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MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
Department
of
Aeronautics
and
Astronautics
16.060:
Principles
of
Automatic
Control
Fall
2003
PROBLEM
SET
9
Due:
12/04/2003
Problem
1:
Representing
a
Pure
Delay
in
the
Frequency
Domain
One
situation
in
which
frequency
response
techniques
are
useful
is
when
a
transfer
function
can
not
be
represented
easily
in
terms
of
poles
and
zeros.
A
very
common
example
is
a
pure
delay,
which
is
always
present
in
any
control
system
implemented
on
a
digital
computer
(e.g.
Simulink).
For
a
pure
delay
of
time
τ
,
the
output
y
(
t
)
in
terms
of
the
input
u
(
t
)
is
given
by:
y
(
t
)
=
u
(
t
−
τ
)
1.
Using
the
de±nition
of
the
Laplace
transform,
±nd
the
transfer
function
G
(
s
)
=
Y
(
s
)
U
(
s
)
corresponding
to
a
pure
delay.
2.
Draw
the
polar
plot
for
G
(
s
)
for
a
time
delay
of
1
second.
(The
polar
plot
is
the
part
of
the
Nyquist
plot
corresponding
to
0
< ω <
∞
.)
Problem
2:
Nyquist
Plots
with
Negative
Gain
For
each
of
the
following
openloop
transfer
functions,
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.
 Fall '03
 willcox
 Aeronautics, Astronautics

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