A low-order repetitive control (RC) design in continuous-time for nanopositioning applications is presented. It focuses on achieving high performance and sufficient robustness to uncertainties. The design is mainly applicable to analog implementation, but due to the exceptionally low order, it also results in a fast and efficient digital implementation. Experimental results for an analog implementation using a bucket brigade device (BBD), as well as a digital implementation, is presented. RC can provide fast and accurate tracking of periodic reference signals, which is useful in many scanning probe microscopy and nanofabrication applications.
Eielsen, A. A., Gravdahl, J. T., & Leang, K. K. (2015). Low-order continuous-time robust repetitive control: Application in nanopositioning. Mechatronics, 30, 231–243. https://doi.org/10.1016/j.mechatronics.2015.07.006