Modern Control Engineering

438 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method

Caution. In drawing a Nyquist plot, where a MATLAB operation involves “Divide

by zero,” the resulting Nyquist plot may have an erroneous or undesirable appearance.

For example, if the transfer function G(s)is given by

then the MATLAB command

num = [1];

den = [1 1 0];

nyquist(num,den)

produces an undesirable Nyquist plot. An example of an undesirable Nyquist plot is

shown in Figure 7–38. If such an undesirable Nyquist plot appears on the computer,

G(s)=

1

s(s+1)

Real Axis

− 2 −1.5 − 1 −0.5 0 0.5 1 1.5 2

Imaginary Axis

− 1

0.5

− 2

2

−0.5

−1.5

0

1

1.5

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

Figure 7–37

Nyquist plot of

G(s)=

1

s^2 +0.8s+ 1

.

Real Axis

−1.4 −1.2 − 1 −0.8 −0.6 −0.4 −0.2 0

Imaginary Axis

− 150

150

− 50

− 100

0

50

100

Nyquist Diagram

Figure 7–38

Undesirable Nyquist

plot.

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