中文摘要：

多自由度纳米精度工件台的精度直接受电机力常数和增益平衡矩阵的影响，需要进行周期性测试。因实际电机负载与理论计算负载有差异且随时间发生改变，导致其电机力常数变化，直接采用理论计算负载会降低工件台精度。采用传递函数计算电机实际负载，建立电机负载与电机力常数间的关系，实现了电机力常数的校准。引入串扰系数描述不同电机轴间的串扰，并提出了增益平衡矩阵的详细计算方法。实验验证了该方法的正确性，并实现了工件台10nm的定位精度。

英文摘要：

The nano-precision wafer stage with multi-degree-of-freedom is affected directly by motor force constants and the gain balance matrix which needs to be calibrated periodically. The actual motor load is not equal to the theoretical motor load and it changes with time, so it reduces the performance of the wafer stage to use theoretical motor load directly. In order to perform the motor force constant calibration, the actual motor load is calculated according to the transfer function derived from the mathematical model of the wafer stage and the relationship between the motor load and the motor force constant is determined. Coefficients are introduced to describe the crosstalk between different axes and a new calculation method for gain balance matrix is also proposed. This calibration method is verified by an experiment and the wafer stage achieves positioning accuracy of 10 nm.