Fractional delay filter based repetitive control for precision tracking: Design and application to a piezoelectric nanopositioning stage

Abstract The development of nanotechnology requires a precision tracking of periodic signals in order to complete repetitive industrial or scientific tasks. Although repetitive control is an intuitive choice to realize precisely periodic signal’s tracking, an integer number should match the period of signals for a digital control system otherwise the performance would be deteriorated significantly. Thus, in this paper, a fractional delay filter based repetitive control (FDFRC) is developed to achieve precision signal tracking with arbitrary periods. According to the internal model principle, a fractional delay filter with the spectrum-selection property is designed by using of a Farrow structure to address integer/non-integer delays. The stability of FDFRC is also given and analyzed in frequency domain to facilitate controller implementation. The proposed FDFRC allows an easy, simple and practical realization with only one parameter to be adjusted for different integer/non-integer delays. Comparative experiments with different frequencies of triangular waves for x axis and Lissajous scanning for x – y plane on a piezoelectric nanopositioning stage are conducted to further verify the significant improvements on the tracking performance of the proposed controller.