伴随卫星最优小推力释放与回收控制

A Different Method for Optimal Low-Thrust Control of Release and Retrieval of a Concomitant Satellite

伴随卫星是在主星附近作周期性运动并为主星服务的卫星 ,其释放与回收控制是一项关键技术。文中研究了伴随卫星释放与回收的最优小推力控制。根据相对运动方程 ,利用最优控制中的极小值原理 ,建立了用恒值、连续工作、牛顿级小推力进行伴随卫星释放与回收的时间最短控制问题的数学模型 ,求得了最优解析解的表达式 ,并采用牛顿下山法求解了释放与回收的小推力工作最优时间、最优方向和最优变轨轨迹。

A concomitant satellite revolves around its main satellite, serving and observing it. The distance between the two satellites is usually about 1 km. Different from existing methods for optimal low thrust control of release and retrieval of a concomitant satellite, we will propose a new method. Like existing methods, we control the release and retrieval movement with a Newton grade thrust--a very low thrust that is constant in value and works continuously. Like them again, we use Minimum Principle in optimal control theory to establish the mathematical model of optimal control of release and retrieval from the usually used C W equations. Unlike existing methods, which are numerical ones, we obtain a convenient analytic solution, eq. (13), on the assumption that the two satellites run along equally high orbits. Using eq. (13) requires the determination of the end time of the motion; this determination can be done quite simply with Newton iteration method. We give a numerical simulation example. Simulation results, given in Table 1 and Figs. 1 through 6, show preliminarily that our method for optimal low thrust control of release and retrieval movement of a concomitant satellite is feasible.