A receptance method for robust and minimum norm partial quadratic eigenvalue assignment. (November 2021) - Xie, Huiqing
Highlights: A receptance method for partial quadratic eigenvalue assignment problem (PQEAP) is proposed by formulating the PQEAP as an optimization problem. The proposed method only needs the receptance matrices and the undesired eigenpairs of open-loop system. The system matrices and the unchanged eigenpairs of open-loop system are not required. The norms of feedback matrices and the condition number of close-loop system are simultaneously minimized. The real form of the proposed method is developed. The gradient of the objective function is derived. Abstract: This paper considers the partial quadratic eigenvalue assignment problem (PQEAP) in active vibration control using state feedback. A receptance method is proposed for PQEAP such that the norms of feedback matrices and the condition number of close-loop system are simultaneously minimized. The real form of the proposed method is developed. The proposed method only uses receptance matrices and the unwanted eigenpairs of open-loop system. The system matrices and the unchanged eigenpairs of open-loop system are not required. The efficiency of the proposed method is illustrated by some numerical examples.