The article develops a mathematical model of the variable flow pump of the aircraft power supply, designed to simulate the operation of the power supply depending on the speed of the sustainer engine, oil temperature, pressure and supply (removable power). In addition, a control algorithm has been developed that provides the required quality of the transient process, which is achieved by installing additional hydraulic resistances between the servo piston cavity, the drain hydraulic line and the control spool, which change the flow characteristic of the pump and contribute to the fastest attenuation of the transient process and reduce its oscillation.