Modern Control Engineering

Then we have

a = [1 4.02 0.08]

b = [1 5 4 0]

c = [40 24 3.2]

Using the following MATLAB program, we obtain the denominator polynomial.

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

a = [1 4.02 0.08];

b = [1 5 4 0];

c = [40 24 3.2];

p = [conv(a,b)] + [0 0 0 c]

p =

1.0000 9.0200 24.1800 56.4800 24.3200 3.2000

MATLAB Program 7–33

%*Unit-step response

num = [40 24 3.2];

den = [1 9.02 24.18 56.48 24.32 3.2];

t = 0:0.2:40;

step(num,den,t)

grid

title('Unit-Step Response of Compensated System')

Amplitude

1.2

0.4

0

1

0.2

0.6

0.8

Unit-Step Response of Compensated System

Time (sec)

0105 15 20 25 30 35 40

Figure 7–154

Unit-step response

curve of the

compensated system.

MATLAB Program 7–33 is used to obtain the unit-step response of the compensated system.

The resulting unit-step response curve is shown in Figure 7–154. (Note that the gain-adjusted but

uncompensated system is unstable.)

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