用图论法进行结构振动控制的极点配置

Pole Placement of Structural Vibration Control by Graph Theory Method

本文介绍了用图论法进行结构振动控制极点配置的方法。控制结构振动的实质就是改善结构振动的频率和阻尼即结构的极点。通过求解特征多项式可以得到结构的极点。而特征多项式的系数与有向图的圆族有着密切的关系。本文利用这种关系,根据结构矩阵的有向图中不同宽度的圆族,对给定的结构极点进行配置,求出反馈增益。最后,给出了一个数值例子,以说明文中介绍的方法。

In this paper, the poles of structural vibration control were placed by graph theory methods. The crux of controlling structural vibration depends on improving structural frequency and damping, or structural poles, which can be obtained through solving eigen-polynomial expressions. And the coefficients of eigen-polynomial expressions were closely related to the circular sets of a directional graph. According to the different width circular sets in the directional graph of a structural matrix, the feedback can be obtained by the relationships of a directional graph to a determinant, for structural poles given. Finally, a numerical example was presented in order to show the method of this paper.