MEEN 364
Notes from Session on October 27, 2004
304 Fermier Hall, 6:00~7:00 pm
1
Notes for session on October 27, 2004.
1. The unit step response of the system described by the following block diagram is shown
below it.
Determine the values of the gains
k
1
,
k
2
, and the other pole of the plant,
b
. Also obtain
the peak, rise, and settling time for 1% criterion.
(
2
(2
1
2
k
sbs
++
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Step Response
Time (sec)
Amplitude
d
c
b
a
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Notes from Session on October 27, 2004
304 Fermier Hall, 6:00~7:00 pm
2
Solution:
The transfer function is given by:
(
2
(2
1
12
1
2
()
(
)2
22
k
Ys
TF
R
s
sb
s
kk
k
s
b
s b kk
==
+
++
=
++ ++
(1)
Since
R(s) = 1 / s
(unit step input), the steady state value of the output is:
1
0
lim
2
s
k
S
S
TF
b kk
→
+
(2)
From the figure for the step response,
SS
= 1, so, equation (2) becomes:
1
21
2
b k
+=
(3)
Now we compare equation (1) with the standard expression for the transfer function of a second
order system, given in problem 1.a:
2
1
2
nn
k
k
an
db
w
zw
+
=+
(4)
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