ME 375
HOMEWORK 12
Spring 2009
Out:
Thur., April 23
Due:
Wed., April 29
PROBLEM 1
(30%)
Given the following expression for the denominator of the closedloop transfer function
for a system that uses a proportional controller
K
:
2
1
10
(
2)(
10
34)
K
ss
s
+=
++
+
(a)
Determine the roots of this characteristic equation when
K
= 0.
(b)
To get an idea of where the roots go when
K
gets large, determine the imaginary axis
crossings.
(Hint: set
s
=
j
ω
and solve for
and
K
.)
(c)
Sketch the root locus on graph paper.
You can use Matlab command
rlocus
to help
you.
(d)
Determine the range of gain
K
for which this system is stable.
PROBLEM 2
(35%)
The dynamics of one axis of a Cartesian robot with compliance in the power transmission
element are described by the following transfer function:
()
2
22
1
2
Xs
Fs
=
+
Since vibration during motion is to be minimized, it has been suggested that the
acceleration
ax
=
±±
be used for feedback.
(a)
Determine the transfer function that relates the transformed acceleration
A
2
(
s
) to the
transformed force
F
(
s
).
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 Spring '10
 Meckle
 16%, 2%, 30%, 2 seconds

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