A Receptance-Based Optimization Approach for Minimum Norm and Robust Partial Quadratic Eigenvalue Assignment (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 structuresby active feedback control. We present a receptance-based optimization approach forsolving this problem. We provide a new cost function to measure the robustness andthe feedback norms simultaneously, where the robustness is measured by the unitarityor orthogonalization of the closed-loop eigenvector matrix. Based on the measuredreceptances, 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.