Modern Control Engineering

196 Chapter 5 / Transient and Steady-State Response Analyses

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Unit-Impulse Response of G(s)= 1/(s^2 +0.2s+1)

Time (sec)

Amplitude

0 5 10 15 20 25 30 35 40 45 50

1

0.8

0.2

–0.6

–0.8

0.6

0.4

0

–0.2

–0.4

Figure 5–24

Unit-impulse-

response curve.

MATLAB Program 5–8 will produce the unit-impulse response. The resulting plot is shown in

Figure 5–24.

MATLAB Program 5–8

num = [1];

den = [1 0.2 1];

impulse(num,den);

grid

title(‘Unit-Impulse Response of G(s) = 1/(s^2 + 0.2s + 1)‘)

Alternative Approach to Obtain Impulse Response. Note that when the initial

conditions are zero, the unit-impulse response of G(s)is the same as the unit-step

response of sG(s).

Consider the unit-impulse response of the system considered in Example 5–5. Since

R(s)=1for the unit-impulse input, we have

We can thus convert the unit-impulse response of G(s)to the unit-step response of

sG(s).

If we enter the following numanddeninto MATLAB,

num = [0 1 0]

den = [1 0.2 1]

=

s

s^2 +0.2s+ 1

1

s

C(s)

R(s)

=C(s)=G(s)=

1

s^2 +0.2s+ 1

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