# Delay Analysis and the Control of Electro-Hydrostatic Actuators
## 1 Introduction  
In aviation, more electric aircraft (MEA) is becoming a hotspot as it outperforms traditional aircraft in terms of weight reduction, performance improvement, and increasing efficiency [1, 2]. The \"more electric\" that uses electricity as the primary power source for the control system can reduce the number of power transfer systems. It utilizes the potential of ultra-reliable miniaturized power electronics, fault-tolerant electrical distribution systems, and electric generator/motor drives/actuators to increase performance and to reduce costs [3, 4]. A power-by-wire (PBW) flight control system is the critical technology for MEA. It removes the centralized hydraulic system to obtain the advantages of the MEA, promoting broad use of electro-hydrostatic actuators (EHA). The EHA system is a form of PBW and the PBW makes the system more reliable. The PBW increases efficiency of MEA, and is needed in next generation all-electric aircraft (AEA) [5]. It is widely recognized that the EHA is an essential component of PBW [6, 7, 8]. Electro-hydrostatic actuators (EHA) were proposed in the 1990s, allowing the transmission of power from the electric to the hydraulic [9, 10, 11]. Compared to the traditional electro-hydraulic control system, the EHA system uses PBW technology that has high energy density, making it stand out from the numerous actuator systems and become a research hotspot for aircraft control [12, 13]. In 1992, [PERSON] applied EHA in the F-18 control system, and an experimental verification was performed on the flaps of the F18 in1994 [14], which obtained an excellent result. Over the past decades, EHA has been applied to aircraft successfully. Due to the incompressibility of oil, the hydraulic lock can keep the position output of the EHA system unchanged when the load changes. To further save energy and to avoid the energy loss caused by the continuous operation of the motor when the load changes or the pump becomes a hydraulic motor due to the load change after the motor stops working, the hydraulic lock is applied in the EHA system to realize an internal contracting brake. As mentioned above, the EHA is applied to the MEA, and the EHA system can be used in the control of the MEA on the angle of the compressor guide vane. The angle of the compressor guide vane is adjusted only when the rotor speed changes greatly, but the load of the aeroengine guide vane on the EHA system is constantly changing. Therefore, the position control of the aeroengine guide vane angle needs a low response speed, so the BHL-EHA system has good adaptability, which makes full use of the advantages brought by the hydraulic lock that is applied in the EHA system. However, the EHA has a position delay output, especially when the load is large or the hydraulic lock is applied in the system. Particularly when the motor speed of the EHA system is low, the delay is especially obvious. So, it is still necessary to analyze the delay of the BHL-EHA system with a low-rated motor speed. The reason for the delay is that it takes time for the pressure to reach the threshold that can start the piston cylinder in the EHA system. So, the factor that influences the pressure and the pressure requirement needs to be analyzed. [PERSON] proposed the EHA with a pressure accumulator [15] to maximize efficiency, but they did not use hydraulic locks and the delay in their system is not significant. [PERSON] proposed an EHA system with two pressure accumulators and an electromagnetic valve as a hydraulic lock [16]. Although the pressure accumulator improves the dynamic performance of the EHA, it gains the weight of the EHA and they did not study the delay. Many EHA systems realize the hydraulic lock using an electromagnetic valve [16; 17], which can reduce the delay by controlling the electromagnetic valve, but it makes control more complicated. References [18; 19] introduced the pilot check valve as the hydraulic lock, but the influence of the hydraulic lock was not studied, and the delay was not shown in their study.