Journal of the Brazilian Society of Mechanical Sciences and Engineering ( IF 2.2 ) Pub Date : 2021-11-17 , DOI: 10.1007/s40430-021-03267-z Saman Zarei 1 , Kamran Daneshjou 1 , Majid Bakhtiari 2
The Geometric method is one of the nonlinear methods for expressing the large-scale relative motion of satellites. In this paper, the equations of the Geometric method for perturbed orbits have been developed in the presence of third-body and \({J}_{2}\) gravitational perturbation. Then, these equations are employed for relative tracking and attitude control of two satellites to apply inter-satellite links. To validate the developed equations, the results obtained from these equations are compared to the main-body-centered-based relative motion (MCRM) model. Also, two control laws are designed to track and control the relative attitude of both satellites with consideration of external disturbances, the inertia uncertainty (due to fuel sloshing), and actuator saturation (due to bounded thrust). To establish inter-orbital links, it is necessary that the payload of satellites (the receiver and transmitter's antennas) are aligned in the same direction (named the reference trajectory). Due to the uncertainty in the attitude dynamics of systems and external disturbances, a robust controller must be applied to obtain control laws. The controller of the base satellite is designed so that the base satellite tracks the desired path (the reference trajectory) obtained from the relative motion equations. Furthermore, simultaneously and continuously, the target satellite control system tracks the base satellite antenna. For this reason, the external disturbances imposed on the base satellite affect the tracking control system of the target satellite. Also, a new definition of modified Rodrigues parameters (MRP) vector is proposed to design the tracking controllers that improve the control effort and convergence rate for the application of the inter-satellite links. Finally, two appropriate control laws for two satellites are designed through sliding mode control (SMC) theory subject to actuator saturation, inertia uncertainties, and external disturbances.
中文翻译:
存在第三体摄动并考虑致动器饱和的两颗卫星的相对姿态跟踪
几何方法是表示卫星大尺度相对运动的非线性方法之一。本文在第三体和\({J}_{2}\)引力扰动。然后,将这些方程用于两颗卫星的相对跟踪和姿态控制,以应用星间链路。为了验证所开发的方程,将从这些方程获得的结果与以主体为中心的相对运动 (MCRM) 模型进行比较。此外,设计了两个控制律来跟踪和控制两颗卫星的相对姿态,同时考虑到外部干扰、惯性不确定性(由于燃料晃动)和执行器饱和(由于有界推力)。为了建立轨道间链路,卫星的有效载荷(接收器和发射器的天线)必须对准同一方向(称为参考轨迹)。由于系统姿态动力学和外部干扰的不确定性,必须应用鲁棒控制器来获得控制律。基地卫星的控制器被设计成基地卫星跟踪从相对运动方程获得的期望路径(参考轨迹)。此外,目标卫星控制系统同时且连续地跟踪基地卫星天线。为此,施加在基星上的外部干扰会影响目标卫星的跟踪控制系统。此外,提出了修正罗德里格斯参数 (MRP) 向量的新定义,以设计跟踪控制器,以提高卫星间链路应用的控制工作和收敛速度。最后,在致动器饱和的情况下,通过滑模控制(SMC)理论为两颗卫星设计了两个合适的控制律,