Section 6–3 / Plotting Root Loci with MATLAB 293EXAMPLE 6–4 Consider the negative feedback system whose open-loop transfer function G(s)H(s)is
There are no open-loop zeros. Open-loop poles are located at s=–0.3+j3.1480,
s=–0.3-j3.1480, s=–0.5,ands=0.
Entering MATLAB Program 6–2 into the computer, we obtain the root-locus plot shown in
Figure 6–17.=
K
s^4 +1.1s^3 +10.3s^2 +5sG(s)H(s)=K
s(s+0.5)As^2 +0.6s+ 10 BMATLAB Program 6–2
% --------- Root-locus plot ---------
num = [1];
den = [1 1.1 10.3 5 0];
r = rlocus(num,den);
plot(r,'o')
v = [-6 6 -6 6]; axis(v)
grid
title('Root-Locus Plot of G(s) = K/[s(s + 0.5)(s^2 + 0.6s + 10)]')
xlabel('Real Axis')
ylabel('Imag Axis')
Real Axis–6 –4 –2 0 2 4 6Imag Axis6–24–620–4Root-Locus Plot of G(s)=K/[s(s+0.5)(s^2 +0.6s+10)]Figure 6–17
Root-locus plot.
Notice that in the regions near x=–0.3, y=2.3andx=–0.3, y=–2.3two loci approach
each other. We may wonder if these two branches should touch or not. To explore this situation,
we may plot the root loci using smaller increments of Kin the critical region.