Contouring control of biaxial systems based on a new task coordinate frame

This paper proposes a new task coordinate frame (TCF) for contouring control of biaxial systems. Existing task coordinate frames are only locally defined based on the desired contouring trajectory to be tracked and the calculated contour error is an approximation to the actual contour error only. As such, they are applicable to contouring tasks with small curvature and little actual trajectory tracking errors only. In contrast, the proposed task coordinate frame is globally defined based on the geometry of the desired contour only and the resulting coordinate errors correspond to the actual contouring error and the tangential error on the contour directly. To demonstrate the high contouring performance nature of the proposed task coordinate frame, the system dynamics of a biaxial linear motor gantry is transformed into this task coordinate frame. A discontinuous projection based adaptive robust controller (ARC) which explicitly takes into account the dynamic coupling effect is then employed to improve the contouring performance under both parametric uncertainties and uncertain nonlinearities. Comparative experimental results obtained on a high-speed industrial biaxial gantry driven by linear motors are presented to verify that the proposed TCF is effective for achieving excellent contouring performance even when large-curvature contouring control tasks are of concern.