Adaptive Pre-Compensation of the Contouring Error for High-Precision Parametric Curved Contour Following

Tasks of parametric curved contour following can be widely seen in computer-numerical-control (CNC) machining of parts with complex geometric features. Due to the existence of the contouring error in contour-following tasks, the machining precision of CNC machine tools will be seriously degraded. To reduce this error, methods such as cross-coupled control are extensively researched. However, these methods focus on compensation of the already happened contouring error, based on approximation of the error value according to the online measured actual motion positions. This paper presents an adaptive real-time pre-compensation approach, so as to control the contouring error before it really occurs. First, actual motion positions of the feed axes at the next sampling period are predicted, according to the z-domain model of each feed-drive system. To improve the adaptive capacity of the actual position prediction, the feed-drive models are identified online using the least-square method. After that, an accurate contouring-error calculation method, based on tangential-error backstepping using a moving frame, is proposed. Finally, the adaptive estimated contouring error at the next sampling period is compensated at the current period, thus beforehand improving the contour accuracy. Simulation and experimental tests are conducted to demonstrate the feasibility of the presented methods. From the testing results, it can be seen that the presented error-estimation method can precisely compute the contouring error, and the pre-compensation approach improves the contour-tracking accuracy dramatically, which is of great significance for improving the machining precision of the CNC machine tools.