面向纳米栅格扫描的时滞压电微动平台耦合补偿  

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

作　　者：张志名 闫鹏[1,2] ZHANG Zhiming;YAN Peng(School of Mechanical Engineering,Shandong University,Jinan 250061,China;Key Laboratory of High-efficiency and Clean Mechanical Manufacture of the Ministry of Education,Jinan 250061,China)

机构地区：[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

出　　处：《光学精密工程》2023年第11期1641-1651,共11页Optics and Precision Engineering

基　　金：山东省自然科学基金重大基础研究项目(No.ZR2019ZD08)。

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H∞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。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 H∞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.

关 键 词：压电微动平台 耦合补偿 动力学建模 周期干扰观测器 时滞 H∞优化 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] TH113[自动化与计算机技术—控制科学与工程]