AME451: Midterm Examination
Fall 2007
November
7
,2007
The examination is closed notes and closed books. Calculators are allowed.
Duration of the examination is 1 hour and 15 minutes.
1. (50 points) Given the system in the
f
gure.
+

R(s)
Y(s)
s
2
1
+
K(s)
2
+

(a) Assume a controller
K
(
s
)
given by
K
(
s
)=
K
s
+
a
where
K>
0
,a>
0
.
The following requirements for the closedloop performance are spec
i
f
ed
i. A. Percent overshoot to step input
M
p
≤
16
.
3%
B. Steady state error to
unit step
input
e
ss
≤
0
.
1
C. Settling time
t
s
<
0
.
5sec
Find the relations in terms of
K
and
a
that need to be satis
f
ed
in order to achieve the above speci
f
cations.
ii. What is a steady state error for ramp input?
1
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View Full Document(b) Assume the following controller
K
(
s
)=
K
s
N
(
s
+
a
)
,
where
K>
0
,a>
0
,N
≥
0
,N
an integer
i. What is a minimum steady state error to ramp input for
N
=1
?
Express your answer in terms of the parameter
a.
ii. What is a minimum steady state error to parabolic input
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 Fall '07
 Flashner
 Kp Kv Ka

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