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The power quality of grid-connected inverters has drawn a lot of attention with the increased application of distributed power generation systems. The repetitive control technique is widely adopted in these systems, due to its excellent tracking performance and low output total harmonic distortion (THD). However, in an actual system, the ratio of the sampling frequency to the grid frequency cannot always maintain an integer, and then, the resonant frequencies of the repetitive control technique will deviate from the real grid fundamental and harmonic frequencies. This will degrade the performance of the system, particularly when the grid frequency varies. Even if the ratio is a fixed integer, the auxiliary function for stabilization in the conventional repetitive control technique will also increase the steady-state tracking error and THD of the system. In this paper, an improved repetitive control scheme with a special designed finite impulse response (FIR) filter is proposed. The FIR filter cascaded with a traditional delay function can approximate the ideal repetitive control function of any ratio. The proposed scheme varies the FIR filter according to varied grid frequency and maintains its resonant frequencies matching the grid fundamental and harmonic ones. Finally, the simulation and experimental results show that the improved repetitive control scheme can effectively reduce the tracking error and compensate harmonics of the inverter systems.