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HW/CE# 4
Due Wednesday, March 24, 2010
1.
Suppose we have the following specifications:
M
p
<
40%
settling time t
s
<
5 sec
rise time t
r
<
1.0 sec
Choose phase margin PM and crossover frequency
ω
c
so that we meet the above.
Use the
“more exact” tabulations on the second page of the reference sheets.
Hint:
start with ζ =
0.30.
2.
Assume
G(s) =KL(s)
, shown below, is the openloop gain in a unity feedback system.
(Note that this is the same
G(s)
you did the root locus and Bode plot for in the last
homework exercise.)
Make hand sketches showing the Nyquist plots for:
)
125
10
(
)
(
)
(
2
+
+
=
=
s
s
s
K
s
KL
s
G
For
K
= 1000, 1250, and 1500.
Show critical points (crossover values on the real axis)
for all three cases.
Describe closed loop system stability for the 3 cases, i.e., marginally
stable, unstable, etc.
Verify your sketches by submitting MATLAB generated Nyquist
plots.
3.
Suppose we have a plant
G(s):
)
16
.
1
(
4
.
8
)
(
+
=
s
s
s
G
in a unity feedback system.
a)
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 Spring '10
 Brown
 Frequency

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