挠性系统谐振频率摄动范围的几何解法

Geometrical solution to perturbation range of resonant frequency for flexible systems

摘要:

基于D分割法研究了挠性系统弱阻尼谐振频率的摄动范围问题. 由于挠性系统的谐振频率分别出现在一次项和二次项中,因此其摄动是非线性的. 通过引入两个摄动因子,将问题转化为二维参数鲁棒摄动问题,设计了一种基于D分割法的几何分析方法,求得两个因子的鲁棒摄动区域,该区域与特定直线的交点即为谐振频率的摄动边界值. 通过算例验证了该方法的有效性,解决了挠性系统中谐振频率的摄动范围求解问题,同时揭示了谐振频率摄动与H∞范数的对应关系.

Abstract:

The range of the lightly damped resonant frequency in the flexible system is investigated based on D-decomposition approach. In the flexible system, the resonant frequency exists in the first-order and second-order terms, making its perturbation possess a nonlinear form. In this paper, two perturbation factors are introduced to reformulate the problem as a two-dimension parameter perturbation problem. Then, a geometric algorithm based on the D-decomposition approach is developed to determine the precise robust area of the two factors. The perturbation range of the resonant frequency can be obtained as the intersection points between the boundary of this area and a specific line. Numerical examples are provided to illustrate the effectiveness of the proposed method. Meanwhile, the relationship between the perturbation range and the H∞ norm is also revealed.