基于Krylov子空间法的柔性航天器降阶研究  

Model Order Reduction of Flexible Spacecraft Based on Krylov Subspace Method

作　　者：李莉[1] 刘铸永[1] 洪嘉振[1] 

机构地区：[1]上海交通大学工程力学系,上海200240

出　　处：《空间控制技术与应用》2015年第2期24-29,共6页Aerospace Control and Application

基　　金：国家自然基金资助项目(11132007);青年基金资助项目(11202126);上海市自然基金资助项目(11ZR1417000)

摘　　要：带大型柔性附件的复杂航天器,其弹性变形通常用有限单元法描述.由于有限元节点坐标数目庞大将会给动力学方程求解和控制策略的实现带来巨大负担,因此对柔性太阳电池阵的动力学模型降阶进行研究.利用单向递推组集推导带太阳电池阵的航天器的刚柔耦合动力学方程,分别采用模态截断法、模态价值分析法和Krylov子空间法对太阳电池阵进行模型降阶,比较不同降阶模型和全有限元模型的动力学仿真结果.仿真结果表明,无论是否考虑大范围运动的影响,采用Krylov方法只需要较低的自由度就可以得到和采用有限元方法完全一致的结果.说明Krylov方法能够有效地降低航天器柔性附件的自由度,提高动力学仿真的效率,便于驱动控制的实现.Modern complex spacecrafts usually have large flexible appendages, the elastic deformations of which are usually described by finite element method. However, the number of finite element nodal coor- dinates is large, which leads to a large computational burden on dynamics and control. Therefore, model order reductions of flexible solar arrays are investigated in this paper. The rigid-flexible coupling dynamic equations of a spacecraft with solar arrays are derived based on one-way recursive assembly formulation. Modal truncation method, modal value analysis method and Krylov method are used to reduce the de- grees-of-freedom of solar arrays. The results using those order reduction methods are compared with the results using the finite element method. The numerical simulations show that with the Krylov method smaller orders are needed, which is in good agreement with that of the finite element method. It means that Krylov method is an efficient method in reducing the degrees-of-freedom of flexible spacecraft, which will improve the efficiency of dynamic simulation and the implement of control.

关 键 词：太阳电池阵 刚柔耦合 动力学仿真 模型降阶 Krylov子空间法 

分 类 号：V448[航空宇航科学与技术—飞行器设计]