Modern Control Engineering

(Chris Devlin) #1
aa

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
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