Modern Control Engineering

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Example Problems and Solutions 247

MATLAB Program 5–23

num = [5];

den = [1 1 5];

t = 0:0.05:10;

r = 2+t;

c = lsim(num,den,r,t);

plot(t,r,'-',t,c,'o')

grid

title('Response to Input r(t) = 2 + t')

xlabel('t Sec')

ylabel('Output c(t) and Input r(t) = 2 + t')

Response to Input r(t) = 2 + t

t Sec

012345678910

Output

c(

t) and Input

r(

t) = 2 +

t

12

0

4

2

6

8

10

Figure 5–61
Response to input
r(t)=2+t.

2

s(s + 1)

R(s) C(s)

+

−

Figure 5–62
Control system.

Solution.A possible MATLAB program is shown in MATLAB Program 5–23. The resulting

response curve, together with a plot of the input function, is shown in Figure 5–61.

A–5–14. Obtain the response of the system shown in Figure 5–62 when the input r(t)is given by

[The input r(t)is the unit-acceleration input.]

r(t)=

1

2

t^2