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Steady State Error
Q
UESTION
13
For the system shown in Figure 13 with
(
29
(
29
n
K
F s
s
s
a
=
+
, calculate the parameters
K
,
n
, and
a
such that the closed–loop system has 10% overshoot and
e
(∞) = 0.01 for unit ramp inputs.
+

R(s)
F(s)
Y(s)
E(s)
Figure 13
(
29
(
29
(
29
1
1
E s
R s
F s
=
+
For finite steady–state error to ramp inputs, the system type is
n
= 1. The steady–state error is
(
29
(
29
(
29
(
29
2
2
0
0
1
1
1
lim
lim
0.01
1
s
s
s s
a
a
e
s
s
K
s
s s
a
K s
K
s s
a
→
→
+
∞ =
=
=
=
+
+
+
+
For 10% overshoot,
2
2
10
ln
100
0.5912
10
ln
100
ζ
π

=
=
+
. The closed–loop poles characteristic
equation is
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This note was uploaded on 02/01/2012 for the course MECH ENG 279 taught by Professor Landers during the Spring '11 term at Missouri S&T.
 Spring '11
 LANDERS

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