压电定位平台低阻尼谐振特性辨识及高带宽控制

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (18) : 287-296.

论文

压电定位平台低阻尼谐振特性辨识及高带宽控制

刘浩天1，张桂林1，周克敏2

作者信息 +

Identification of low-damping resonance characteristics and the high-bandwidth control of a piezo-positioning stage

LIU Haotian1, ZHANG Guilin1, ZHOU Kemin2

Author information +

文章历史 +

摘要

本文研究降低低阻尼谐振特性对压电定位平台跟踪带宽的限制。首先，在Prandtl-Ishlinskii逆模型线性化的基础上，将基于脉冲响应的Hankel矩阵系统辨识法应用到压电定位平台线性动态特性的辨识中，并在其中提出一种改进的相关函数计算方法进一步提高低阻尼谐振频段的辨识精度。其次，根据辨识得到的传递函数模型，采用零极点对消加超前补偿器的方法设计陷波器补偿低阻尼反谐振及谐振特性，并在串联陷波器的基础上设计PI（proportional integral）控制器提高闭环回路的鲁棒性及跟踪性能。最后，实验结果表明，PI控制器的闭环带宽为97Hz，含有陷波器的PI控制器闭环带宽为244Hz，由于陷波器的加入，闭环带宽提高了151.5%，从而说明了本文辨识及控制方法的有效性。

Abstract

This paper studies the limitations of reducing low-damping resonance characteristics on the tracking bandwidth of piezo-positioning stages. Firstly, based on the linearization of the Prandtl-Ishlinskii inverse model, the impulse response-based Hankel matrix system identification method is applied to the identification of linear dynamic characteristics of piezo-positioning stages, in which an improved method of correlation function calculation is proposed to further improve the accuracy of the identification of the low-damping resonance frequency band. Secondly, based on the transfer function model obtained from the identification, the zero-pole pair elimination plus overshoot compensator method is used to design the notch filter to compensate the low-damping anti-resonance and resonance characteristics, and the PI controller is designed based on the series trap to improve the closed-loop robustness and tracking performance. Finally, the experimental results show that the closed-loop bandwidth of the PI controller is 97Hz, and the closed-loop bandwidth of the PI controller with the notch filter is 244Hz. Due to the addition of the notch filter, the closed-loop bandwidth has been increased by 151.5%, thus illustrating the validity of the identification and control method of this paper.

导出引用

刘浩天1, 张桂林1, 周克敏2. 压电定位平台低阻尼谐振特性辨识及高带宽控制[J]. 振动与冲击, 2024, 43(18): 287-296

LIU Haotian1, ZHANG Guilin1, ZHOU Kemin2. Identification of low-damping resonance characteristics and the high-bandwidth control of a piezo-positioning stage[J]. Journal of Vibration and Shock, 2024, 43(18): 287-296

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