Fractional Compound Odd Repetitive Control for a Grid-Tied Inverters Using an IIR Filter

Due to the lack of rapidity of repetitive controllers, compound control strategies are generally adopted. Therefore, a compound structure based on PIMR (proportional integral multi-resonant) is proposed. Although the PIMR controller based on the RC (repetitive control) internal model architecture has improved speed and anti-disturbance, due to the RC core architecture, the system has a delay of sampling period $N$, so the PIMR-ORC(odd repetitive control) architecture is proposed. PIMR-ORC can provide high gains at the fundamental frequency and its odd harmonic frequencies, which reduces the delay link by half, so PIMR-ORC has a wider bandwidth and faster response speed. However, PIMR-ORC's control effect is barely satisfactory under the fluctuation of the grid frequency. Therefore, this paper proposes a double fractional implementation of PIMR-ORC on the basis of PIMR-ORC and renamed as Fractional Compound Odd Repetitive Control(FC-ORC). Through the fractional approximation of the compensation link $z^{m}$ and $N$, the FC-ORC is more adaptable to the change of the grid frequency. The paper analyzes the stability of FC-ORC and gives MATLAB/Simulink to demonstrate the effectiveness and feasibility of the reform plan.