## 1 Introduction  
Heavy-duty machinery has many features, such as big load inertia, huge flow rate, and a vast amount of energy transmission; hence, hydraulic servo systems are widely used in those industrial applications. The separating-metering electro-hydraulic system (SMEHS) dismissed the mechanical linkage between the metering-in orifice and the metering-out orifice when compared with the traditional spool valve-controlled system, so the SMEHS has more freedom of degrees and it has more control flexibility [1; 2; 3; 4; 5]. However, the pressure of the cylinder metering-out chamber was often designed to be small to save energy. When the load force drastically changes, the SMEHS is easy to overshoot and oscillation, which means that the SMEHS does not have enough damping.  
Some control schemes were developed by researchers to increase system damping [6; 7; 8]. Generally, these schemes fall into two categories. The first category is the \"passive\" damping scheme. Theseschemes typically add accumulators or orifices to the hydraulic circuits [9] or they use the properties of the leakage and viscous friction to improve the system damping ratio. Although this technique is simple to use and easy to adjust, it causes energy loss and decreases the efficiency of the servo system under steady-state conditions. Besides, the passive damping scheme achieves limited damping effects; at the same time, it increases the nonlinearity of the servo system and then increases the difficulty when designing the controller. [PERSON] and [PERSON] analyzed the damping characters and presented a method to dimension the outlet orifice area in pressure compensated closed center mobile systems [10]. That method was a kind of passive damping method that transferred the kinetic energy into the thermal energy by the outlet orifice.  
The second category is the \"active\" damping scheme. The term \"active\" means that these system parameters are monitored, and signals are generated to control the hydraulic actuators in such a way that the oscillations are cancelled out [11; 12]. This method applied external energy into the system. [PERSON], [PERSON], and [PERSON] designed an active damping control law to suppress the vibration of the wheel loader [13]. A gain scheduler that was based on the real-time operating condition determined the parameters. [PERSON] and [PERSON] discussed the active compensation methods while using acceleration and pressure transducer signals in the electro-hydraulic servo system [14].  
In this paper, the damping characteristics of the SMEHS are studied. The main contributions are: The novel active damping strategy for separating-metering electro-hydraulic system is proposed to increase the system damping, in which the robust backstepping controller with tracking differentiator and nonlinear disturbance observer is designed to increase the damping and suppress the oscillation.  
The rest of this paper is organized, as follows. In Section 2, the active damping strategy is proposed and the effectiveness of the active damping strategy is theoretically proved. In Section 3, the mathematical model of SMEHS is developed. In Section 4, the robust backstepping controller with tracking differentiator and nonlinear disturbance observer is designed. In Section 5, the experiment and discussion are conducted. The last section presents the conclusions. Besides, there are many abbreviations in this paper. For ease of understanding, all the abbreviations and their definitions are listed in Nomenclature.