Universal Fractional-Order Design of Linear Phase Lead Compensation Multirate Repetitive Control for PWM Inverters

Abstract

Abstract-Repetitive control (RC) with linear phase lead compensation provides a simple but very effective control solution for any periodic signal with a known period. Multirate repetitive control (MRC) with a downsampling rate can reduce the need of memory size and computational cost, and then leads to a more feasible design of the plug-in repetitive control systems in practical applications. However, with fixed sampling rate, both MRC and its linear phase lead compensator are sensitive to the ratio of the sampling frequency to the frequency of interested periodic signals: (1) MRC might fails to exactly compensate the periodic signal in the case of a fractional ratio; (2) linear phase lead compensation might fail to enable MRC to achieve satisfactory performance in the case of a low ratio. In this paper, a universal fractional-order design of linear phase lead compensation MRC is proposed to tackle periodic signals with high accuracy, fast dynamic response, good robustness, and cost-effective implementation regardless of the frequency ratio, which offers a unified framework for housing various RC schemes in extensive engineering application. An application example of programmable AC power supply is explored to comprehensively testify the effectiveness of the proposed control scheme.Index Terms-repetitive control, DC/AC inverter, multirate repetitive control, phase lead compensation, Lagrange interpolation polynomial, programmable AC power supply

Virtual Variable Sampling Repetitive Control of Single-Phase DC/AC PWM Converters

“…In contrast to fractional-order RC [27]- [29], VVS-RC is able to deal with a signal with larger frequency variation range. For instance, a 3rd-order FIR filter in [27]- [29] is able to approximate the fractional delay z −N f from z 0 to z −3 . For a 10 kHz sampling frequency system, it can deal with the reference signal with the frequency from 59.17 Hz to 60.24 Hz when the overall delay range is set from z −166…”

“…is approximated by an n th -order finite impluse response (FIR) filter in [27]- [29]. A linear-phase-lag low-pass filter was designed to compensate the fractional delay length [30].…”

“…A linear-phase-lag low-pass filter was designed to compensate the fractional delay length [30]. Although these methods show improvements, novel and generic solutions are needed since the complex correction factor in [26] is difficult to be implemented, the compensation methods in [27]- [29] are only designed to approximate the fractional delay part of the ratio of sampling frequency to reference frequency. If the variable reference frequency leads to fractionalorder delay length N f beyond the range [0, n], the fractional delay method is not able to provide an accurate compensation.…”

Optimal Performance Design Guideline of Hybrid Reference Frame Based Dual-Loop Control Strategy for Stand-Alone Single-Phase Inverters

“…Step 1: Specify the phase margin and the gain margin of the system, determine the satisfactory region of f c and f g according to (10), (11) and define K>0 and K p >0;…”

“…However, the parametric sensitivity, which exists in the system due to the high-order plant controlled by the deadbeat controller, can reduce the system stability margin. In [10]- [16], the repetitive control is presented, which shows an excellent control performance for periodic signals. This feature makes it very effective for suppressing the harmonics and emulating various scenarios of power grids.…”