A Compound Control Based on the Piezo-Actuated Stage with Bouc–Wen Model

Jiwen Fang,Jia Wang,Chong Li,Wei Zhong,Zhili Long

doi:10.3390/mi10120861

Abstract

The piezoelectric actuator (PA) is one of the most commonly used actuators in a micro-positioning stage. But its hysteresis non-linearity can cause error in the piezo-actuated stage. A modified Bouc–Wen model is presented in this paper to describe the hysteresis non-linearity of the piezo-actuated stage. This model can be divided into two categories according to the input frequency: rate-independent type and rate-dependent type. A particle swarm optimization method (PSO) is employed to identify these parameters of the Bouc–Wen hysteresis model. An inverse model feedforward compensator is established based on the modified Bouc–Wen model. The fuzzy proportional-integral-derivative (PID) controller combined with the feedforward compensator is implemented to the piezo-actuated stage. The experimental results indicate that the proposed control strategy can compensate for the hysteresis phenomenon.

Highlights

The piezoelectric actuator has been widely utilized in ultra-precision positioning
There are two ways to alleviate the hysteresis effects of the piezoelectric actuator: one, an inverse control based on the hysteresis model is used to address the non-linearity of piezoelectric actuator (PA); two, the non-linearity of the piezoelectric actuator is taken as a disturbance, and the robust adaptive control without hysteresis model can handle the non-linearity by suppressing the disturbance [1]
Consequentl4y,otfh1e3 hysteresis characteristic of the PA is generally divided into two parts according to the input frequency: o[1n4e,1t6h]e. hCyosntesreeqsuisenpthlyen, othmeehnyosnteisrersaitse-cihnadreapcetenrdisetnict wofhethnethPeAinips ugtefnreeqraulelyncdyivisiduenddeinrt1oHtwz;otwpoa,rtisf tahcecoinrdpiuntgfrteoqutheenciynpisultarfgreeqr utheanncy1: Honz,et,htehehyhsytesrteesriessibsecpohmenesomseernioouns iasndrantee-eidnds etopebneddeenstcrwibheednbtyhae rinatpeu-dt efpreeqnudeennctymiosdueln. der 1 Hz; two, if the input frequency is larger than 1 Hz, the hysteresis becomes serious and needs to be described by a rate-dependent model

Summary

Introduction

The piezoelectric actuator has been widely utilized in ultra-precision positioning. the existence of hysteresis of the piezoelectric ceramics can lead to poor control performance of the stage. Jinqiang Gan proposed a generalized Bouc–Wen hysteresis model by applying relaxation functions to describe rate-dependent and rate-independent hysteresis behaviors of piezoelectric actuator [3]. A modified Bouc–Wen model, identified by the particle swarm optimization (PSO) method, is employed to estimate the hysteresis of the piezo-actuated stage [4]. The general classical Bouc-Wen model is employed to improve the control performance of the piezo-actuated stage when the input frequency is within 1 Hz. If the input frequency is higher than 1 Hz, the proposed mathematical expression in this paper is as follows: x. The coefficients α, β, γ, ε are the parameters of the modified Bouc-Wen model, λ is control factor related to the bias input signal, and η is the adjustable factor for the hysteresis of the different input signal.

Control

Experimental Results and Discussion

Conclusions