This article investigates the attitude control and stability analysis of an electric solar wind sail (E-sail) by considering elastic deflection of tethers while assuming main spacecraft and remote units as point masses. The attitude and orbital motion of the E-sail is analyzed by a high-order high-fidelity E-sail model derived from the nodal position finite-element method, where the attitude angles are implicitly described via the nodal coordinates. To overcome the difficulty in handling the stability analysis of high-order model under the Lyapunov framework, the E-sail's attitude dynamics is approximated explicitly by a reduced order analytical model with only three attitude angles. A sliding mode control law is proposed for the E-sail attitude control based on the reduced order analytical E-sail model and its stability is proved by the Lyapunov theory. Finally, two schemes are derived to map the control torque to either the control thrust at remote units or the voltages of main tethers respectively, which are applied to the high-fidelity E-sail model for attitude control. Numerical simulation demonstrates that the proposed control law performs similarly with the high-fidelity and reduced order analytical E-sail models if proper control gains are selected. It shows that the control law developed from the reduced order analytical E-sail model can stably control the attitude of a real E-sail. The investigation also indicates that the high-order flexible E-sail model provides an effective virtual testbed to evaluate the E-sail attitude control strategy derived from the reduced order attitude dynamics.

中文翻译：

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电动帆姿态控制与稳定性分析

本文在假设主要航天器和远程单元为点质量的情况下，通过考虑系绳的弹性偏转，研究了电动太阳风帆（E-sail）的姿态控制和稳定性分析。E-sail 的姿态和轨道运动通过节点位置有限元方法导出的高阶高保真 E-sail 模型进行分析，其中姿态角通过节点坐标隐式描述。为了克服李雅普诺夫框架下处理高阶模型稳定性分析的困难，通过只有三个姿态角的降阶分析模型明确地近似了E-sail的姿态动力学。基于降阶分析E-sail模型，提出了一种用于E-sail姿态控制的滑模控制律，并通过Lyapunov理论证明了其稳定性。最后，推导出两种方案将控制力矩分别映射到远程单元的控制推力或主系绳的电压，并将其应用于姿态控制的高保真E-sail模型。数值模拟表明，如果选择适当的控制增益，所提出的控制律与高保真和降阶分析 E-sail 模型的性能相似。结果表明，由降阶分析 E-sail 模型发展而来的控制律可以稳定地控制真实 E-sail 的姿态。