高空系留气球建模与稳定性分析

祝明; 左宗玉

高空系留气球建模与稳定性分析

祝明¹,
左宗玉²

1.
北京航空航天大学航空科学与工程学院, 北京 100191
2. 北京航空航天大学自动化科学与电气工程学院, 北京 100191

基金项目: 北京市教委共建重点学科基金资助项目(XK100060422)

详细信息

中图分类号: V 212.11
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出版历程
- 收稿日期: 2009-06-23
- 网络出版日期: 2010-08-30

Modeling and stability analysis for high altitude tethered balloon

Zhu Ming¹,
Zuo Zongyu²

1.
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
2. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

摘要

摘要: 平流层高空系留气球是典型的无控制欠阻尼自治系统,因此平台本身应当具有较好的稳定性,然而该系统的线性化模型含有零特征根,导致经典的Lyapunov第一方法难以从理论上获得其稳定性结论.从一般刚体的Newton-Euler方程出发,根据刚体对任一点的平动和转动方程,建立基于广义坐标的高空系留气球二阶非线性动力学模型,并针对Lyapunov方法证明稳定性的局限性,从能量的角度运用拉格朗日定理证明了高空系留气球的稳定性,数值仿真结果与理论结果一致.
- 气球 /
- 广义坐标 /
- 动力学建模 /
- 稳定性 /
- 拉格朗日定理
Abstract: Stratosphere high altitude tethered balloon (HATB) is a typical under-damping autonomous system, so it is required for the platform itself to be stable. However, it is hardly to investigate the platform stability theoretically through the classical Lyapunov first method, because there exist zero eigenvalues in the linearized model. The rigid translation and rotation equations with respect to any arbitrary point were presented, and then the general coordinate-based, second order, nonlinear dynamic model was proposed for HATB. In view of the limitation of the Lyapunov method, Lagrange theorem was applied to prove the platform stability problem from the perspective of energy. Numerical simulations demonstrate the coincidence with the theoretical analysis.
- balloon /
- generalized coordinates /
- dynamic modeling /
- stability /
- Lagrange theory

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参考文献(1)

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