Study of improving nano-contouring performance by employing   cross-coupling controller
  For the tracking stage path planning, we design a two-axis cross-coupling control system which uses the PI controller to compensate the contour error between axes. In this paper, the stage adoptive is designed by our laboratory (Precision Machine Center of National Formosa University). The cross-coupling controller calculates the actuating signal of each axis by combining multi-axes position error. Hence, the cross-coupling controller improves the stage tracking ability and decreases the contour error. The experiments show excellent stage motion. This finding confirms that the proposed method is a powerful and efficient tool for improving stage tracking ability. Also found were the stages tracking to minimize contour error of two types circular to approximately 25nm. 
Wen Yuh Jywe, Shih Shin Chen, Hung-Shu Wang, Chien Hung Liu, Hsin Hung   Jwo, Yun Feng Teng, and Tung Hsien Hsieh