Research of dynamic error compensation for nano-positioning system based on grey model

LI Ming-ming; GONG Zhen-bang; CHENG Wei-ming; SUN Lin-zhi

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Research of dynamic error compensation for nano-positioning system based on grey model

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- Research of dynamic error compensation for nano-positioning system based on grey model
- Optics and Precision Engineering Vol. 14, Issue 1, Pages: 89-94(2006)
- 作者机构：
  
  上海大学精密机械研究所上海,200072
- 作者简介：
- 基金信息：
- DOI：
  CLC： TH703
- Received：25 September 2005，
  
  Revised：15 October 2005，
  
  Published Online：20 February 2006，
  
  Published：20 February 2006
- 稿件说明：
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LI Ming-ming, GONG Zhen-bang, CHENG Wei-ming, et al. Research of dynamic error compensation for nano-positioning system based on grey model[J]. Optics and precision engineering, 2006, 14(1): 89-94.
DOI：

LI Ming-ming, GONG Zhen-bang, CHENG Wei-ming, et al. Research of dynamic error compensation for nano-positioning system based on grey model[J]. Optics and precision engineering, 2006, 14(1): 89-94. DOI：

摘要

对等步距多工位工作的纳米工作台

采用灰色模型能够同时对定位误差中的系统误差和随机误差进行动态补偿。讨论了提高灰色模型精度的方法

建立了改进背景值的等维新息GM(1

1)灰色预测模型。用5 μm步距定位误差进行了一步预测分析

结果表明该模型具有较高的预测精度;5 μm和3 μm步距的定位误差预测补偿实验表明

工作台的定位误差可以控制在40 nm以内。实验证明了灰色预测模型用于纳米定位系统动态补偿的有效性

且需要的建模数据很少、计算量小

适用于具有时变特征的精密定位系统。

Abstract

For a nano-stage worked in the way of multi-positions and single step

the grey model can be used to compensate the systemic errors and random errors simultaneously. A method of improving the precision of grey model was discussed

and the GM(1

1) model with equal dimension

new-information and improved background value was established. By discussing of one step prediction using the positioning step of 5 μm

the model proved to be high prediction precision. The compensation tests with 5 μm and 3 μm positioning steps proved that the positioning errors of the stage are less than 40 nm. The effectiveness of grey model is testified used in dynamic positioning errors prediction and compensation. For having the strong points the grey model needs less modeling data and compu ting works

so that it is greatly suitable for time-variable precise positioning systems.

关键词

Keywords

references

. 赵仲生,张润孝,林其骏. 基于时间序列理论的误差预测补偿技术[J]. 制造技术与机床,1998,(12):36-38. ZHAO ZH SH, ZHANG R X, LIN Q J. Error forecast compensating method based on time series theory[J]. Manufacturing Technology and Machine Tool, 1998, (12): 36-38.(in Chinese)

. 邓聚龙. 灰色系统基本方法[M]. 武汉:华中理工大学出版社,1987. DENG J L. Basic methods of grey system[M]. Wuhan: Huazhong University of Science and Technology Publishing House, 1987.(in Chinese)

. 谭冠军. GM(1,1)模型的背景值构造方法和应用(Ⅰ)[J]. 系统工程理论与实践, 2000,(4):98-103. TAN G J. The structure method and application of background value in grey system GM(1,1) model (Ⅰ)[J]. Theory and Practice of System Engineering, 2000, (4): 98-103.(in Chinese)

. 周铭,王洪发. 基于遗传算法的灰色GM(1,1)模型 . 南昌大学学报(理科版),2002,26(4):331-333. ZHOU M, WANG H F. Grey model GM(1,1) based on genetic algorithm[J]. Journal of Nanchang University (Natural Science), 2002,26(4):331-333.(in Chinese)

. 王军平,陈全世. 灰色－神经网络综合预测模型[J]. 计算机工程与应用,2004,9:13-15. WANG J P, CHEN Q SH. Grey neural network integrated forecasting model[J]. Computer Engineering and Application, 2004, 9: 13-15. (in Chinese)

. 陈正平,苏虹,王钟羡. 灰色系统建模数据的一种变换方法[J]. 江苏理工大学学报,1999,20(3):91-94. CHEN ZH P, SU H, WANG ZH M, Method of the original data transformation for grey systems modeling[J]. Journal of Jiangsu University of Science and Technology, 1999, 20(3): 91-94.(in Chinese)

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