Coupled hysteresis model and its inverse compensation for three-degree-of-freedom tip-tilt-piston piezoelectric stage

SIMA Jinfu; LAI Leijie; LI Pengzhi; FANG Yu; ZHU Limin

doi:10.37188/OPE.20233120.2964

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Coupled hysteresis model and its inverse compensation for three-degree-of-freedom tip-tilt-piston piezoelectric stage

Micro\/Nano Technology and Fine Mechanics | 更新时间：2026-03-25

- Coupled hysteresis model and its inverse compensation for three-degree-of-freedom tip-tilt-piston piezoelectric stage
- Optics and Precision Engineering Vol. 31, Issue 20, Pages: 2964-2974(2023)
- 作者机构：
  
  1.上海工程技术大学机械与汽车工程学院，上海 201620
  2.格鲁斯特大学计算与工程学院，英国切尔滕纳姆 GL50 2RH
  3.中国科学院长春光学精密机械与物理研究所，吉林长春 130033
  4.上海交通大学机械与动力工程学院机械系统与振动国家重点实验室，上海 200240
- 作者简介：
  
  E-mail：fangyu_hit@126.com
- 基金信息：
- DOI：10.37188/OPE.20233120.2964
  CLC： TN384
- Received：11 May 2023，
  
  Revised：2023-07-04，
  
  Published：25 October 2023
- 稿件说明：
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司马津甫,赖磊捷,李朋志等.三自由度压电偏摆台耦合迟滞模型建模与逆补偿[J].光学精密工程,2023,31(20):2964-2974.

SIMA Jinfu,LAI Leijie,LI Pengzhi,et al.Coupled hysteresis model and its inverse compensation for three-degree-of-freedom tip-tilt-piston piezoelectric stage[J].Optics and Precision Engineering,2023,31(20):2964-2974.
司马津甫,赖磊捷,李朋志等.三自由度压电偏摆台耦合迟滞模型建模与逆补偿[J].光学精密工程,2023,31(20):2964-2974. DOI： 10.37188/OPE.20233120.2964.

SIMA Jinfu,LAI Leijie,LI Pengzhi,et al.Coupled hysteresis model and its inverse compensation for three-degree-of-freedom tip-tilt-piston piezoelectric stage[J].Optics and Precision Engineering,2023,31(20):2964-2974. DOI： 10.37188/OPE.20233120.2964.

摘要

为了解决三自由度压电驱动纳米偏摆台中的多轴耦合与迟滞问题，设计了一种可以同时表征多个压电驱动器间耦合效应及其自身迟滞效应的耦合迟滞模型，并利用其逆模型进行前馈补偿以提升平台的定位和轨迹跟踪精度。首先，搭建了三自由度压电驱动偏摆台的控制系统并建立其运动学模型，将末端平台三自由度运动转化为三个压电驱动器的输出。然后，建立基于Prandtl-Ishlinskii模型的耦合迟滞模型，并对该模型及其逆模型的参数进行辨识。最后，通过开环逆模型前馈补偿来验证模型的有效性，并利用结合逆模型前馈和反馈的复合控制方法进行轨迹跟踪控制。实验结果表明：逆模型开环前馈补偿使三个压电驱动器间最大耦合位移均降低了70%以上，证明了所建立耦合迟滞模型的有效性，结合闭环反馈的复合控制方法对空间轨迹进行跟踪的最大均方根误差仅为0.06 mrad和0.42 μm，相比单纯闭环反馈分别减少了72%和87.5%，最大误差也减少了76%以上，有效消除了平台中耦合迟滞的影响，提高了平台的定位精度。

Abstract

To solve the problems of multi-axis coupling and hysteresis in a three-degree-of-freedom tip–tilt–piston piezoelectric stage， a coupled hysteresis model was designed to simultaneously characterize the coupling effect between multiple piezoelectric actuators and their own hysteresis effect. Its inverse model was used for feedforward compensation to increase the positioning and trajectory tracking accuracies of the stage. First， the control system and kinematics model of the three-degree-of-freedom piezoelectric stage were developed， and the three-degree-of-freedom motion of the end-effector was transformed into the outputs of three piezoelectric actuators. Then， a coupled hysteresis model based on the Prandtl–Ishlinskii model was established， and the parameters of the model and its inverse model were identified. Finally， the effectiveness of the coupled hysteresis model was verified through open-loop inverse model feedforward compensation， and a compound control method combining inverse model feedforward and feedback was used for trajectory tracking control. The experimental results indicate that the inverse open-loop compensation reduced the maximum coupling displacements between the three piezoelectric actuators by >70%， confirming the effectiveness of the developed coupling hysteresis model. The maximum root mean square errors of the compound control method combined with closed-loop feedback for tracking the spatial trajectory are only 0.06 mrad and 0.42 μm， which are reduced by 72% and 87.5%， respectively， compared with those in the case where only closed-loop feedback was used， and the maximum error is reduced by at least 76%. The proposed coupled hysteresis model and its inverse compensation can eliminate the influence of coupling hysteresis in the stage， and significantly increase the positioning accuracy of the stage.

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