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in
One spring
with constant
4
k
Proof mass,
m
p
Case mass
m
c
b
)
(
t
F
University of California
Mechanical Engineering Department
ME 132 Dynamic Systems and Feedback
Spring 2006
Final Examination:
May 12, 2006 (Friday), 12:303:30 p.m.
Open reader, open notes.
All problems are equally weighed: i.e. 20 pts for each of
5 problems.
[1]
Consider a fourth order plant under Pcontrol sketched below.
0
c
k
a.
Find
k
c
and all closed loop poles at the stability limit.
(Hint: You may first find the
control gain and the frequency of oscillation at the stability limit.)
b.
If
2
=
c
k
, what is the gain margin?
For a unit reference input (i.e.
r
= 1), find the
asymptotic final value of
y
,
)
(
lim
t
y
y
t
ss
∞
→
=
.
c.
Now we consider PID control instead of Pcontrol.
Tune the parameters of the PID
controller by the ultimate sensitivity method of Ziegler and Nichols.
[2]
A single axis accelerometer is sketched below.
The accelerometer is to be tested by mounting it on a
shaker table which provides a force input
)
(
t
F
in
to the
instrument package.
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This note was uploaded on 08/01/2008 for the course ME 132 taught by Professor Tomizuka during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Tomizuka
 Mechanical Engineering

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