亏损系统振动模态的可控可观性

利用奇异值分解方法来讨论系统广义模态的可控可观性的量度问题,得到了亏损系统广义模态可控可观性的量度指标,同时用实例说明了本文方法是有效的。

Controllability and observability in vibration control of defective systems

The vibration control of the defective system with repeated eigenvalues and a near-defective system with close eigenvalues is an important problem in the actual engineering. Most of the previous discussions have focused on the non-defective system which results cannot be used to deal with the defective and near-defective system. However, in the actual engineering, such as general damping systems and flutter analysis of aero-elasticity etc., the system called "defective system" does not have a set of complete eigenvectors to span the eigenspace. For the special cases, the state matrix A cannot be diagonalized. In this paper, the singular values of modal controllable and observable matrices can be used as the quantitative measures of modal controllability and observability of the defective modes, and the necessary and sufficient conditions of controllability and observability of all the defective eigenvalues has been obtained. The analysis for modal controllability and observability of a near defective system with close eigenvalues can be transformed into one of the defective system with repeated eigenvalues, which are equal to the average value of the close eigenvalues. The results given by numerical example show that the present procedure is valid and effective.