Compensation of Variable Fractional Delays in the $6k\pm 1$ Repetitive Controller

Repetitive schemes, aimed for harmonic compensation, are formed by the interconnection of delay lines. They are usually implemented in a digital way, where delay lines are replaced by discrete delays. Each discrete delay is obtained as the ratio between the required delay time in continuous time and the sampling period. A problem arises whenever the delay time of the controller is not an integer multiple of the sampling period. This is referred to in the literature as the fractional delay issue. In repetitive schemes, the delay time is a function of the fundamental frequency of the signals under study. Applications where the fundamental frequency varies with time entails variations in the delay time and, in particular, in its fractional part. This issue is referred to as variable fractional delay (VFD). This work presents a simple solution to implement repetitive schemes subject to a VFD issue. The introduction of an additional filter structure, called the Farrow structure, to each delay line is proposed. Theoretical analysis and design guidelines for the Farrow-structure-based repetitive scheme are provided. In particular, this paper focuses on the $6k\pm 1$ repetitive scheme. Experimental results are presented to confirm the benefits of the proposed solution.