A time-delay-based sliding mode controlling method for reducing contour errors of machine tools

This article presents a time delay-based sliding mode controller to reduce contour errors for machine tools subject to friction and model error. Through decoupling the actual dynamic model of machine tools into a nominal component and an error component, a proportional differential (PD) controller, which is mathematically deduced from the sliding mode controller (SMC), is designed for the nominal model. A time delay estimation (TDE) strategy that considers the friction effect is designed to compensate for the error component. Therefore, tracking accuracy is guaranteed. Based on TDE results, a Kalman state prediction method that considers model error is developed to make a high state prediction accuracy even if the model error is large. By adding the predicted contour errors of the next sampling time into the command trajectory, the pre-compensation of contour errors is realized. Moreover, a new contour error estimation (CEE) method that can improve computing efficiency is proposed. Experiments and comparisons are conducted to verify the effectiveness of proposed method.