根轨迹的中心点研究

摘要

Root locus property on asymptote centroid determines the coordinate of the asymptote centroid. In this paper,a new proof on asymptote centroid is given. Firstly,it is proved that if the transfer function of the plant is strictly real,the root loci process asymptote. Secondly,the angle of the asymptotes is determined;finally,the coordi-nate of the asymptote centroid is calculated by constructing the vector equation of the asymptote. Compared with the conventional proof,the new method has clear geometrical sense.%根轨迹的中心点性质确定了根轨迹中心点的坐标。本文给出了根轨迹中心点性质的新证明方法。首先，证明了当被控对象的传递函数为严真时，根轨迹存在渐近线；然后，计算了根轨迹渐近线的倾斜角；最后，通过建立渐近线的矢量方程，确定了根轨迹的中心点坐标。与传统的证明方法相比，本文提出的证明方法具有明确的几何意义。