LAUSR

Using Lissajous scan trajectory is a promising way to get rid of issues resulting from the raster scan trajectory in several advanced applications, like atomic force microscopy and fast steering mirror. Although the repetitive control based schemes, which are tailed to track periodic trajectories, have been successfully utilized to improve the tracking performance of the Lissajous trajectories, the enabled performance is limited due to the unavoidable dynamic cross-coupling effect. To address this issue, this paper proposes a dual-notch based repetitive control (DNRC) scheme via generating the dual-notch loop shaping behaviors at two sets of fundamental frequencies as well as their harmonics for eliminating the errors distributed at these frequencies. The design process and the parameters determination are provided in detail. Comparative experiments with the modified repetitive control (MRC) and the baseline PI tracking controller are conducted on a piezo-actuated nano-scanner for typical scanning rates of 50- and 100-Hz. The results show that the maximum tracking errors under the scanning rate of 100-Hz is reduced greatly from 0.1562 μm with PI+MRC and 7.1788 μm with PI to 0.0337 μm, confirming the effectiveness of the proposed DNRC in high performance Lissajous scanning.