In DC distribution networks, a large number of converters lead to significant challenges in coordinated control. Traditional global optimization algorithms suffer from slow computational speeds and cannot meet the real-time converter control requirements, making it difficult to quickly respond to voltage deviations and converter load imbalances caused by fluctuations in load and renewable energy output. To address the decoupling problem between global optimization and real-time control for multiple converters in DC distribution networks, a coordinated optimal control method based on integral linear quadratic optimal control is proposed, which transforms the complex global optimization problem into a fast real-time tracking control task. First, a multi-objective optimization model for DC distribution networks is established, aiming at voltage restoration and load balancing among converters. By applying the principle of minimum, the optimal operating point of the system is determined. Second, an integral linear quadratic optimal control model is established based on the linear power flow of DC distribution networks. By solving the algebraic Riccati equation offline, optimal feedback and integral gains are obtained, enabling fast real-time control online. Finally, it is simulated and verified on the PSCAD/EMTDC platform. The results demonstrate that the proposed control method enables the system to rapidly converge to the globally optimal operating point within two control cycles, significantly reducing node voltage deviations and converter load imbalance.