Long-term ultra-precision synchronization between optical frequency combs (OFCs) and microwave oscillators is important for various fields, including scientific observation, smart grid, positioning and navigation, etc. Here, a phase-locked loop system based on fiber loop optical-microwave phase detector (FLOM-PD) is proposed to realize the synchronization of the repetition rate of OFCs and rubidium atomic clocks. Firstly, the scheme and locking process of the system are elaborated, then the mathematical model of the system is established, and the feasibility of the scheme is proved by theoretical analysis and experimental verification. After synchronization, the instability of the system reaches 8.69×10-12 at 1 s and 2.94×10-13 at 1 000 s, indicating that the phase synchronization system can achieve ultra-precision and stability of OFCs repetition rate.