Online Koopman Operator-Based Feedforward Compensation Strategy for Fast Tool Servos With Robust High-Bandwidth Control

To improve the servo accuracy for fast tool servo (FTS) applications, this article presents an online Koopman operator-based feedforward compensation strategy and combines it with the robust high-bandwidth controller. The robust high-bandwidth control is achieved by employing an optimized dual-loop feedback controller integrated with a disturbance observer. To realize the almost zero dynamic lag tracking, a Koopman operator-based data-driven learning methodology is proposed for real-time tracking error prediction and compensation. Thanks to the high computational efficiency, this methodology could fulfill the error prediction in a very short time, and thus is applicable to online applications extensively encountered in FTS operations. The error elimination mechanism is deduced and analyzed theoretically. The experimental results indicate that the root-mean-squared error is only 4.2 nm for tracking a random nonuniform rational B-splines curve with a travel range of 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mathbf{\mu}}$</tex-math></inline-formula>m. The proposed control strategy enables robust high-bandwidth and almost zero dynamic lag tracking for general and real-time generated trajectories, which is significant for improving the manufacturing efficiency and accuracy of the FTS.