Coupling compensation for nano raster scanning of piezoelectric nano-stages with delays

ZHANG Zhiming; YAN Peng

doi:10.37188/OPE.20233111.1641

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Coupling compensation for nano raster scanning of piezoelectric nano-stages with delays

Micro/Nano Technology and Fine Mechanics | 更新时间：2023-07-08

- Coupling compensation for nano raster scanning of piezoelectric nano-stages with delays
- Optics and Precision Engineering Vol. 31, Issue 11, Pages: 1641-1651(2023)
- 作者机构：
  
  1.山东大学机械工程学院，山东济南 250061
  2.高效洁净机械制造教育部重点实验室，山东济南 250061
- 作者简介：
- 基金信息：
- DOI：10.37188/OPE.20233111.1641
  CLC： TP273;TH113
- Received：10 January 2023，
  
  Revised：01 February 2023，
  
  Published：10 June 2023
- 稿件说明：
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张志名,闫鹏.面向纳米栅格扫描的时滞压电微动平台耦合补偿[J].光学精密工程,2023,31(11):1641-1651.

ZHANG Zhiming,YAN Peng.Coupling compensation for nano raster scanning of piezoelectric nano-stages with delays[J].Optics and Precision Engineering,2023,31(11):1641-1651.
张志名,闫鹏.面向纳米栅格扫描的时滞压电微动平台耦合补偿[J].光学精密工程,2023,31(11):1641-1651. DOI： 10.37188/OPE.20233111.1641.

ZHANG Zhiming,YAN Peng.Coupling compensation for nano raster scanning of piezoelectric nano-stages with delays[J].Optics and Precision Engineering,2023,31(11):1641-1651. DOI： 10.37188/OPE.20233111.1641.

摘要

针对栅格纳米扫描特别是高速扫描应用中，带测量滞后的压电纳米平台轴间周期耦合补偿的问题，提出一种无需复杂逆模型求解的鲁棒周期干扰观测控制策略。建立压电平台的机电耦合多扰动模型用以描述平台系统的动力学行为。在此基础上，构建周期干扰观测控制结构。通过推导的性能优化函数和鲁棒稳定性条件，将最优控制器参数求解问题转化为延时系统的混合灵敏度优化问题，并通过无穷维

∞

控制方法进行求解。最后，在压电纳米平台上进行综合的实验探究。结果表明，建立的动力学模型能够有效拟合平台的实验响应；相较于无干扰观测器的方法和传统的周期干扰观测控制方法，提出的鲁棒优化方法在基频的抗干扰性能分别有超过99%和50%的提升。提出的鲁棒周期干扰控制方法有优越的抗干扰和不确定补偿性能。

Abstract

Aiming to compensate for the cross-periodic coupling of piezoelectric nano-stages with measurement delays in raster nano-scanning， particularly in high-speed scanning applications， this paper presents a robust periodic disturbance observer （PDOB） control strategy that does not require solving complex inverse models. First， an electromechanical multi-perturbation model is developed to describe the dynamic behavior of piezoelectric stage systems. Then， a PDOB control structure based on the model is constructed. The problem of optimal controller parameter solution is transformed into a mixed sensitivity optimization problem for time-delay systems with the formulated performance optimization function and robust stability condition， which is solved via the infinite-dimensional

∞

control method. Finally， comprehensive experimental investigations are conducted on the piezoelectric nano-stage. The results indicate that the developed dynamic model can effectively fit the experimental response of the stage and that the proposed robust periodic disturbance control method has superior anti-disturbance and uncertainty compensation performance to the method without disturbance observer and the conventional PDOB control method， with improvements of

99% and

50%， respectively， in the anti-disturbance performance at the fundamental harmonic frequency.

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Keywords

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