Example Problems and Solutions 533Real Axis– 3 – 2 – (^10123)
Imag Axis
- 3
- 5
1- 1
- 4
- 2
0Nyquist Plot of G(s)= 20(s^2 +s+0.5)/[s(s+1)(s+10)]Figure 7–128
Nyquist plot for the
positive-frequency
region.
MATLAB Program 7–18
num = [20 20 10];
den = [1 11 10 0];
w1 = 0.1:0.1:10; w2 = 10:2:100; w3 = 100:10:500;
w = [w1 w2 w3];
[re,im,w] = nyquist(num,den,w);
plot(re,im)
v = [-3 3 -5 1]; axis(v);
grid
title('Nyquist Plot of G(s) = 20(s^2 + s + 0.5)/[s(s + 1)(s + 10)]')
xlabel('Real Axis')
ylabel('Imag Axis')
A–7–13. Referring to Problem A–7–12, plot the polar locus of G(s)whereLocate on the polar locus frequency points where v=0.2, 0.3, 0.5, 1, 2, 6, 10, and 20 radsec.
Also, find the magnitudes and phase angles of G(jv)at the specified frequency points.Solution.In MATLAB Program 7–19 we used the frequency vector w, which consists of
three frequency subvectors:w1,w2, and w3. Instead of such a w, we may simply use theG(s)=20 As^2 +s+0.5B
s(s+1)(s+10)MATLAB Program 7–18 uses this frequency region. Using this program, we obtain the Nyquist
plot shown in Figure 7–128.