Modern Control Engineering

Section 7–3 / Polar Plots 437

MATLAB Program 7–5

num = [1];

den = [1 0.8 1];

nyquist(num,den)

grid

title('Nyquist Plot of G(s) = 1/(s^2 + 0.8s + 1)')

MATLAB Program 7–6

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

num = [1];

den = [1 0.8 1];

nyquist(num,den)

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

grid

title('Nyquist Plot of G(s) = 1/(s^2 + 0.8s + 1)')

Real Axis

− 1 −0.5 0 0.5 1 1.5

Imaginary Axis

−1.5

1.5

−0.5

− 1

0

0.5

1

Nyquist Plot of G(s) = 1/(s^2 + 0.8s+ 1)

Figure 7–36
Nyquist plot of

G(s)=

1

s^2 +0.8s+ 1

.

If we wish to draw the Nyquist plot using manually determined ranges—for example, from –2

to 2 on the real axis and from –2to 2 on the imaginary axis—enter the following command into

the computer:

v = [-2 2 -2 2];

axis(v);

or, combining these two lines into one,

axis([-2 2 -2 2]);

See MATLAB Program 7–6 and the resulting Nyquist plot shown in Figure 7–37.