Volume 2, Issue 2
A Receptance-Based Optimization Approach for Minimum Norm and Robust Partial Quadratic Eigenvalue Assignment

Min Lu & ZhengJian Bai

CSIAM Trans. Appl. Math., 2 (2021), pp. 357-375.

Published online: 2021-05

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  • Abstract

This paper is concerned with finding a minimum norm and robust solution to the partial quadratic eigenvalue assignment problem for vibrating structures by active feedback control. We present a receptance-based optimization approach for solving this problem. We provide a new cost function to measure the robustness and the feedback norms simultaneously, where the robustness is measured by the unitarity or orthogonalization of the closed-loop eigenvector matrix. Based on the measured receptances, the system matrices and a few undesired open-loop eigenvalues and associated eigenvectors, we derive the explicit gradient expression of the cost function. Finally, we report some numerical results to show the effectiveness of our method.

  • AMS Subject Headings

65F18, 93B55, 93C15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-2-357, author = {Lu , Min and Bai , ZhengJian}, title = {A Receptance-Based Optimization Approach for Minimum Norm and Robust Partial Quadratic Eigenvalue Assignment}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2021}, volume = {2}, number = {2}, pages = {357--375}, abstract = {

This paper is concerned with finding a minimum norm and robust solution to the partial quadratic eigenvalue assignment problem for vibrating structures by active feedback control. We present a receptance-based optimization approach for solving this problem. We provide a new cost function to measure the robustness and the feedback norms simultaneously, where the robustness is measured by the unitarity or orthogonalization of the closed-loop eigenvector matrix. Based on the measured receptances, the system matrices and a few undesired open-loop eigenvalues and associated eigenvectors, we derive the explicit gradient expression of the cost function. Finally, we report some numerical results to show the effectiveness of our method.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2021.nla.06}, url = {http://global-sci.org/intro/article_detail/csiam-am/18889.html} }
TY - JOUR T1 - A Receptance-Based Optimization Approach for Minimum Norm and Robust Partial Quadratic Eigenvalue Assignment AU - Lu , Min AU - Bai , ZhengJian JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 357 EP - 375 PY - 2021 DA - 2021/05 SN - 2 DO - http://doi.org/10.4208/csiam-am.2021.nla.06 UR - https://global-sci.org/intro/article_detail/csiam-am/18889.html KW - Partial quadratic eigenvalue assignment, robustness, optimization method, receptance measurements. AB -

This paper is concerned with finding a minimum norm and robust solution to the partial quadratic eigenvalue assignment problem for vibrating structures by active feedback control. We present a receptance-based optimization approach for solving this problem. We provide a new cost function to measure the robustness and the feedback norms simultaneously, where the robustness is measured by the unitarity or orthogonalization of the closed-loop eigenvector matrix. Based on the measured receptances, the system matrices and a few undesired open-loop eigenvalues and associated eigenvectors, we derive the explicit gradient expression of the cost function. Finally, we report some numerical results to show the effectiveness of our method.

Min Lu & Zheng-Jian Bai. (2021). A Receptance-Based Optimization Approach for Minimum Norm and Robust Partial Quadratic Eigenvalue Assignment. CSIAM Transactions on Applied Mathematics. 2 (2). 357-375. doi:10.4208/csiam-am.2021.nla.06
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