Structure-preserving balanced truncation for flexible spacecraft using cross Gramian
-
摘要: 对于柔性航天器动力学方程的降阶问题,传统的内平衡降阶方法破坏了原方程的动力学结构.为了解决这一问题,提出了一种牺牲严格内平衡状态,而保留原系统动力学特性的近似内平衡降阶方法.该方法利用混合Gramian描述系统的模态价值,针对柔性航天器动力学方程的特殊形式,给出了混合Gramian的闭合解析解.该方法得到的降阶模型可以保留原系统包括二阶结构,对称和正定性在内的所有动力学特性.数值算例表明该方法不但可以达到与传统一阶内平衡方法相当的降阶精度,而且降阶速度有大幅度提升.Abstract: For model reduction of flexible spacecraft, conventional first-order balanced truncation(FOBT) method will destroy the second-order structure and dynamic properties of original system. In order to overcome this drawback, a new structure-preserving approximated balanced truncation method for model reduction of flexible spacecraft was proposed. The modal cost was described by a cross Gramian and the closed-form solution of cross Gamian was obtained via special form of dynamical equation of flexible spacecraft. The new method preserves the second-order structure, symmetry and positive definiteness of the original system. The numerical results show that the new method is superior to conventional first-order balanced truncation(FOBT) method for improving efficiency without sacrificing accuracy.
-
Key words:
- reduction /
- flexible structures /
- state space methods
-
[1] Moore B C, Principal component analysis in linear system: controllability, observability and model reduction[J]. IEEE Transactions on Automatic Control, 1981, 26(1):17-32 [2] Fernando K, Nicholson H. On the structure of balanced and other principal representations of SISO systems[J]. IEEE Transactions on Automatic Control, 1983, 28(2):228-231 [3] Fernando K, Nicholson H. On the cross-Gramian for symmetric MIMO systems[J]. IEEE Transactions on Circuits and Systems, 1985, 32(5): 487- 489 [4] Sorensen D C, Antoulas A C. The Sylvester equation and approximate balanced reduction[J]. Linear Algebra and Its Applications,2002, 351(2):671-700 [5] Meyer D G, Srinivasan S. Balancing and model reduction for second-order form linear systems[J]. IEEE Transactions on Automatic Control, 1996, 41(11): 1632-1644 [6] Safonov M G, Chiang R Y. A schur method for balanced model reduction[J]. IEEE Transactions on Automatic Control, 1989, 34(7):729-733 [7] Chahlaoui Y, Dooren P V. A collection of benchmark examples for model reduction of linear time invariant dynamical systems .SLICOT Working Note 2002-2, 2002 -
点击查看大图
计量
- 文章访问数: 3002
- HTML全文浏览量: 199
- PDF下载量: 916
- 被引次数: 0
下载:
