5 Program 6.6 OGATA 4edition (root locus, damping ratios, undamped natural frecuency)

Laplace.T	Root-locus	Transient response	Frecuency response

5 Program 6.6 OGATA 4edition (root locus, damping ratios, undamped natural frecuency)

Let us calculate the roots-locus with indication of damping factor $\zeta$ =0.5,0.707 and not damped natural frequency $\omega_{n}$ =0.5, 1 and 2 by Scilab, a closed loop system with feedback unit whose transfer function in open-loop is:

$\begin{displaymath}G(s)=\frac{K}{(s^{3}+4\cdot s^{2}+5\cdot s)}\end{displaymath}$
Program in Scilab
num=poly([1 0 0 0],'s','coeff');
den=poly([0 5 4 1],'s','coeff');
g=syslin('c',num/den);
clf;
evans(g);
v=[-3 1 -2 2];
mtlb_axis(v)
sgrid([0.5, 0.707],[0.5, 1, 2],32);