## 1 Introduction
the stiffness characteristics of the flight control actuation system can be divided into three parts according to frequency: (1) Within the bandwidth of the closed control system, the stiffness can be controlled due to the controller' function that can guarantee the actuator output track the input. (2) At the reversal point of the frequency, the controller's adjustment effect is positive feedback to cause the actuator output to alter greatly, so the system stiffness is the lowest. (3) Since it is too late for the actuator to respond to the disturbance at high frequencies, its stiffness is related to the passive components of the system. EHA is developed as a potential substitute for the valve-control actuation system in the flight control actuation system, its stiffness is also a major consideration [21; 22; 23]. the stiffness characteristics of EHA and the valve-controlled actuator are distinct, especially at direct current and low frequencies. Regarding the stiffness of the valve-controlled actuator, the valve opening is not affected by the load pressure perturbance that keeps closed and its two chambers hold blocked. the impedance of the valve-controlled actuator is governed by the hydraulic stiffness of the two choked chambers of the actuator, where the enclosed oil has ability to counteract the load. If it is a double-rod actuator (the pressure goes up on one side of the piston and lowers on the other when the actuator is loaded), the impedance at the middle of the actuator stroke is \(4\beta A_{a}/L\) (where \(\beta\) is elastic modulus of oil, while \(A_{a}\) and \(L\) represent the area and stroke of the cylinder respectively), however, the stiffness of the single active side actuator is half of the former's. Thus, stiffness is related to piston displacement. When the dynamic side has the shortest liquid column length, the stiffness is the largest, and when the high pressure side has the longest liquid column length, the stiffness is the smallest at the other end of the cylinder. the minimum stiffness of the single-rod actuator is a quarter of the one of the double-rod actuators. Compared with the valve-controlled actuator, in fact, the EHA has no real impedance, since EHA is a combination of electric and hydraulic and its two chambers cannot be obstructed, considering the increasing load pressure can drive the motor rotation back. Therefore, the stiffness of EHA depends on the hydraulic stiffness of the actuator and the electrical stiffness of the motor. Load disturbance will drive the motor to rotate and cause the actuator output displacement to vary, so it is necessary to improve the electrical stiffness. the displacement of EHA-FPVM cannot be adjusted, so the disturbance torque of the motor cannot be regulated, so its electrical stiffness is constant. For the new configuration of ALS-EHA mentioned in this paper, the displacement can be actively shifted, so the disturbance torque to the motor can also be lowered, and the stiffness of the new configuration can also be enhanced. The structure for the whole paper is arranged as follows: Section 2 mainly presents the research on the principle analysis and mathematical modeling of ALS-EHA based on DLS-EHA configuration. Section 3 mainly studies the dynamic stiffness of ALS-EHA and the relationship between the stiffness at low frequencies and the hydraulic transmission ratio. Section 4 mainly compares the power matching of ALS-EHA with that of EHA-FPVM, and then further analyzes the former matching rule. In Section 5, the experiments of EHA-FPVM and ALS-EHA are compared to verify the performance of the latter, and final conclusions are presented.