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本文中利用闭环系统的频率响应与开环频率响应之间的关系获得一个阻尼比分布半圆。根据奈魁斯特的稳定判据,稳定系统的开环频率响应的奈氏轨迹必与这个半圆相交,交点所对应的频率就是系统的无阻尼自然频率;而过交点作到(-1+j0)点直线,此直线与负实轴的夹角β可以在图上量取,最后由tgβ=1/(2ξ)得到阻尼比ξ。
In this paper, the relationship between the frequency response of the closed-loop system and the open-loop frequency response is used to obtain a damping ratio distribution semicircle. According to Nyquist’s stability criterion, the Nessler’s trajectory of steady-state open-loop frequency response must intersect with this semicircle, and the frequency corresponding to the intersection point is the undamped natural frequency of the system. The crossing point makes (-1 + j0 ) Point of the straight line, the straight line and the negative real axis angle β can be taken in the graph, the final by tgβ = 1 / (2ξ) damping ratio ξ.