Taylor series expansion error compensation for a bi-axial CNC machine

In this paper, an approach using the Taylor series expansion is explored for error compensation in bi-axis CNC machines. The objective is to improve the contouring accuracy in these machines. The contour errors that will occur if the desired reference inputs are directly applied to the control loops are first predicted using the known axial dynamic models. The Taylor series expansion is then used to obtain an expression of the contour error around the current tool position. A robust numerical method is devised which is then used to compute the modified reference components along individual axes for cancellation of the predicted contour errors. Simulation results show that, with perfect knowledge of the machine´s dynamic models, the proposed strategy can perfectly cancel out the contour errors for both linear and circular contours despite the mismatches in the axes dynamics.