The hydraulic support liquid supply system provided power for the hydraulic support, serving as the core to ensure safe support of the coal mining face and to maintain continuous, efficient, and stable advancement of the coal mining operations. The hydraulic support faced complex loads while operating on the fully mechanized mining face. To meet the requirement of rapidly following the coal mining machine’s movement, numerous actuators of the hydraulic support frequently performed sequential actions, and the liquid demand of the hydraulic support varied strongly over time, causing the hydraulic system to endure constant pressure and flow shocks, making it difficult to ensure the production efficiency and equipment reliability of comprehensive working face. This study analyzed the pressure and flow characteristics of the liquid supply system during the periodic actions of the hydraulic support. To address the strong time-varying load and liquid demand during the simultaneous actions of the hydraulic support, an Extended State Observer (ESO) was designed for observation and compensation. An Active Disturbance Rejection Control (ADRC) method suitable for the configuration of a rapid pump-controlled liquid replenishment and pressure stabilization system was proposed, and a co-simulation model of the mechanical and control systems was developed by comparing indicators such as the pressure fluctuation amplitude and the execution time of the hydraulic support actions. The pressure stabilization control effects of the ADRC method, the PID control method, and the traditional multi-pump coordinated liquid supply mode under typical time-varying conditions were analyzed and compared. A simulation test system was constructed to validate the results, demonstrating that the ADRC rapid fluid replenishment and pressure stabilization control method can suppress load disturbances, reduce the system pressure fluctuation amplitude by 20.8%, and shorten the hydraulic support operation time by 2.6%.