A new approach for the pointing of satellite’s payload is improving the dynamics of satellites to more than 3-DOF. In this approach, there would be no requirement for satellite complete rotations to perform the payload’s mission. The purpose of this study is to derive Four Degrees of Freedom (4-DOF) equations of motion of a satellite and its payload. Therefore, the payload can observe an area of the earth, and simultaneously, the satellite can transfer data to the earth station. Lagrange dynamics are utilized to derive 4-DOF dynamic equations of the system. Then, the system of payload-satellite is controlled by the sliding mode control method with three different sliding functions. Environmental disturbances and appropriate time delay for Low Earth Orbit are applied to the nonlinear attitude equations. Numerical simulations demonstrate the effectiveness of the 4-DOF nonlinear dynamics of the payload-satellite system and indicate that the controller negates the effects of the nonlinear external disturbances and time delay. According to the results, the attitude states attain the reference targets of Euler angles and the time-varying payload with excellent precision and high convergence speed.

中文翻译：

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4自由度运动姿态方程：一种模拟灵活卫星动力学的新方法，有效载荷随时间变化而不受时间延迟和干扰

一种指向卫星有效载荷的新方法正在将卫星的动力学提高到超过 3 自由度。在这种方法中，不需要卫星完全旋转来执行有效载荷的任务。本研究的目的是推导出卫星及其有效载荷的四自由度 (4-DOF) 运动方程。因此，有效载荷可以观测地球的一个区域，同时卫星可以向地球站传输数据。拉格朗日动力学用于推导系统的四自由度动力学方程。然后，采用三种不同滑模函数的滑模控制方法对有效载荷卫星系统进行控制。低地球轨道的环境扰动和适当的时间延迟应用于非线性姿态方程。数值模拟证明了有效载荷卫星系统的四自由度非线性动力学的有效性，并表明控制器消除了非线性外部干扰和时间延迟的影响。结果表明，姿态状态达到了欧拉角和时变载荷的参考目标，精度高，收敛速度快。