Modern Control Engineering

Section 7–3 / Polar Plots 439

Real Axis

− 212 −1.5 − 10 −0.5 0.5 1.5

Imaginary Axis

− 2

1

− 5

5

− 1

2

− 3

− 4

0

3

4

Nyquist Plot of G(s) = 1/[s(s+1)]

Figure 7–39
Nyquist plot of

G(s)=

1

s(s+1)

.

then it can be corrected if we specify the axis(v). For example, if we enter the axis

command

v = [-2 2 -5 5]; axis(v)

in the computer, then a desirable form of Nyquist plot can be obtained. See Example 7–11.

EXAMPLE 7–11 Draw a Nyquist plot for the following G(s):

MATLAB Program 7–7 will produce a desirable form ofNyquist plot on the computer, even

though a warning message “Divide by zero” may appear on the screen. The resulting Nyquist plot

is shown in Figure 7–39.

G(s)=

1

s(s+1)

MATLAB Program 7–7

% ---------- Nyquist plot----------

num = [1];

den = [1 1 0];

nyquist(num,den)

v = [-2 2 -5 5]; axis(v)

grid

title('Nyquist Plot of G(s) = 1/[s(s + 1)]')

Notice that the Nyquist plot shown in Figure 7–39 includes the loci for both v>0andv<0.

If we wish to draw the Nyquist plot for only the positive frequency region (v>0), then we need

to use the command

[re,im,w]=nyquist(num,den,w)