2.171
Quiz
#2
Nov.
20,
2006
This
quiz
is
openbook.
You
may
also
refer
to
two
8
1/2”
by
11”
sheets
of
notes.
There
is
one
problem;
all
seven
sections
of
the
problem
will
count
equally.
Problem
1
This
problem
considers
a
continuoustime
system
with
a
transfer
function
2
a
H
(
s
) =
.
(1)
s
2
−
a
2
This
might
model
the
linearized
behavior
of
a
magnetic
suspension.
Note
that
both
poles
are
realaxis,
with
one
in
the
righthalf
plane.
a)
Calculate
the
zero
order
hold
equivalent
H
eq
(
z
)
for
this
system
with
a
sampling
time
T
.
b)
Show
that
for
a
=
40,
T
= 0
.
001
sec,
H
eq
(
z
)
becomes
8
×
10
−
4
(
z
+
1)
H
eq
(
z
) =
z
2
−
2
.
0016
z
+ 1
.
(2)
Please
use
this
transfer
function
for
all
subsequent
work
even
if
your
answer
does
not
agree
with
it.
Clearly
state
if
this
is
the
case,
and
then
use
the
answer
we
are
providing
above.
Plot
the
poles
and
zeros
of
this
system
on
the
zplane.
Do
the
poles
map
as
z
=
e
sT
?
c)
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 Fall '06
 DavidTrumper
 Unit Circle, Root Locus, Heq

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