Newton-AGTCF reference trajectory modification scheme for precision biaxial contouring motion control

This paper proposes a Newton extremum seeking algorithm based accurate global task coordinate frame (Newton-AGTCF) for precision contouring motion control of biaxial systems under complicated free-form contouring tasks. Specifically, a cost function is defined based on the reference contour and the current position. The point on the reference contour, where the minimal value of the cost function can be obtained through a on-line Newton algorithm, is defined as the contour error point. Consequently, the calculated contour error point can almost overlap with the actual one even under free-form contouring tasks with high-speed and large-curvature. AGTCF is constructed according to the contour error point, the desired point and the current position. Thus the tangential error and the contour error can be calculated in AGTCF. Through the controllers with reasonable weights adjustment, these two errors are utilized to modify the reference trajectory for contouring control accuracy improvement. The proposed Newton-AGTCF strategy is tested on a biaxial linear motor stage, and the experimental results consistently validate that the proposed strategy achieves not only nearly perfect contour error estimation but also excellent contouring control performance in various complicated contouring tasks.