Modern Control Engineering

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

EXAMPLE 7–13 Consider the system defined by

This system involves two inputs and two outputs. There are four sinusoidal output–input re-

lationships: and Draw Nyquist

plots for the system. (When considering input u 1 , we assume that input u 2 is zero, and vice

versa.)

The four individual Nyquist plots can be obtained by the use of the command

nyquist(A,B,C,D)

MATLAB Program 7–10 produces the four Nyquist plots. They are shown in Figure 7–42.

Y 1 (jv)U 1 (jv),Y 2 (jv)U 1 (jv),Y 1 (jv)U 2 (jv), Y 2 (jv)U 2 (jv).

B

y 1

y 2

R = B

1

0

0

1

RB

x 1

x 2

R + B

0

0

0

0

RB

u 1

u 2

R

B

x# 1

x# 2

R = B

- 1

6.5

- 1

0

RB

x 1

x 2

R +B

1

1

1

0

RB

u 1

u 2

R

Real Axis

• 0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1 1.2

Imag Axis

• 1

0

1.5

• 0.5

0.5

• 1.5

1

Nyquist Plot

Figure 7–41

Nyquist plot of

system considered in

Example 7–12.

MATLAB Program 7–10

A = [-1 -1;6.5 0];

B = [1 1;1 0];

C = [1 0;0 1];

D = [0 0;0 0];

nyquist(A,B,C,D)

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