Symmetry preserving partial eigenvalue assignment for undamped structural systems

Abstract

a b s t r a c tIn this paper, the partial eigenvalue assignment problem for undamped structural systems by output feedback control where the output matrix is also a designing parameter is considered. We propose a method to solve this problem in which the unwanted eigenvalues are move to desired values and all other eigenpairs remain unchanged. In addition, our method can preserve symmetry of the systems. Numerical example shows that the proposed method is effective.

A New Approach for Symmetry Preserving Partial Eigenstructure Assignment of Undamped Vibrating Systems

“…It can be seen that our approach can accurately solve the partial eigenvalue assignment problem. Interestingly, the symmetric matrix BGB obtained here is the same as that in [21].…”

“…Additionally, we can compute ‖M 0 Y 1 Σ 1 −(K 0 +BGB )Y 1 ‖ = 1.2071 −015 and ‖M 0 X 2 Λ 2 − (K 0 + BGB )X 2 ‖ = 5.1580 − 015. This also means that our approach can accurately solve the partial eigenstructure assignment problem, which is a distinctive advantage with respect to the approach proposed in [21].…”

“…In this section, a numerical example in [21] is used to illustrate our approach. For an undamped vibrating system, it has the stiffness and mass matrices as follows:…”

“…Its eigenvalues are {0.0, 0.3564, 1.5403, 3.8816, 7.6127, 11.3551}. Two eigenvalues {0.3564, 1.5403} among them are to be reassigned to {0.75, 1.85}, which is also the assignment in [21]. We have Λ 1 = diag(0.3564, 1.5403) and Σ 1 = diag(0.75, 1.85).…”

“…Ram [20] solved the eigenvalue assignment problem for the vibrating rod. More recently, Liu and Li [21] suggested a method for the symmetry preserving partial eigenvalue assignment of undamped structural systems. They adapted the method proposed in [22] to the requirement of the symmetry preserving.…”