# SMCSPO-Based Robust Control of AUV in Underwater Environments including Disturbances
## 1 Introduction  
An autonomous underwater vehicle (AUV) is a robot that autonomously explores underwater environments without an operator's control. AUVs are being researched for the unmanned exploration of the underwater environment. When an AUV moves underwater, external forces such as added mass and drag force affect the operation of the AUV. In order to overcome the effects of various disturbances in the underwater environment, many studies have been carried out on the dynamics analysis and control theories of underwater vehicles [1, 2, 3, 4, 5, 6]. [PERSON] proposed the dynamics equation of the underwater vehicle, which consists of axial-lateral-normal force and rolling-pitching-yawing moment equations [1]. [PERSON] derived and linearized the 6-DOF dynamics equation to conduct an experiment with an AUV to which a PID controller was applied [2]. [PERSON] performed simulations using sliding mode control, integral sliding mode control, super twisting, and real twisting algorithms to control the lateral dynamics of an AUV and compared the results [3]. The real twisting algorithm showed the best performance in terms of the lateral dynamics of position and velocity control of the AUV of the proposed controllers. [PERSON] designed a thickness of a boundary layer and switching gain in the sliding mode control (SMC) algorithm to reducethe chattering phenomenon amplitude of the control input [4]. However, the chattering phenomenon is still observed in sliding mode control under strong disturbances. The SMC algorithm is a robust control theory that has been studied for AUV control in an underwater environment with strong nonlinearities and disturbances [3; 4; 5; 6]. However, SMC can cause the chattering phenomenon due to the use of high switching gain to suppress high uncertainty terms and disturbances when the nonlinear terms of the system dynamics are large. Chattering can adversely affect the control of underwater vehicles, and it can also overload the control fins due to chattering by high-frequency control input. [PERSON] proposed a sliding perturbation observer (SPO) to compensate for the chattering weakness of SMC control [7]. The SPO can compensate the assumed uncertainties and disturbances by estimating the nonlinear terms of the system dynamics. Therefore, the magnitude of SMC control input can be reduced by compensating the estimated terms. This method significantly reduces chattering in strong nonlinear systems by reducing the high switching gain of the SMC. Sliding mode control with a sliding perturbation observer (SMCSPO) has been used in several studies to robustly control the system and estimate perturbations. In surgical robot [8; 9; 10], hydraulic servo system [11; 12; 13; 14], robot manipulator [15; 16], and hot rolling simulator [17] areas, SMCSPO estimated the assumed uncertainties and disturbances of the system and showed better control performance than SMC. In this paper, an SMCSPO controller for AUVs is designed to increase the robustness of the orientation control of the vehicle, and its control performance is evaluated. In order to apply SMCSPO to the underwater vehicle, we derived the coefficients related to the underwater vehicle dynamics, which are required for the design of the robust controller. In addition, the control parameters of the SMCSPO are determined and the control stability is analyzed to ensure that the underwater vehicle can be stably controlled. To evaluate whether the SMCSPO controller is suitable for the control of an AUV, a MATLAB simulation is performed under several conditions and compared with the results of the PID controller. It is confirmed that the results using SMCSPO are superior to those using PID control, and the results show that the vehicle is stably controlled without chattering. The rest of this paper is organized as follows. Section 2 introduces the dynamics equation and the perturbation terms of the underwater vehicle. In Section 3, the controller and observer of SMCSPO and PID controller are designed for AUV orientation control.