The recently proposed space tether-sail system could enable various interesting and important potential space missions thanks to its thin and long connecting tether and solar radiation pressure (SRP) force without consuming propellants. This paper focuses on nonlinear libration and its control of a tether-sail system in Earth polar orbits. Firstly, nonlinear coupled in-plane and out-of-plane dynamics of the system with a rigid mass-distributed tether and two point masses (a chief satellite and sail respectively) is established using the Lagrangian equation method. Secondly, the predicted occurrence of chaotic in- and out-of-plane librational motions is verified utilizing numerical tools such as presenting the time history of libration, the phase plane, the Poincaré section and power spectral density(PSD). Specifically, the paper investigates the sensitivity of nonlinear dynamical responses to initial values, focuses on the chaotic motion caused by the coupling between the in- and out-of-plane librations, the perturbation of the Earth gravitational field and the small eccentricity of the orbits, also studies the nonlinear librational characteristics influenced by the initial mechanical energy (the Hamiltonian). Thirdly, chaotic librational motions will be controlled merely using modulatable SRP force by the sail propellantlessly. A sliding mode controller based on exponential approaching law is developed. To mitigate the effects of control torque saturation, an input compensator based on Radial Basis Function (RBF) neural network is designed. In addition, to address the cumbersome and inefficient manual tuning of control parameters for the sliding mode controller, a parameter tuning algorithm based on Learning Automata is designed. This algorithm is capable of tuning a high-quality set of controller parameters within 100 iterations. The effectiveness of the propellantless actuators for chaotic libration motion control and developed control algorithm is supported by numerical simulations.

中文翻译：

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J2扰动下地球极轨道空间系绳帆系统的混沌振动与控制


最近提出的太空系绳帆系统由于其细而长的连接系绳和太阳辐射压力（SRP）力而无需消耗推进剂，可以实现各种有趣且重要的潜在太空任务。本文重点研究地球极轨道系绳帆系统的非线性振动及其控制。首先，利用拉格朗日方程方法建立了具有刚性质量分布系绳和两个点质量（分别是主卫星和帆）的系统的面内和面外非线性耦合动力学。其次，利用振动时程、相平面、庞加莱截面和功率谱密度（PSD）等数值工具验证了混沌面内和面外振动运动的预测发生。具体来说，本文研究了非线性动力学响应对初始值的敏感性，重点研究了面内和面外振动耦合、地球引力场摄动和轨道小偏心率引起的混沌运动。 ，还研究了受初始机械能（哈密顿量）影响的非线性解放特性。第三，仅使用帆的可调节 SRP 力即可控制混沌平动运动，而无需推进力。开发了一种基于指数逼近律的滑模控制器。为了减轻控制扭矩饱和的影响，设计了一种基于径向基函数（RBF）神经网络的输入补偿器。此外，针对滑模控制器手动整定控制参数繁琐、低效的问题，设计了一种基于学习自动机的参数整定算法。 该算法能够在 100 次迭代内调整一组高质量的控制器参数。用于混沌振动运动控制的无推进剂执行器和开发的控制算法的有效性得到了数值模拟的支持。