(untitled) (CSIAM Transactions on Applied Mathematics, 2021)
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.