## 1 Introduction  
Hydraulic actuators have more advantages than electric motors such as a large force output at high speed, high stiffness and durability, and rapid response [1; 2]. Due to these advantages, hydraulic systems are widely used in many applications including construction, mining, and nuclear industries, where semi-automatic control systems are being adopted as means of improving the efficiency, quality, and safety of operations. [PERSON] et al. [3] designed a manipulator using hydraulic actuators for nuclear decommissioning. However, hydraulic systems are more complex than electrical systems due to their highly nonlinear dynamics caused by phenomena such as fluid compressibility, nonlinear servo valve flow pressure characteristics, and dead band due to the internal leakage and hysteresis [4]. Besides its nonlinear dynamics, the main challenge of developing a control system for a hydraulic manipulator is the reaction force generated from the environment when it works as an excavator or dismantling manipulator. To obtain outstanding trajectory tracking performance, much of the research uses nonlinear control methods to compensate for the nonlinear features of an electro-hydraulic system. Furthermore, torque/force sensors are always used to measure the payload or reaction force from the environment. Sliding mode control is the most widely used nonlinear control algorithm for a hydraulic system with bounded disturbances, nonlinear terms, and system uncertainties. For example, in Reference [5],a sliding mode control with varying boundary layers is used for an electro-hydraulic position servo system. [PERSON] et al. [6] used a non-singular higher order terminal sliding mode approach for vehicle suspension control with a hydraulic actuator. Adaptive control is also widely used for hydraulic actuators in combination with sliding mode control for varying dynamics and disturbances. Many researchers apply adaptive control to overcome system parameter variations, and sliding mode control is used as an effective way for controlling nonlinear systems with uncertainties. However, precise and detailed modeling of the system is needed to adopt the update law to compensate for the variable dynamic parameters. For instance, a sliding mode control with adaptive update law for a hydraulic system with unknown nonlinear parameters is proposed in [7]. In [8], a sliding mode control with adaptive update law of uncertain load disturbances is used to control a hydraulic parallel robot. The adaptive update law is used to update the system's dynamic parameters with a detailed and precise dynamic model which contains the bulk modulus of the fluid, the coefficient of internal leakage, etc. In [9], an adaptive control scheme based friction disturbance compensator structure was proposed for motion control, which approximates the friction term with RBF-type neural network. However, in adaptive control, the dynamic modeling should be built complicatedly or precisely for adapting the adaptation law, which is difficult to design and implement in a real system [10]. In recent years, much research also applies the adaptive algorithm on the sliding mode control named as adaptive SMC (sliding mode control). Some adaptive-gain-based sliding mode control are mentioned for more robustness, which selects the adaptive gain of the switching surface [11; 12]. Some improved versions for an adaptive-robust controller with a time-delayed approach are shown in [13; 14], which do not require any knowledge of system dynamic information. Initially, however, the no model based adaptive SMC showed a lot of tracking error in their results. In this paper, we applied terminal mode control with a sliding perturbation observer (TSMCSPO) for a hydraulic system whose dynamics are only modeled as a simple second order system. The uncertainties, nonlinear terms, dynamic modeling errors of the system and disturbances are included by the definition of perturbation, which is estimated by the SPO (Sliding Perturbation Observer).