## 1 Introduction  
As the \"skeleton\" and \"muscle\" of the aircraft structure, the flight control actuation system plays an irreplaceable role in its structure [1; 2; 3]. At present, most civil and military aircraft use a central hydraulic oil source for centralized fluid supply, adopt engine-driven pumps to provide high pressure, and employ servo valves to implement servo control of the rudder surface and landing gear through the throttle principle [2; 3; 4]. This method has mature technology and good dynamic performance, but low efficiency and complex pipeline layout problems have become the main factors restricting the further improvement of aircraft performance [5]. In modern battlefields, it is increasingly demanding for fighter jets maneuverability, energy efficiency, fuselage layout, survivability, etc., and this raises a higher challenge requirement for flight control actuator system as one of the key components of airborne electromechanical systems and flight control systems [6]. With the exploded appearance and swift advancement of more/all-electric-aircraft (MEA/AEA), a power-by-wire actuation system has become main steam behind aviation progression, which exterminates the desideratum for the aircraft's classical hydraulic system and only requires a variety of energy procreation (electric power) resulting in simplifying secondary energy systems, so it brings about more advanced reliability and lowers design and maintenance costs [7; 8; 9]. EHA is an attractive category of power by wire, and it utilizes a hydraulic pump as a transmission reducer to transform the motor's rotational motion into the linear motion of the actuator's output with other components, such as oil supply circuit, bypass valve and safety valve, as shown in Figure 1. Hydraulic coupling allows greater flexibility in integrated design of EHA components. the installing position and direction of the motor and pump relative to the actuator can be flexibly adjusted to satisfy the demand for integrated volume size. This is a superiority of EHA compared to another candidate power-by-wire electromechanical actuator (EMA). the installing position and direction of motor and gear of EMA do not allow to be dexterously shifted [10]. EHA can regulate the transmission ratio by controlling the pump displacement. Adjustable transmission ratio can increase the actuator stiffness, reduce integration volume, and decrease system heating. In the flight control system, using EHAs instead of the currently used relatively mature electro-hydraulic valve-controlled actuators, there are three prevailing concerns, namely heating, size, and stiffness [11]. So far, the average efficiency of the EHA applied in the aviation field is about 35%, and the bandwidth is generally about 7 Hz [12]. EHA heating is an imperative dilemma. In a central hydraulic pump system, heat loss is transferred from the actuator to the central heat exchanger via hydraulic fluid, however EHA has no fluid exchange, so a separate heat exchanger mounted on the EHA or a fluid radiator added to the aircraft is required for cooling, which will greatly increase the difficulty for the confined space to package the actuator neighboring the control surface. an important source of heat loss is the nature of the aerodynamic load. the operating conditions of EHA include forward load and reverse load. When EHA operates under aiding load condition, the aerodynamic load works on the actuator, reversely driving the pump to rotate the motor as generator. the aiding-load energy is converted into electric energy which moves in the form of a current in the system. Another vital reason for EHA heating is the low efficiency of the system components. the most remarkable one is the motor copper loss. the motor torque is proportional to its current. the torque required to balance the load is proportional to the pump displacement which necessarily matches the motor speed and the actuator piston area to meet the actuator speed.