Modern Control Engineering

Section 7–3 / Polar Plots 441

MATLAB Program 7–9

A = [0 1;-25 -4];

B = [0;25];

C = [1 0];

D = [0];

nyquist(A,B,C,D)

grid

title('Nyquist Plot')

Nyquist plots for this system may be obtained by the use of the command

nyquist(A,B,C,D)

This command produces a series of Nyquist plots, one for each input and output com-

bination of the system. The frequency range is automatically determined.

The command

nyquist(A,B,C,D,iu)

produces Nyquist plots from the single input iuto all the outputs of the system, with

the frequency range determined automatically. The scalar iuis an index into the inputs

of the system and specifies which input to use for the frequency response.

The command

nyquist(A,B,C,D,iu,w)

uses the user-supplied frequency vector w. The vector wspecifies the frequencies in

radians per second at which the frequency response should be calculated.

EXAMPLE 7–12 Consider the system defined by

Draw a Nyquist plot.

This system has a single input uand a single output y. A Nyquist plot may be obtained by

entering the command

nyquist(A,B,C,D)

or

nyquist(A,B,C,D,1)

MATLAB Program 7–9 will provide the Nyquist plot. (Note that we obtain the identical result by

using either of these two commands.) Figure 7–41 shows the Nyquist plot produced by MATLAB

Program 7–9.

y =[1 0]B

x 1

x 2

R +[0] u

B

x

1

x# 2

R = B

0

- 25

1

- 4

RB

x 1

x 2

R + B

0

25

Ru