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 - <p style="text-align: justify;">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.</p>