地球同步轨道三星编队位置平衡研究

Research on Position Equilibrium of Three-Craft Formation In Geosynchronous Orbit

针对三卫星库仑力编队在地球同步轨道构型与指向控制问题,研究编队位置平衡解.旨在为稳定控制设计提供能控性依据与前馈平衡解。研究挑战一方面在于三星库仑力编队系统的仿射非线性,另一方面需保证平衡电荷解为实数解。首先在希尔坐标系下建立以构形参数为自变量的动力学模型,然后在特定假设条件下根据平衡解条件去解算平衡解对应的构形参数与控制输入,使得库仑力和重力抵消掉航天器间的相对加速度,实现航天器相对希尔坐标系的位置保持。最后通过数值方法得到了等腰三角形编队在不同希尔坐标轴平面内电荷量与方位角和顶角的关系,以及可行域百分比与顶角的关系。

This study focuses on the position equilibrium solution for three-craft Coulomb formation in GEO, and it aims at providing controllability and feed-forward charge solution for the stable control law. The control problem is challenging because the system is nonlinear and nonaffine. Besides, the solution of the control charges must be real. Firstly, the dynamic equation of the formation was derived. Then, the configuration parameters and control inputs were solved on certain condition, which makes the Coulomb forces and the gravitational forces to cancel relative acceleration between spacecrafts to realize the position equilibrium. Finally, by numerical simulations, we obtainedthe relationship between charge and orientation and vertex angle in different Hill-frame plane as well as the relationship between the percentage of feasible region with vertex angle.