Stability estimation of high dimensional vibrating systems under state delay feedback control

H. Y. Hu*, E. H. Dowell, L. N. Virgin

*此作品的通讯作者

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40 引用 (Scopus)

摘要

The paper presents a method of assessing the stability of high dimensional vibrating systems under state feedback control with a short time delay. It is first proved that if the time delay is sufficiently short, an n -degree-of-freedom system with feedback delay maintains 2n eigenvalues near those of the corresponding system without feedback delay. A perturbation approach is then proposed to determine the first order variation of an arbitrary eigenvalue and corresponding eigenvector of the system with feedback delay by solving a set of linear algebraic equations only. The computation in this approach can be simplified to a matrix multiplication provided that the product of the time delay and the modulus of the eigenvalue is much less than 1. Furthermore, the approach is directly related to the Newton-Raphson iteration in the continuation of eigenvalues for long time delay. The efficacy of the approach is demonstrated via a number of case studies on two feedback delay systems of two degrees of freedom and ten degrees of freedom respectively.

源语言英语
页(从-至)497-511
页数15
期刊Journal of Sound and Vibration
214
3
DOI
出版状态已出版 - 16 7月 1998
已对外发布

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Hu, H. Y., Dowell, E. H., & Virgin, L. N. (1998). Stability estimation of high dimensional vibrating systems under state delay feedback control. Journal of Sound and Vibration, 214(3), 497-511. https://doi.org/10.1006/jsvi.1998.1548