A Receptance-Based Optimization Approach for Minimum Norm and Robust Partial Quadratic Eigenvalue Assignment
Year: 2021
Author: Min Lu, ZhengJian Bai
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2021.nla.06
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 2 : pp. 357–375
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Partial quadratic eigenvalue assignment robustness optimization method receptance measurements.