Robust minimum norm partial eigenstructure assignment approach in singular vibrating structure via active control

In this paper, the robust minimum norm partial eigenstructure assignment problems (PESAPs) are studied in a singular vibrating structure via acceleration-velocity-displacement active control. The solvability and stabilization conditions are given by using the singular value decomposition method and no spill-over property of eigenvalues and corresponding eigenvectors. A new parametric method is proposed for solving the PESAPs using the imposed modal constraints technique. Based on the derived condition number of closed-loop eigenvalues, the robust and minimum norm PESAPs are considered by setting appropriate weight factors. Algorithms are presented for solving the corresponding problems. Two numerical examples are reported to verify the effectiveness of algorithms.