This paper considers the dynamics of the circular restricted three-body problem (CRTBP) for the Earth–Moon system designing stationkeeping controllers at periodic orbits. Taking into account the \(L_1\) and \(L_2\) equilibrium points in this dynamics, it is constructed a family of periodic orbits in the vicinity of these libration points, called halo orbits. The orbits are constructed using an analytical approach as a first guess with a numerical method in addition, in order to correct the linear approximation procedure. Withal the stability of these libration points, trajectories are analyzed and proved to be unstable; a spacecraft moving near these points must use some correction maneuver to remain close to the nominal orbit. Two types of controllers are proposed for stationkeeping maneuvers performed by low-thrust power-limited propulsion system . The first controller is based on the linear quadratic regulator (LQR) and the second one is based on the nonlinear feedback control which uses the state-dependent Riccati equation control (SDRE). Finally, a parameters comparison analysis is performed taking into account different values of the weight matrices for both controllers at both halo orbits.

本文考虑了地球-月球系统在周期轨道上设计驻地控制控制器的圆形受限三体问题 (CRTBP) 的动力学。考虑到\(L_1\)和\(L_2\)在这个动力学的​​平衡点，它在这些平衡点附近构建了一个周期轨道族，称为晕轨道。轨道是使用解析方法作为第一猜测以及数值方法构建的，以校正线性近似程序。随着这些振动点的稳定性，轨迹被分析并证明是不稳定的；在这些点附近移动的航天器必须使用一些修正机动来保持靠近标称轨道。提出了两种类型的控制器用于由低推力功率限制推进系统执行的站位机动。第一个控制器基于线性二次调节器 (LQR)，第二个控制器基于使用状态相关 Riccati 方程控制 (SDRE) 的非线性反馈控制。最后，