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针对刚性航天器姿态机动问题设计了能够有效减小能量损耗的非线性状态反馈控制器。由于修正罗德里格斯参数(modified rodrigues parameter,MRP)原始集在特征轴旋转角为±360°时存在奇异点,而相应的MRP映射集(shadow set)的奇异点处于特征轴旋转角为0°。将MRP原始集与映射集结合起来,实现全局非奇异姿态描述,解决了航天器姿态控制中的退绕(unwinding)问题。利用平方和(SOS)方法设计非线性状态反馈控制律,实现航天器全局姿态渐近稳定控制,同时实现更短控制路径,保证了控制过程中特征轴旋转角|Φ|≤180°。仿真结果表明了在干扰条件下该控制方法可有效控制航天器姿态稳定,且对能量损耗给出了定量分析结果。
A nonlinear state feedback controller that can effectively reduce energy loss is designed for the attitude maneuver of rigid spacecraft. Since the original set of Modified Rodrigues Parameter (MRP) has a singularity when the rotation angle of the feature axis is ± 360 ° and the singularity of the corresponding MRP shadow set is at a rotation speed of 0 °. The MRP original set and the mapping set are combined to realize the global non-singular pose description and solve the unwinding problem in spacecraft attitude control. The method of square sum (SOS) is used to design the nonlinear state feedback control law to realize asymptotic stability control of the global attitude of the spacecraft and to achieve a shorter control path, ensuring that the rotation angle of the characteristic shaft | Φ | ≤180 ° during the control process. The simulation results show that the proposed control method can effectively control the attitude stability of the spacecraft under disturbance conditions and give quantitative analysis results for the energy loss.