Force compensation for precise positioning in machine tools via state observer design

In machining, cutting force generated is identified as input disturbance to the servo drive systems of the positioning table. In frequency domain, the cutting force magnitudes can be synthesized according to various harmonic components depending on the cutting tool spindle speed rotation. This paper focuses on compensation of high-frequency harmonic components of the cutting force using a state estimator named disturbance force observer (DFO) which explicitly estimates the input disturbance force. The force estimation error and tracking performances of the state estimator and the cascade P/PI positioning controller were analyzed experimentally on a single axis ball screw driven positioning table resembling a milling machine. The cascade P/PI controller was designed using traditional loop shaping frequency domain method while the force observer simultaneously estimated the input disturbance force based on the fundamental frequency dictated by the spindle rotational speeds. In experimental validations, a single, double, and triple harmonic-based force observers were designed at fundamental frequencies of 0.2 Hz, 0.5 Hz, and 0.8 Hz, and at amplitudes of 0.5 mm, 0.3 mm, and 0.2 mm, respectively. In time domain, the tracking performances of the system were analyzed and evaluated using root mean square of the position errors (RMSE) while in frequency domain, fast Fourier transform (FFT) analyses were performed on the tracking error signals. Results of the spectral analyses showed a 99.82% (single harmonic), 99.87% and 98.79% (two harmonics), and 99.83%, 97.13%, and 99.18% (three harmonics) reduction in respective force component magnitudes indicating close to successful estimation of the disturbance force observer. Meanwhile in time domain, numerical results of RMSE values showed reductions of 94.82%, 96.83%, and 94.01% for the three different input disturbance configurations while the experimental result showed reduction of 96.10%, 92.76%, and 92.44%, respectively. The work is to be expanded to include actual measured cutting forces as the input disturbance.