Disturbance suppression, especially high-frequency disturbance suppression beyond the closed-loop bandwidth, is the core of realizing high-precision stability control for tip-tilt correction systems. Repetitive control has good performance of periodic trajectory tracking and disturbance suppression, which is applied to the stability control of high-precision systems. The high-frequency disturbance suppression problem of the tip-tilt correction system is analyzed in this paper, and the performance of high-frequency disturbance suppression based on repetitive control is summarized. To solve the problems of natural frequency drift and waterbed amplification in traditional repetitive controllers, a comb-like repetitive controller based on Youla parameterization is designed to suppress high-frequency disturbances beyond the closed-loop bandwidth. In order to solve the problem that the integer-order repetitive control is only effective for specific frequency points, especially in most high frequency regions, the controller will fail due to disturbance fluctuations and uncertainty, an all-pass frit-order delay filter is optimized to suppress the high frequency disturbance at any frequency point up to Nyquist frequency in the tip-tilt correction system. Finally, a parallel repetitive control scheme is designed to suppress the vibration of aperiodic structures which is difficult to suppress, and its robust stability and effectiveness are discussed.