Dynamic Compensation of Distorted Measured Forces Using Improved Luenberger Observer

Accurate measurement of milling forces is essential for monitoring and optimizing the milling process. The table dynamometer is widely used to measure the milling force because it does not change the dynamic characteristics of the spindle. However, the measured milling force will be distorted because it is conditioned by the vibration of the surrounding system and the natural frequency of the table dynamometer. Therefore, it is necessary to compensate for these dynamically induced errors in milling force measurement. This work aims to develop and test a novel compensation technique based on the improved Luenberger observer. First, the reason for the distortion of the milling force measured by the dynamometer is analyzed by the impact hammer test. Second, the transfer function fitting accuracy is improved by a band-fitting method. Third, the
$l_{1}$
performance is introduced to obtain the gain parameter of the improved Luenberger observer, and the assumption that some prior knowledge about the process disturbance is removed. Finally, the effectiveness of the proposed method is verified by numerical simulation and experiment, and the specific application of the proposed method in milling force measurement is presented.