Notch-filter-based repetitive control of fast tool servos for high-performance tracking of periodic trajectories

The achievable performance of conventional repetitive control (CRC) is constrained by the error amplification at the non -harmonic frequencies, the intrinsic sensitivity to the signal period shift and the limited tracking frequency range under fixed sampling rate. To remedy these undesirable behaviors, a notch -filter -based repetitive control (NF -RC) is proposed based on the spectrum -selection filtering scheme in this paper with application to fast tool servos (FTSs). The loop -shaping property of this NF -RC can be flexibly designed by the cascade of a series of parameterized IIR notch filters without the aforementioned limitations of the CRC, so as to provide a unified formula for various RCs and even resonant control schemes. A general realization along with several simplified versions of the IIR notch filter is derived for the digital implementation of the NF -RC. Comparative trajectory tracking experiments on a self -developed FTS have validated the superiorities of the proposed NF -RC in terms of the performance improvement for periodic reference tracking, the robustness against the signal period variations and the trackable frequency range under fixed sampling rate. Taking advantage of an excellent comprehensive performances of the NF -RC scheme, the radial sinusoidal surface and the water -drop surface were successfully produced with high form precision and excellent surface quality after the FTS-based diamond turning.