Gurfil Pini
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA.
Ann N Y Acad Sci. 2004 May;1017:190-209. doi: 10.1196/annals.1311.012.
This paper investigates the problem of low-thrust orbital transfer using orbital element feedback from a control-theoretic standpoint, concepts of controllability, feedback stabilizability, and their interaction. The Gauss variational equations (GVEs) are used to model the state-space dynamics. First, the notion of accessibility, a weaker form of controllability, is presented. It is then shown that the GVEs are globally accessible. Based on the accessibility result, a nonlinear feedback controller is derived that asymptotically steers a vehicle from an initial elliptic Keplerian orbit to any given elliptic Keplerian orbit. The performance of the new controller is illustrated by simulating an orbital transfer between two geosynchronous Earth orbits. It is shown that the low-thrust controller requires less fuel than an impulsive maneuver for the same transfer time. Closed-form, analytic expressions for the new orbital transfer controller are given. Finally, it is proved, based on a topological nonlinear stabilizability test, that there does not exist a continuous closed-loop controller that can transfer a spacecraft to a parabolic escape trajectory.
本文从控制理论的角度，利用轨道要素反馈，研究了低推力轨道转移问题，包括可控性、反馈可镇定及其相互作用的概念。高斯变分方程（GVEs）用于对状态空间动力学进行建模。首先，提出可达性的概念，它是一种较弱形式的可控性。然后证明了高斯变分方程是全局可达的。基于可达性结果，推导了一种非线性反馈控制器，该控制器可将飞行器从初始椭圆开普勒轨道渐近引导至任何给定的椭圆开普勒轨道。通过模拟两个地球同步轨道之间的轨道转移来说明新控制器的性能。结果表明，在相同的转移时间内，低推力控制器比脉冲机动消耗的燃料更少。给出了新轨道转移控制器的闭式解析表达式。最后，基于拓扑非线性可镇定性测试证明，不存在能将航天器转移到抛物线逃逸轨道的连续闭环控制器。
