The remote programmable constant current source is an important part of the servo control, and its dynamic model of whole control process is of great significance for the strategy generation and control optimization of the servo control. Aiming at the dynamic performance analysis and remote control of programmable constant current source, this paper proposes a dynamic modeling method based on edge-cloud collaboration. The proposed method takes into account the communication delay, data packet loss and other related situations in the cloud control process. It can simultaneously identify the structure and parameters of the model. Through the transformation of transfer functions of discrete domain and continuous domain, the continuous dynamic model of the constant current source is obtained to support the efficient control of the servo system, it overcomes the inconvenience of re-establishing the discrete model for different control time intervals in traditional side-end control. Finally, simulation verification and application simulation verification show that the method can accurately identify the dynamic model of the constant current source in the continuous domain and can apply to the actual edge-cloud cooperative program control system.