Design and application of a data driven controller using the small-gain constraint for positioning control of a nano-positioner

In this paper, the design of a data driven controller using a small-gain theorem approach for improving the positioning accuracy of a piezoelectric tube scanner (PTS) is demonstrated. Open-loop frequency responses of both the X-PTS and Y-PTS are measured using a band-limited sweep sine signal and are used as primary data for this control design. The frequency response of the controllers is synthesized by the application of the small-gain theorem constraints over the entire frequency range for both the axes. The experimental implementation of this feedback data driven controller provides significant vibration reduction, with 19 dB and 15 dB damping at the resonance frequencies of the X and Y-axes of the PTS, respectively. A comparison between the open-loop and closed-loop tracking performance for triangular signals shows significant improvement up to the scanning frequency of 150 Hz. Moreover, the design of this data driven controller is less complex than conventional controller design methods as it does not need a system model.