Minimum norm partial quadratic eigenvalue assignment with time delay in vibrating structures using the receptance and the system matrices
Minimum norm partial quadratic eigenvalue assignment with time delay in vibrating structures using the receptance and the system matrices
复制标题
使用接收矩阵和系统矩阵对振动结构中具有时间延迟的最小范数部分二次特征值赋值
DOI：
10.1016/j.jsv.2012.10.015
复制
发表时间：
2013-02
影响因子：
4.7
通讯作者：
Datta, Biswa Nath
中科院分区：
文献类型：
--
作者：
Bai, Zheng-Jian;Chen, Mei-Xiang;Datta, Biswa Nath
部分二次特征值分配问题（PQEAP）是计算一对反馈矩阵，使得结构中少量不需要的特征值被重新分配到合适的位置，而其余大量的特征值和相关的特征向量保持不变。这是结构振动主动控制中的一个重要问题。对于实际应用，仅仅计算反馈矩阵是不够的。它们应该以这样一种方式计算，即闭环特征值灵敏度和反馈范数都尽可能小。此外，为了实际的有效性，状态的测量和反馈控制器的实施之间的时间延迟应考虑，而解决PQEAP。这些问题通常只使用系统矩阵来解决，而不一定要利用可通过测量得到的接收系数。在本文中，我们提出了混合方法，结合系统矩阵和实测接收，多输入PQEAP和最小范数PQEAP的解决方案，无论是系统的时滞和无时滞。这些混合方法比只使用系统矩阵而不使用接收器的标准方法更有效。与标准方法相比，这些混合方法还提供了其他几个计算优势。我们的结果推广了Ram等人的近期工作[Partial pole placement with time delay in structures using the receptance and the system matrices，Linear Algebra and its Applications 434（2011）1689-1696]。数值实验结果表明了所提方法的有效性。
The partial quadratic eigenvalue assignment problem (PQEAP) is to compute a pair of feedback matrices such that a small number of unwanted eigenvalues in a structure are reassigned to suitable locations while keeping the remaining large number of eigenvalues and the associated eigenvectors unchanged. The problem arises in active vibration control of structures. For real-life applications, it is not enough just to compute the feedback matrices. They should be computed in such a way that both closed-loop eigenvalue sensitivity and feedback norms are as small as possible. Also, for practical effectiveness, the time-delay between the measurement of the state and implementation of the feedback controller should be considered while solving the PQEAP. These problems are usually solved using only system matrices and do not necessarily take advantage of the receptances which are available by measurements. In this paper, we propose hybrid methods, combining the system matrices and measured receptances, for solutions of the multi-input PQEAP and the minimum-norm PQEAP, both for systems with and without time-delay. These hybrid methods are more efficient than the standard methods which only use the system matrices and not the receptances. These hybrid methods also offer several other computational advantages over the standard methods. Our results generalize the recent work by Ram et al. [Partial pole placement with time delay in structures using the receptance and the system matrices, Linear Algebra and its Applications 434 (2011) 1689–1696]. The results of numerical experiments demonstrate the effectiveness of the proposed methods.
登录
查看更多内容
影响因子：
4.7
作者：
Y. Ram;S. Elhay
通讯作者：
Y. Ram;S. Elhay
DOI：
10.1090/conm/280/04631
发表时间：
2007
期刊：
--
影响因子：
--
作者：
B. Datta;D. Sarkissian
通讯作者：
B. Datta;D. Sarkissian
影响因子：
2.5
作者：
Y. Ram;J. Mottershead
通讯作者：
Y. Ram;J. Mottershead
DOI：
10.1016/b978-0-12-203590-6.x5000-9
发表时间：
1994
期刊：
--
影响因子：
--
作者：
Daniel Boley;B. Datta
通讯作者：
Daniel Boley;B. Datta
DOI：
10.1365/s40111-010-0255-2
发表时间：
2010
期刊：
ATZextra worldwide
影响因子：
--
作者：
J. Linseisen;Michael Schneider;T. Ott
通讯作者：
J. Linseisen;Michael Schneider;T. Ott