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±m-order harmonic repetitive controller (FO-NG-nk±m RC), composed of a proposed new generation of nk±m RC (NG-nk±m RC) and a Taylor Series expansion based fractional delay (FD) filter using Lagrange interpolation with Farrow structure, is proposed. Compared with conventional nk±m RC, NG-nk±m RC has more advantages while achieving the same performance as the conventional nk±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±m RC to track or eliminate any specific nk±m-order harmonics will be seriously degraded. However, without changing the sampling rate, the proposed FO-NG-nk±m RC can be used to improve the frequency adaptive performance. What's more, FO-NG-nk±m RC provides a unified framework for integer/fractional-order nk±m RCs. Experimental results of FO-NG-nk±m RC controlled three-phase PWM inverter system show the effectiveness and advantages of the proposed FO-NG-nk±m RC scheme.

A Novel Fractional Delay Proportional–Integral Multi-Resonant-Type Repetitive Control Based on a Farrow-Structure Filter for Grid-Tied Inverters

“…Expression (22) indicates that to maintain the stability of the PIMR-RC system while ω varies from zero to the Nyquist frequency, the vector (1 − z m k r S(z)P 0 (z)) should fall within the unit circle. Accordingly, the system stability condition is independent of the FFD filters.…”

“…Accordingly, the system stability condition is independent of the FFD filters. Thus, according to the literature [12], Equation (22) can be derived as…”

“…Define the error convergence function for the system by H(e jωT s ) = 1 − k r e jωmT s S(e jωT s )P 0 (e jωT s ) (27) According to the system stability Formula (22), the Nyquist graph of the H(e jωT s ) should be within the unit circle to ensure system stability. Figure 9 shows the trajectories H(e jωT s ), with k r varying from 14 to 18.…”

“…For each new delay, the polynomial coefficients of the filter remain unchanged, which greatly decreases the computational load of the controller. Moreover, the Farrow-structure filter is easier to implement in hardware and reduces hardware complexity [21,22]. Another benefit of the Farrow-structure filter is that the fractional delay item d is independent of the specific filter coefficients [23].…”

Novel Fractional-Order Repetitive Controller Based on Thiran IIR Filter for Grid-Connected Inverters

“…The solutions to this problem can be divided into three categories: variable sampling frequency scheme [12], higherorder RC (HORC) [13], and fractional-order RC (FORC) [14], [15]. [12] proposes a scheme for ensuring that the ratio of the sampling frequency to the grid frequency is an integer by changing the sampling rate to enhance the frequency adaptability of CRC.…”