Discrete-Time Repetitive Control for Multi-Harmonic Reference Trajectories with Arbitrary Frequency⁎The financial support by the Christian Doppler Research Association, the Austrian Federal Ministry for Digital and Economic Affairs, the National Foundation for Research, Technology and Development, and voestalpine Stahl GmbH is gratefully acknowledged. Issue 2 (2020) - Marko, L.; Saxinger, M.; Bittner, M.; Steinboeck, A.; Kugi, A.
Abstract: In this work, a repetitive control approach for the tracking of harmonic reference trajectories in the presence of actuator backlash and sticking friction is presented. A spatial Fourier series formulation is utilized to obtain a learning law which is independent of the desired reference frequency. Subsequently, discrete-time averaging is employed, which results in a simple convergence criterion for the closed-loop system. Furthermore, all updates are calculated in a time-recursive manner, which avoids the necessity of large data windows and allows for a discrete-time implementation with a uniform sampling time. Finally, experimental results of a fully assembled spindle drive are presented. This demonstrates the effectiveness of the proposed control scheme as well as its suitability as an add-on strategy in existing positioning devices.