关于闭环特征多项式的数值解及其应用问题

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。

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

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.