A Novel Contour Error Estimation for Position Loop-Based Cross-Coupled Control

Reduction of contour error is the main control objective in contour-following applications. A common approach to this objective is to design a controller based on the contour error directly. In this case, the contour error estimation is a key factor in the contour-following operation. Contour error can be approximated by the linear distance from the actual position to the tangent line or plane at the desired position. This approach suffers from a significant error due to linear approximation. A novel approach to contour error calculation of an arbitrary smooth path is proposed in this paper. The proposed method is based on coordinate transformation and circular approximation. In this method, the contour error is represented by the coordinate of the actual position with respect to a specific virtual coordinate frame. The method is incorporated in a position loop-based cross-coupled control structure. An equivalent robust control system is used to establish stability of the closed-loop system. Experimental results demonstrate the efficiency and performance of the proposed contour error estimation algorithm and the motion control strategy.