Integral design of contour error model and control for biaxial system

This paper focuses on the contour following accuracy improvement for biaxial systems using cross-coupled control (CCC). It proposes an integral design method including contour error model, contour control effort distribution and the CCC algorithm. First, a contour error model using the contour algebraic equation and its partial derivatives is established without the small tracking error assumption. This model satisfies the condition that it equals to zero if and only if the real contour error value vanishes, which makes perfect contour following become possible in theory. Then, in order to decouple the contour following the feed-direction tracking, contour control effort distribution is decided to be in line with the normal vector at the desired point. Through expanding the proposed contour error model with Taylor series to make it be related to tracking errors of both axes, the stability condition of CCC is analyzed by the contour error transfer function (CETF). Experiments are carried out on an X–Y motion stage to verify the proposed method. The results show that it improves the contour following accuracy greatly in various conditions, even when large tracking errors occur.