Tangential velocity tracking-based cross-coupled control method with variable feedrate for biaxial parametric curve following

To address the inaccurate contour error calculation problem in traditional cross-coupled control (CCC) methods for biaxial motion systems, this paper presents a novel CCC method based on a recently developed tangential velocity tracking (TVT) strategy. It has the advantage that existing high-precision algorithms for searching the foot point can be directly integrated to obtain the excellent estimation accuracy of contour error. The cumbersome parameter tuning for position controllers of each axis is unnecessary. Moreover, a velocity interpolator for parametric curves is developed to extend the TVT strategy to the variable feedrate case. The stability of the TVT-based CCC system is proved using a quadratic Lyapunov function. Comparative experiments are carried out, and the results indicate that the estimation deviation of contour error in the TVT-based CCC method can be constrained within 1 mu m. The maximum contour error is significantly reduced by 65.32% and 50.10% compared with the traditional CCC methods based on tangential and circular approximations, respectively.