A modified optimization method for robust partial quadratic eigenvalue assignment using receptances and system matrices

Abstract

In this paper, we focus on the robust partial quadratic eigenvalue assignment problem for vibrating structures by active feedback control. This problem is reformulated as an minimization problem, where the cost function can measure both the sensitivity of the closed-loop eigenvalues and the feedback norms. This can be seen as a modified version of the minimization problem proposed by Bai et al. (2016) [5], where there exist additional equality constraints involving determinants of linear functions of the parameter matrix. By using the receptance measurements, the system matrices and a few undesired open-loop eigenvalues and associated eigenvectors, we propose a modified gradient-based optimization method for solving the minimization problem, where the explicit gradient formula of the cost function is derived. To implement our method in real operation, the real form of our method is also presented. Finally, some numerical examples are given to illustrate the validity of the proposed method.