裸电动力绳系航天器非线性动力学及控制

Based on the particularity of structure of bare electrodynamic tethers and complexity of space environment, this project will establish a model for bare electrodynamic tethered spacecraft under multi-coupling effects. Then, inherent coupling factors for the multi-dimensional system are discussed, as well as perturbation factors. And nonlinear dynamics and control of the system are studied in detail. Next, a safety domain which makes the system long-term stable operation is proposed. Furthermore, with the help of physical experiment platform, all kinds of space environment perturbation would be simulated, such as vacuum, ionization, geomagnetism, microgravity and thermal alternating. Through dynamical scale model, a large number of nonlinear phenomena would be demonstrated, such as chaotic motion, parametric excitation vibration, thermal vibration, and magneto-elastic buckling. The project will focus on solving the following key issues, such as how to reasonably establish a model for bare electrodynamic tethered spacecraft under multi-coupling effects, how to study nonlinear characteristic which comes from the multi-dimensional time-varying system, how to find a safety domain which make the system stable operation in a large time scale, how to simulate the real space environment with multi-physical field coupling, how to accomplish the principle experimental verification of electrodynamic tethered system.

针对裸电动力绳结构特殊性及所处空间环境复杂性，本项目首先构建多场耦合作用下裸电动力绳系航天器模型，考虑其内在耦合关系及摄动因素，讨论该高维系统非线性动力学及控制问题。同时，提出一个能使系统长期稳定工作的安全域。最后，利用物理实验平台模拟真空、电离、地磁、热交变等空间环境，通过动力学缩比模型揭示系统存在的混沌运动、参激振动、热振动、磁弹屈曲等非线性现象。项目将重点解决以下关键问题：合理构建多场耦合作用下裸电动力绳系航天器模型；研究高维时变系统非线性问题；寻找一个大时间尺度下能使系统在轨稳定运行的安全域；实验模拟多物理场耦合的真实空间环境；完成电动力绳系统的原理性实验验证。

基于空间探测、碎片移除、能量传输等各类太空活动的迫切需求，本项目研究了一类在轨裸电动力绳系统的非线性动力学特性。首先，充分考虑环境热冲击、电流非线性分布等因素，针对带状裸电动力绳系统，构建能描述系统动力学行为的一系列含约束的离散刚体单元，基于多体系统动力学方法建立带状裸电动力绳系卫星刚-柔耦合模型。数值结果表明，所建立动力学模型可准确描述系绳的扭转、弯曲、构形变化等。其次，推导出一套欠驱动绳长变化解析控制律，能够对空间绳系卫星系统进行稳态释放。通过Floquet理论证明了系绳释放过程的局部稳定性。值得注意的是，即使对于运行在偏心率较大的椭圆轨道下的空间绳系系统，该绳长变化控制律亦能对释放系绳的面内及面外摆动实现有效抑制。同时，引入大气阻尼及地球扁率等摄动作用，研究了绳系系统面内混沌运动的存在性。自无扰系统先找到系统的双曲平衡点及异宿轨道，继而通过Melnikov函数研究在摄动作用下系统是否存在由于异宿轨道横截相交而产生的横截异宿点，最终给出发生混沌的必要条件。最后，本项目进一步拓展研究了一类环形绳系编队系统的自旋稳定性，对空间微重力环境下自旋绳系编队系统进行数值仿真及等效实验。建立地面等效实验系统，并得出该地面实验系统的动力学方程；导出使该空间闭环绳系编队系统的动力学方程与地面等效实验系统的动力学方程变换到同一个无量纲动力学方程的参数条件，以保证天-地系统的一致性；再利用达朗贝尔原理将地面等效实验系统转化为静力平衡系统。地面实验结果与数值结果一致，从而验证了该实验方法的正确性，给出了此类编队系统自旋稳定的临界值。

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