Discrete-Time Repetitive Control for Multi-Harmonic Reference Trajectories with Arbitrary Frequency

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.