoelectric Ceramic Actuators

“…In the figure, ( ) u t and ( ) y t represent the input voltage and output displacement, respectively. The static nonlinear part H can use the classical PI model [109], the modified PI model [106], and the Bouc-Wen model [108], as well as other forms such as least square support vector machine, neural network, and polynomial [106]. The dynamic linear part ( ) G z can use the ARX (auto-regressive model with exogenous input) model as shown in Equations ( 56) and ( 57) [108].…”

“…The author of reference [108] used the Hammerstein model composed of the Bouc-Wen model and the ARX model to establish the rate-dependent hysteresis model for piezoelectric ceramic actuators. In order to describe the rate-dependent hysteretic and creep behavior of actuators, the author of reference [109] combined the Hammerstein model with a fractional-order model for describing creep, in which the Hammerstein model was formed by connecting the classical PI model with the ARX model. The author of reference [110] superimposed a butterfly hysteresis operator based on exponential function with the asymmetric Bouc-Wen model to form a hybrid static hysteresis model, which was used as the static nonlinear part of Hammerstein model to improve the modeling accuracy of the static part, while the dynamic linear part still used the second-order transfer function.…”

Comprehensive compensation of dynamic hysteresis and creep for piezoelectric actuator

“…Liu et al [18] implemented an inverse feedforward controller on the basis of fractional-order creep and the Bouc-Wen hysteresis model to improve the positioning and scanning accuracy of piezoelectric actuators. Li et al [19] implemented the inversion of the fractional-order model and the PI model as the feedforward compensations and designed an adaptive control to adjust the tracking performance of the piezoelectric-actuated positioning stage. The fractional-order creep model is embedded within the hysteresis model, exhibiting a high degree of coupling.…”