## 1 Introduction  
The electro-hydraulic servo loading system is a hydraulic force (moment) control system which is used to apply the requested load to the actuating component or the manipulation component. For example, the experiment on the hydraulic booster in the helicopter-manipulating system needs this system. The hydraulic booster is in charge of transmitting the manipulation displacement signal and amplifying the manipulating force; meanwhile, it must respond to the driver's command with high accuracy and fast speed under the high-frequency aerodynamic load. Through the electro-hydraulic loading system, which is employed to simulate the aerodynamic load on the ground, the control performance with the load of the booster can be evaluated, and this has vital significance in product performance experiments and improvement. There are two types of loading: active and passive. The difficulty in the passive loading system is achieving the desired loading force on the condition of accompanying the motion of the loaded plant. There exists an unavoidable problem in such a loading system, namely how to restrain the motion disturbance (the so-called extraneous force [1]), which originates from the motion of the loaded plant. This disturbance seriously affects the force-tracking accuracy, reduces the closed-loop bandwidth of the loading system, and seriously causes gradation in the force control performance. Therefore, extraneous force suppression is the key issue to ensure the reliability and confidence level of the experiment. As noted by [PERSON] and [PERSON] [2], for hydraulic loading systems, the tracking performance is limited by flow nonlinearity, parametric uncertainty, and motion disturbance, and cannot be guaranteed with a simple PID control algorithm. Thus, the online self-tuning fuzzy PID [3] and the grey predictor fuzzy PID [4] control algorithm were implemented, respectively. Robust control technologies, such as quantitative feedback theory (QFT) [5; 6], the H\(\infty\) mixed sensitivity method [7], variable structure control [8; 9], neural network control [10; 11], and fractional order adaptive robust control [12] had been investigated for robust force tracking in the presence of disturbances and uncertainty. Focusing on nonlinear characteristics and parameter uncertainty, some nonlinear system control methods [13; 14; 15; 16] had also been investigated. In the above studies, the extraneous force had been treated as a part of the loading error, and the force-tracking performance was obtained through feedback and feed-forward controllers. From the forming mechanism of the extraneous force and the viewpoint of disturbance compensation, [PERSON] [1] in China proposed a disturbance compensation method based on the structure invariance principle, actuator velocity was used to eliminate the actuator's motion disturbance. This feed-forward compensation belongs to the direct disturbance compensation. Although it had made good elimination results in a low-frequency loading system, there were problems in physical implementation and velocity acquisition. Moreover, there is a lack of robustness against system uncertainty. In order to overcome the difficulty in acquiring velocity, a velocity synchronization method [17] was proposed, where the position input of the servo valve was alternatively utilized as a velocity signal to design the compensator. In view of improving the robustness of the compensation term, a hybrid control method [18] and dual-loop control [19] had further been proposed. Considering system uncertainties, the disturbance observer-based controller with a double-loop structure [20; 21] was investigated. Problems of disturbance suppression and force tracking had been solved separately: the inner loop compensator was designed to restrain the disturbances and perturbations and to make the actual plant approximate the given nominal model, and the overall performance of the system was improved by the outer loop controller.