Dual-Notch-Based Repetitive Control for Tracking Lissajous Scan Trajectories With Piezo-Actuated Nanoscanners

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 (RC)-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 article proposes a dual-notch-based RC (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 RC (MRC) and the baseline Proportional-Integral (PI) tracking controller are conducted on a piezo-actuated nanoscanner for typical scanning rates of 50- and 100-Hz. The results show that the maximum tracking error under the scanning rate of 100-Hz is reduced greatly from $0.1562~\mu \text {m}$ with PI + MRC and $7.1788~\mu \text {m}$ with PI to $0.0337~\mu \text {m}$ , confirming the effectiveness of the proposed DNRC in high-performance Lissajous scanning.