The LCL-active power filter can effectively compensate for the harmonic of a power grid, but an LCL filter has a resonance problem. Capacitive current proportional feedback active damping is the main way to suppress LCL resonance. However, with digital control, the resonant point will change with the grid impedance, and this makes it difficult to select the feedback coefficient. To solve this problem, this paper researches a selection method of feedback coefficient to adapt to a wide range of grid impedance variation, derives the stability conditions of the system under different feedback coefficients and harmonic frequencies, and optimizes the design of the feedback coefficient to meet the requirements. In addition, with the increase of grid impedance, the LCL resonant frequency becomes smaller and the system bandwidth becomes narrower. When the traditional quasi PR control is used to compensate for the high order harmonics, it is easy for the phase frequency curve of the system to cross the -180o line at the resonance point of the controller. This leads to instability of the system. Phase compensation is proposed to improve the phase angle at the gain of the controller, and the detailed design method is given. Theoretical analysis shows that the proposed robust controller optimization design method can ensure good harmonic compensation ability and a wider stable operation range of active power filter. Simulation and experimental results verify the correctness of the theoretical analysis. This work is supported by the National Natural Science Foundation of China (No. 51407184).