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ECE 486
Assignment # 3
Issued: February 10
Due: February 17, 2011
Reading Assignment:
Continue reading .
..
FPE
, 5th or 6th ed., Chapters 1–3 (ignoring subsections marked “
N
”).
See also
Belanger
, Chapters 1–3, and
Brogan
Chen
Chapters 1–3.
Problems:
6.
The
speed
y
of a DC motor satisﬁes ˙
y
+60
y
= 600
v

1500
d
, where
v
is the armature
voltage, and
d
is a load. Suppose
v
is deﬁned via the PI control law,
v
=
k
p
e
+
k
I
∫
t
0
e
(
s
)
ds.
where
e
=
r

y
, as usual, with
r
the reference speed.
(a) Deﬁne a disturbance process
˜
d
so that the model can be expressed in the ‘input
disturbance’ form,
Y
=
G
p
(
V
+
˜
D
)
(b) Draw a complete block diagram showing the plant, compensator, input, output,
and the location of disturbance and reference inputs.
(c) Compute the transfer function
H
1
(
s
) =
Y
(
s
)
/R
(
s
) for arbitrary choices of
k
p
,k
I
,
and note the value of
H
1
(0).
(d) Repeat with the transfer function
H
2
(
s
) =
Y
(
s
)
/D
(
s
).
(e) Compute values of
k
p
,k
I
so that the following closed loop speciﬁcations hold
for a step reference input: 5% overshoot, and 1 second settling time.
Note
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This note was uploaded on 03/28/2011 for the course ECE 486 taught by Professor H during the Spring '09 term at University of Illinois at Urbana–Champaign.
 Spring '09
 H

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