航空学报 > 1980, Vol. 1 Issue (2): 67-78

关于闭环特征多项式的数值解及其应用问题

林士谔   

  1. 北京航空学院
  • 收稿日期:1979-03-01 修回日期:1900-01-01 出版日期:1980-12-25 发布日期:1980-12-25

ON THE APPROXIMATE AND EXACT SOLUTIONS OF HIGH ORDER CHARACTERISTIC POLYNOMIAL AND ITS APPLICATION IN SOLVING ROOT-LOCUS EQUATION IN A CLOSED-LOOP SERVOMECHANISM

Lin Shinge   

  1. Beijing Insiiittie of Aeronautics and Astronautics
  • Received:1979-03-01 Revised:1900-01-01 Online:1980-12-25 Published:1980-12-25

摘要: 本文提出应用分析法,在不同的阻尼比数值下,直接计算闭环伺服机构放大系数K的简化法。当K值算出后,可通过高阶特征多项式系数比值近似地解出方程的根值,并可通过劈因解根法,在要求精度内解出根值并绘出根轨迹曲线。

Abstract: It is shown in this paper that the real and complex roots of an nth order characteristic polynomial with gain-constant K may be closely approximated by ratios of coefficients of this polynomial, and solved with good accuracy by the method of successive factorizations. The value of gain constant K may be calculated analytically for given damping ratio, thereby root-locus curves with various K may be plotted analytically.