A hybrid model for pre-compensating servo error in the ball screw system based on high-bandwidth controller

This article presents a hybrid model to predict the positions of the ball screw drive system of machine tool and then modify the trajectory through constructing a pre-compensation method to reduce servo errors in machine motion axes. To achieve this objective, a flexible control model is initially developed to characterize the ball screw drive system, and by leveraging this model, a high-bandwidth controller is constructed, with its physical representation, i.e. the state-space equation, being derived. Subsequently, a data-driven hybrid model is proposed to predict the positions of the ball screw drive system concerning the next multiple time steps from the current time step, and then the predicted positions associated with these steps are utilized as initial conditions to adjust and compensate for the physical model's prediction errors corresponding to these multiple time steps. As a result, a compensated trajectory with high tracking accuracy is generated. Finally, experiments confirm that the proposed prediction method offers superior prediction accuracy and enhanced adaptability, and the pre-compensated trajectory leads to reduced tracking errors.