Robust Inversion-Based Feedforward Control With Hybrid Modeling for Feed Drives

This article presents a robust feedforward design approach using hybrid modeling to improve the output tracking performance of feed drives. Geared toward the use for feedforward design, the hybrid model represents the dominant linear dynamics with a flat analytical model and captures the output nonlinearity by Gaussian process (GP) regression. The feedforward control is based on the model inversion, and the design procedure is formulated as a signal-based robust control problem, considering multiple performance objectives of tracking, disturbance rejection, and input reduction under uncertainties. In addition, the technique of structured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> synthesis is applied, which allows direct robust tuning of the fixed-structure feedforward gains and ensures the applicability in industrial hardware. The proposed methodological approach covers the entire procedure from modeling to control architecture selection and weights design, delivering an end-to-end strategy that accounts for performance and robustness requirements. Validated on an industrial milling machine with real-time capability, the proposed robust controller reduces the mean absolute tracking error in the transient phase by 83% and 63% compared to the industrial standard baseline feedforward and the nominal design, respectively. Even with a variation of 20% in the model parameters, the robust feedforward still reduces the error by 58% in the worst case with respect to the baseline.