## 1 Introduction  
Powerful propulsion sources are necessary for access to space, such as liquid rocket engines, ramjet engines, and their combinations [1, 2, 3, 4]. The traditional propellant feed system of liquid rocket engines mainly includes a turbine pump cycle and pressure-fed system. The pressure-fed system has the advantages of a simple structure, reliable operation, and convenience for multiple starts. However, the thrust chamber pressure is limited by the structural mass of the tank. The performance of a pressure-fed engine is poor, which is generally suitable for engines with low thrust and multiple starts [5, 6]. The turbine pump feed system uses the pump to pressurize the propellant, which greatly reduces the mass of the tank and improves the thrust chamber pressure. These engines have high specific impulse [7, 8, 9]. However, the structure of these engines is complex, generally including components such as gas generators, turbines, and centrifugal pumps. Their thrust adjustment range is small, which struggles to meet the requirements of multiple starts. A high-speed and high-performance motor can replace the traditional turbine as the driving machine of a pump in an electric pump feed system [10, 11, 12]. Previously limited by miniaturized high-energy power supply, accurate propellant control, light high-speed motor, and other technologies, it was once less used in the aerospace field. As technology and manufacturing progressed, especially with regard to the development of high-energy-density batteries, brushless DC motors, and 3D additive manufacturing, its use has gradually emerged in the aerospace field [13; 14; 15]. It has been demonstrated that the propellant can be pressurized by electric pumps, and nitrogen pumps have been manufactured [16]. Compared with the turbine pump, they have the advantages of high efficiency, convenient adjustment, and simple structure. Some researchers have studied the characteristics of electric pumps by building mathematical and analytical models. [PERSON] and others [17; 18] analyzed the concept and characteristics of an electric pump feed system. They proposed that, in the case of a long operating time, high chamber pressure, or large thrust, the electric pump feed system has more obvious advantages than the pressure-fed system. However, they used an empirical formula to calculate the mass, which is not applicable to all propulsion systems. [PERSON] et al. [19] studied the influence of thrust, mixing ratio, and thrust chamber pressure on the weight of the electric pump feed system. The results showed that there is a critical operating time under different chamber pressures. When the operating time is greater than the critical time, the weight of the electric pump system is light. However, under the conditions of 5.0  kN thrust and a combustion chamber pressure not exceeding 10.0 MPa, the critical time of the propulsion system would be inapplicable for different thrust magnitudes. With the development of key technologies such as batteries, rockets with electric pumps have great potential for development in terms of system weight and system stability [20]. For the electric pump feed system, the weight and the driving method have been studied separately. [PERSON] [21] compared the mass of the electric pump feed system and pressure-fed system. The results showed that the motor mass is mainly affected by thrust and thrust chamber pressure, while the battery mass is also affected by operating time. Nevertheless, this theoretical analysis based on a high-performance battery and high-speed brushless motor needs to be verified by engineering practice. [PERSON] et al. [22] used the maximum torque-to-current ratio as the main strategy for energy efficiency optimization of the motor control system. On the basis of this strategy, a permanent magnet synchronous motor energy efficiency optimization control algorithm was proposed. At present, vector control methods are mostly used to regulate the rotation speed of the electric pump in rockets.