Newton-based contour error estimation and robust Cross-Coupling Control for high-precision fast contouring

High-performance position control algorithms for multi-axis servo-systems, due to presence of asymmetric dynamics and disturbance, do not guarantee high-precision contouring. Cross-Coupling Control (CCC) conventionally uses a static Contour Error Estimate (CEE) to reduce the shortest distance between the reference map and actual position, known as contour error. However, reliability of the static CEE deteriorates for high-speed reference feeds and also for sharp corners and deep curves. We propose a dynamic CEE using a Newton-based update law to obtain a precise CEE for fast and highly-curved contours. The Newton-based algorithm uses an estimate of the contour error curvature in order to eliminate the convergence dependence on the contour shape. The proposed CCC design includes one PID controller per axis, and combines the proposed Newton-based CEE with Integral Sliding Mode Control (ISMC) which is well-known for its capability in dealing with parameter uncertainty and external disturbances. The proposed ISMC performance is enhanced with an adaptive disturbance estimate. The proposed CCC algorithm reduces the time-averaged contour error (TACE) at least by an order of magnitude in comparison to conventional CCC algorithms. Various simulation results are presented to highlight the significant improvement achieved by the proposed algorithm.