## 1 Introduction  
The delivery pressure of the axial piston pump used in an airborne hydraulic system shown in Figure 1 must be set according to the highest pressure required by the aircraft load. Most of the hydraulic power is consumed in the form of overflow loss, causing low pressure to account for most of the flight time. The main form of overflow loss is the generation of a large amount of heat, which leads to an increase in temperature of the hydraulic system. This situation accelerates the progress of aging for the hydraulic oil and sealing rubber. The statistic data indicate that service life of mineral oil will be reduced by 90% when the fluid temperature is raised by 15 \({}^{\circ}\)C [1,2]. The variable pressure airborne hydraulic system is an effective method to solve this problem. At present, there are two aircraft hydraulic system pump source forms being proposed: dual pressure variable pump and intelligent variable pressure pump. A dual pressure variable pump (Dual Pressure Pump) airborne system has been put forward by the United States, Britain and other countries. During flight, the dual pressure pump operates in a high-pressure mode when required, and a low-pressure mode is used during the rest of the time. Compared to the constant pressure variable pump, energy efficiency has been greatly improved [3]. The dual-pressure variable pump of 21-35 MPa (3000-5000 psi) has been used in the F/A-18E/F by the United States [4]. Related research on dual pressure pumps can be found in many references. The dynamic mathematical model of the pressure regulation mechanism has been established, and numerical simulation research has been carried out. Methods such as setting the orifice and the effective volume of the pump outlet are used to reduce pressure overshoot [5; 6]. But the matching problem between the delivery pressure of the pump and the aircraft load is only partially solved. If the requirement of aircraft load is slightly above the low-pressure mode and far below the high-pressure mode, the pump needs to operate under a high-pressure mode and the power loss is still considerable. An intelligent variable pressure pump is another method to solve the problem. In the 1980s, engineers started to conduct research on intelligent variable pressure pumps. Because the intelligent hydraulic power supply system can provide fluid according to flight profile requirements, the power loss can be decreased. Abex corporation did some experiments on the F-15 \"Iron Bird\" [7]. The result indicated that the intelligent pump decreases the consumed power by 39% and the discharge fluid temperature decreases between 18 \({}^{\circ}\)C and 24 \({}^{\circ}\)C [8; 9]. Researchers have done a lot of research this. The intelligent pump is optimized by taking the system work efficiency as the objective function and the performance reliability index as the constraint condition. Compared to conventional constant pressure pump systems, the average efficiency of the intelligent pump system increased by 15% [10]. Some control methods such as sliding mode variable structure control, adaptive control strategy, proportional integral derivative (PID) control strategy, etc. are used for precise control of swash plate inclination and outlet pressure of intelligent pumps [11; 12; 13]. But the structure of the intelligent variable pressure pump system is complex, and sensors are needed to detect the signals of pressure, including temperature, swashplate inclination, etc. By introducing electro-hydraulic proportional technology to the existing dual-pressure piston pump, the delivery pressure of pump can be adjusted by the proportional solenoid input voltage. The structure is relatively simple, and the original dual pressure regulation function is retained. The same as for the ordinary constant pressure variable pump, a lot of research works have been done on the dynamic characteristics of the pressure continuous regulation electrohydraulic proportional axial piston pump.