纳米定位系统动态误差灰色模型补偿方法研究

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

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5μm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;5μm和3μm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。

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 5μm, the model proved to be high prediction precision. The compensation tests with 5μm 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 computing works, so that it is greatly suitable for time-variable precise positioning systems.