Contouring Error Vector and Cross-coupled Control of Multi-axis Servo System

The contouring error and cross-coupled gains calculation have always been the critical issues in the application of cross-coupled control. Traditionally, the linear approximation and circular approximation are widely used to determine the contouring error and cross-coupled gains. However, for linear approximation and circular approximation, the contouring error and cross-coupled gains are calculated sophisticatedly, especially in three-dimensional applications. In this paper, a contouring error vector is established under task coordinate frame, then the contouring error and cross-coupled gains can be easily obtained based on the magnitude and orientation of the contouring error vector. The experimental results on a three-axis CNC machine indicate the proposed approach simplifies the calculation of contouring error and cross-coupled gains.