Fractional-Order New Generation of nk ± m-Order Harmonic Repetitive Control for PWM Converters

Abstract

In this paper, a fractional-order new generation of $nk \pm m$ -order harmonic repetitive controller (FO-NG- $nk\pm m$ RC), composed of a proposed new generation of $nk \pm m$ RC (NG- $nk\pm m$ RC) and a Taylor Series expansion based fractional delay (FD) filter using Lagrange interpolation with Farrow structure, is proposed. Compared with conventional $nk \pm m$ RC, NG- $nk\pm m$ RC has more advantages while achieving the same performance as the conventional $nk \pm m$ RC. Different FD approximation algorithms are compared for the first time from the perspective of controller computational burden. The inner relationship between Taylor Series expansion method and Farrow structure FD filter is explained, detailed mathematical derivation is provided, and a complete set of FD filter design methods is formed. When the fundamental frequency is not constant, the performance of $nk\pm m$ RC to track or eliminate any specific $nk \pm m$ -order harmonics will be seriously degraded. However, without changing the sampling rate, the proposed FO-NG- $nk\pm m$ RC can be used to improve the frequency adaptive performance. What’s more, FO-NG- $nk\pm m$ RC provides a unified framework for integer/fractional-order $nk\pm m$ RCs. Experimental results of FO-NG- $nk\pm m$ RC controlled three-phase PWM inverter system show the effectiveness and advantages of the proposed FO-NG- $nk\pm m$ RC scheme.