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Abstract: A new approach for reducing the contour errors in two-dimensional CNC machines is presented in this study. In the approach proposed here, two pre-trained nonlinear autoregressive networks with exogenous inputs (NARX), one for each axis, are used to predict the output position of the machine in the next sampling instant. The contour error in the next instant is then estimated and, based on this, the required compensation terms to be added to the reference input positions to reduce the contour error are determined. In the proposed approach, the compensation terms can be updated through an iteration process which reduces the contour error each time. Simulation experiments applying this approach to linear, circular and parabolic contours show that, even without extensive training of the NARX models, the contour errors can be significantly reduced. Actual experiments conducted on a small two-axis CNC machine confirm the effectiveness of this approach in reducing contour errors for linear, circular, parabolic and a free-form “goggles” contours. [Copyright &y& Elsevier]

Abstract: Cross-coupled control (CCC) is a well-known approach for directly reducing contour errors on contouring systems instead of the indirect approach of reducing axial following errors. An improvement of this approach, the variable-gain CCC, extends its applicability from just the linear contour to any contour defined by a continuously differentiable function. In this paper, the basic concept underlying CCC is used to develop a generalized CCC (GCCC) approach which can be applied for any free-form contour, including those defined only by a series of (x,y) coordinates similar to the reference inputs to CNC machines. Both computer simulation and actual experimental implementation of GCCC on a small two-axis CNC machine using four contours showed that it can effectively reduce the contour errors resulting from mismatched machine dynamics. For the linear, circular and parabolic contours that CCC can also be applied to, GCCC achieved the same level of contour error reduction. In addition experiments showed that GCCC also achieved similar levels of contour error reductions for free-form contours and for corner tracking. Without the need for a knowledge of the functions of the contours, GCCC is thus most suitable for application to CNC machines in which the contours that are to be generated are defined by a series of reference input axial positions. [Copyright &y& Elsevier]