The robust control of a satellite in a three-dimensional ‘halo’ obit is studied. In order to introduce a quantifiable robust stability margin, as well as maintain a pre-selected orbit, a two-degree-of-freedom control strategy is proposed. The control is based on a time-periodic ${\mathcal{H}}_{\mathrm{\infty }}$ state feedback law and a time-periodic feed-forward preview signal that is based on an estimate of the drag influence. The feedback control stabilises the orbit and introduces a robustness margin. By anticipating and compensating for drag effects, the feed-forward control produces improved station keeping (the maintenance of a design orbit). The efficacy of these ideas is demonstrated by simulation results that are based on a Circular Restricted Thee-Body Problem (CRTBP) model. The feedback control is characterised by the solution of a time-periodic ${\mathcal{H}}_{\mathrm{\infty }}$ control Riccati equation. The feed-forward control comes from the solution of a linear time-periodic equation, solved backwards in time, that is driven by a disturbance estimate.

研究了三维“光环”讣告中卫星的鲁棒控制。为了引入可量化的鲁棒稳定裕度，并保持预先选择的轨道，提出了一种二自由度控制策略。控制是基于时间周期的${\mathcal{H}}_{\mathrm{\infty }}$状态反馈定律和基于对阻力影响的估计的时间周期前馈预览信号。反馈控制稳定了轨道并引入了鲁棒性裕度。通过预测和补偿阻力效应，前馈控制产生改进的站保持（维持设计轨道）。基于圆形受限人体问题 (CRTBP) 模型的仿真结果证明了这些想法的有效性。反馈控制的特点是时间周期的解${\mathcal{H}}_{\mathrm{\infty }}$控制 Riccati 方程。前馈控制来自线性时间周期方程的解，在时间上向后求解，由扰动估计驱动。