Increasing dynamic accuracy of machine tools using predictive feedforward optimization with hybrid modeling

Abstract

The paper presents an online optimization-based feedforward design framework using hybrid modeling to increase the dynamic accuracy of machine tools. Designed for use in dynamics simulation and feedforward compensation, the hybrid model combines a physics-based model of the multibody dynamics and a data-driven Gaussian process regressor of the output discrepancy. The feedforward control is based on the predictor–simulator separation, where the accurate but tractable nonlinear hybrid model is used for dynamics simulation, and the linearized predictor is adopted for optimal feedforward design with a receding horizon approach based on convex programming. This strategy allows the advanced modeling techniques to be used for real-time dynamics compensation in an open-loop fashion, where the associated convex optimization problem can be solved efficiently and reliably. We propose a methodological approach that covers the entire design procedure from dynamics modeling to control architecture selection and parameter tuning, providing an end-to-end strategy for practical applications. The algorithm is validated on a real-time industrial CNC machine, where the average computation time is 63 $\mu$s on an Intel i5 CPU. Compared to the industry standard baseline feedforward control, the proposed feedforward framework reduces the mean absolute contour error by 46.1% and 56.8% for constant velocity tracking and freeform butterfly path following, respectively. Even with a mismatch of 30 % in the model parameters, the presented feedforward still reduces the error by 38.5% compared to the baseline.