Iterative tuning notch filter for suppressing resonance in ultra-precision motion control

Wei Teng,Xiaolong Zhang,Liangliang Yang,Yangyang Zhang

doi:10.1177/1687814016674097

Abstract

In this article, a practical iterative algorithm for tuning the parameters of notch filter is presented to suppress high-frequency resonance in ultra-precision motion control. Notch filter is a useful tool to suppress middle- and high-frequency resonance to improve control precision. The traditional tuning method for it depends on the Fourier transform of the positioning error or the modal analysis of the motion stage, which cannot get the optimal control performance. The proposed algorithm can be used to tune the parameters of notch filter iteratively through minimizing a cost function of the positioning error, and it needs only measurement signals in actual motion system rather than detailed model of the motion stage. The proposed algorithm can suppress mechanical resonance and meanwhile minimize positioning error, which are demonstrated by experimental results in wafer stage of photolithography.

Highlights

In ultra-precision motion control system such as hard disk and stage of wafer fabrication equipment, there exist some middle- or high-frequency vibration components due to the excitation of mechanical structure,[1,2] which can reduce control accuracy, even destroy stabilization of the control system
We present an iterative tuning algorithm databased for notch filter to obtain the optimal filter parameters through the minimization of a cost function
An iterative tuning algorithm for the parameters of notch filter in ultra-precision motion control is presented in this article

Summary

Introduction

In ultra-precision motion control system such as hard disk and stage of wafer fabrication equipment, there exist some middle- or high-frequency vibration components due to the excitation of mechanical structure,[1,2] which can reduce control accuracy, even destroy stabilization of the control system. They adopted an adaptive notch filter whose parameters can be adjusted based on fast Fourier transform (FFT) of speed feedback signals to reduce the mechanical resonance. Iterative tuning is a data-based method to adjust controller parameters through minimizing a certain cost function, and it has been applied in many industrial fields due to the advantage of avoiding the need of detailed model of motion system. Niedzwiecki and Kaczmarek tuned the adaptive notch filter by minimizing the tracking error between system output and the estimate one They just focused on the varied frequency estimation without considering the concrete motion control system. The motivation of this article is to present an iterative tuning algorithm to adjust the notch filter parameters adaptively in ultraprecision motion control, which can suppress mechanical resonance appropriately and obtain an optimal control precision. Tan(ptsf1) pts ð7Þ where f1 denotes the designed pole frequency or zero frequency of notch filter, and f2 denotes the prewarped frequency that can be the frequency fp or fz in the coefficients of equation (6)

Objective of iterative tuning

Conclusion