MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
Department
of
Aeronautics
and
Astronautics
16.060:
Principles
of
Automatic
Control
Fall
2003
PROBLEM
SET
8
Due:
11/26/2003
Note:
This
problem
set
is
due
at
the
beginning
of
class
on
Wednesday
!
Problem
1
The
input
to
a
system
with
transfer
function
G
(
s
)
is
r
(
t
)
=
A
sin
t
.
Show,
by
partial
fraction
expansion
and
complex
number
manipulation,
that
the
output
in
steadystate
is:
c
ss
(
t
)
=
AM
(
)
sin(
t
+
±
(
))
where
M
(
)
=

G
(
j
)

and
±
(
)
=
G
(
j
).
Problem
2:
Nyquist
Plots
For
each
of
the
following
openloop
transfer
functions,
draw
a
plot
of
the
s
plane
showing
the
poles
and
zeros
of
G
(
s
)
and
the
Nyquist
Dcontour.
Then
sketch
(by
hand)
the
Nyquist
plot
for
each
system.
Label
points
corresponding
to
important
frequencies
(e.g.
=
0
,
±
)
and
use
arrows
to
show
the
direction
of
increasing
frequency.
1.
G
(
s
)
=
K
s
2.
G
(
s
)
=
s
K
2
3.
G
(
s
)
=
s
K
3
K
4.
G
(
s
)
=
s
+1
5.
G
(
s
)
=
K
(
s
+2)
s
+1
6.
G
(
s
)
=
K
(
s
+1)
s
+2
K
7.
G
(
s
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 Fall '03
 willcox
 Aeronautics, Astronautics, Nyquist plot, Nyquist stability criterion, Department of Aeronautics and Astronautics, p oles

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