## 1 Introduction  
A mobile satcom antenna (MSA) is a kind of satellite communication antenna which can maintain continuous and reliable communications between satellites and users in movement. MSAs are widely applied in vehicle carriers, flying platforms and vessels. The Jet Propulsion Laboratory (JPL) has developed several mobile vehicular antenna systems for the satellite-based applications [1]. Due to the uncertain working environment, such as bumpy roads, sea waves and airflows, there might be strong disturbances in actual systems [2]. MSAs seeking to achieve high data-rate communications require the inertial antenna to be capable of pointing to within fractions of a degree [3]. Stabilization is used in the antenna pointing control system to maintain the line of sight by isolating the disturbances caused by vehicle motion [4]. Generally speaking, the attitude sensor can be an attitude and heading reference system (AHRS) or an inertial measurement unit (IMU) [5]. The outputs of these inertial sensors are widely used as feedbacks for stabilization in antenna control systems [6]. The accuracy of control is influenced by many factors, mainly including the existence of unmodeled nonlinear uncertainty, random bias of states and sensor noises [7] and friction restriction, which decreases the accuracy most. The disturbances and uncertainties can lead to the degradation of tracking and stabilization accuracy of inertial stabilized platform in engineering applications [8]. Various decoupling control and disturbance rejecting methods have been developed to enable MSA with high performance. Though the PID control method is widely applied in engineering practice due to its simplicity and reliability, it is difficult to reduce the disturbances and uncertainties rapidly [8]. Therefore, this method offers low control accuracy and robustness. A feedforward scheme for a two axis inertial stabilized platform (ISP) was adopted to reject the periodic disturbing torque acting on the payload due to the static mass unbalance [9; 10], but the accelerometer signal may be easily distorted by the centripetal acceleration [11]. The \(H_{\infty}\) control method presents strong robustness, but it is highly conservative and the control accuracy is usually sacrificed [12]. Internal mode control can improve the disturbance rejection capability and robustness against model uncertainties, but the exact structural property of the disturbance needs to be known in advance [13]. The sliding mode control method is studied in depth for its unique robust control performance for nonlinear and uncertain systems. In the linear sliding mode, the deviation between the system and the desired trajectory is asymptotically convergent in exponential forms [14]. TSM control is improved and compared with the linear hyperplane based sliding modes, showing that the TSM offers some superior properties such as fast response, finite time convergence [15; 16]. However, the conventional TSM has many defects such as singular problem and chattering phenomena. An initial discussion about avoiding the singularity in TSM control was presented in [17]. In order to avoid the singular problem, many non-singular TSMs were proposed [14; 15; 18; 19; 20]. The good robustness of TSM is based on the large switching control gain, which is determined by the uncertain disturbances [20]. If the switching control gain is small, the uncertainty issues cannot be eliminated, whereas if the gain is large enough, the chattering phenomena would be enhanced. In many practical control systems, including DC motors and aircraft control system, it is important to avoid control chattering by providing continuous or smooth control signals [21]. According to the high order sliding mode algorithm proposed in [22], \"chattering removal\" can be achieved by combining the arbitrary-order sliding mode controller with the dynamic sliding mode. Another well-known way to reduce chattering problem in TSM is to use tanh function instead of the sign function [23].