EECS 314
Winter 2009
Homework set 2
Student’s name ___________________________
Discussion section # _______
(Last, First, write legibly, use ink)
(use ink)
Instructor is
not responsible
for grading and entering scores for HW papers lacking clear
information in the required fields above
© 2009 Alexander Ganago
Page 1 of 2
Scores for the HW set:
Problem
1
2
3
4
5
6
7
Total
Score
Problem 1
Potentiometer as an angular position sensor
The circuit shown on this diagram shows a
potentiometer used as a sensor for the angular
position (angle
α
) of a robotic arm. At
α
= 0, the
potentiometer’s tap is in its middle position so that
R
X
= R
0
= R
P
/2
At an arbitrary, nonzero angle
α
(in degrees) the
resistance equals
R
X
= R
P
/2 + K
⋅
α
where K is constant measured in k
Ω
/degrees.
Part 1 (10 points)
Assume
R
P
= 240 k
Ω
, K = 0.8 k
Ω
/degree.
Calculate in degrees:
α
MIN
,
α
MAX,
and the
Range
of angles
(
α
MAX

α
MIN
)
.
Write your answers:
α
MIN
= _____,
α
MAX
= _____,
Range = _____
As shown in lectures, the output voltage is a linear function of the angle:
V
OUT
= a + b
⋅
α
,
where
a
and
b
depend on
V
S
and the potentiometer.
Assume
V
S
= 30 V
Calculate
a
in volts and
b
in volts/degree. Wirte your answers:
a
= ______________ volts
b
= _______________ volts/degree
Continued on the next page.
Part
1
2
3
4
Total
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View Full DocumentEECS 314
Winter 2009
Homework set 2
Student’s name ___________________________
Discussion section # _______
(Last, First, write legibly, use ink)
(use ink)
Instructor is
not responsible
for grading and entering scores for HW papers lacking clear
information in the required fields above
© 2009 Alexander Ganago
Page 2 of 2
Problem 1, continued
Part 2 (10 points)
Make a computergenerated plot of
V
OUT
vs. the angle
α
over the interval from
– 150 degrees to +150 degrees; attach your computer code or show your work in
handwritten form.
Part 3 (10 points)
Calculate the angles in degrees:
α
4
corresponding to
V
OUT
= 4 V and
α
7
corresponding to
V
OUT
= 7 V
α
4
= ____________˚
α
7
= ____________˚
Assume that the error of readout of
V
OUT
is 10 mV and calculate the error
Δα
of readout of the angle
α
.
Δα
= ____________˚
Briefly discuss how to reduce the error of readout of the angle
α
:
increase/decrease
R
P
;
increase/decrease
K;
increase/decrease
V
S
, etc. (when
you vary one parameter, keep others unchanged)
Part 4 (10 points)
Suppose you have to monitor the angular position of a robotic arm from negative 120˚ to
positive 120˚, with a readout device that accepts voltages from 0 to +5 V, with +2.5 V
readout at the middle position of the potentiometer’s tap.
Can you use the device discussed above (Parts 1 – 3)?
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 Winter '07
 Ganago

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