一类用于结构振动控制的输出反馈控制器的特性研究

本文探讨一类设计简捷的直接输出反馈控制器在结构振动控制方面的应用。由计及作动机构动力学特性的结构振动普遍运动方程出发,从数学上证明了当反馈控制律中的增益因子为小量和趋于无限大时闭环系统特征根的几个重要性质,并导出了计算这些特征根的表达式。当增益因子趋于无限大时,特征根由3个子矩阵的特征值确定,这3个子矩阵中有的只与测量加权矩阵有关,有的与测量加权矩阵和反馈矩阵完全无关,有的只与反馈矩阵有关。当增益因子为小量时,特征根可利用矩阵摄动方法方便求得。上述结果对这类控制器的设计是有指导意义的。文末通过算例证实了文中导出的结果的正确性。

Study on Characteristics of a Kind of Output Feedback Controllers for Structural Vibration Control

The applications of a kind of output feedback controllers which are designed simply and directly are studied in the paper. Based on the general motion equations considering the characteristics of actuators and structures, some important properties of characteristic roots of the closed loop system in the case of the gain of control law approaching small or infinitive values are proved mathematically. At the same time the expressions for calculating those characteristic roots are deduced. When the gain approaches infinitive value, the characteristic roots are determined by the eigenvalues of three submatrices some of which is dependent on the measurement weighting matrix or feedback matrix only, and some of which is entirely independent of those matrices mentioned above. When the gain approaches a small value, the characteristic roots can be calculated by the matrix perturbation method. The results in this paper are instructive for designing such kind of controllers. At last a calculation example shows the correctness of the results deduced in the paper.