Modern Control Engineering

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246 Chapter 5 / Transient and Steady-State Response Analyses

Unit-Ramp Response by Use of Command “lsim”

t Sec

Output

9

5

1

8

6

3

2

4

7

10

Unit-Ramp Input

(a)

(^0012345678910)
Output
Response to Input r 1 = e−0.5t
Inputr 1 = e−0.5t
Output
t Sec
024681012
(b)
Input and Output
1
0.1
0
0.4
0.2
0.3
0.5
0.6
0.7
0.8
0.9
Figure 5–60
(a) Unit-ramp
response curve;
(b) response to
exponential input
r 1 =e–0.5t.
A–5–13. Obtain the response of the closed-loop system defined by
when the input r(t)is given by
r(t)=2+t
[The input r(t)is a step input of magnitude 2 plus unit-ramp input.]
C(s)
R(s)

=

5

s^2 +s+ 5

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