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16.31
Handout
#1
Prof.
J.
P.
How
September
7,
2007
T.A.
TBD
Due:
September
14,
2007
16.31
Homework
Assignment
#1
Goals:
Refresh
skills
for
Matlab
and
classical
analysis.
1.
(Root
Locus
Analysis)
[FPE
3.32,
page
159].
Suppose
that
you
are
to
design
a
unity
gain
feedback
controller
for
a
±rst
order
plant
(see
±gure).
A
speci±c
controller
con±g
uration
has
been
selected
(it
is
PI).
The
objective
is
to
pick
the
control
gains
so
that
the
poles
lie
in
the
regions
shown
in
the
±gure
to
the
right.
Figure
1:
Problem
#
1
(a)
What
values
of
ω
n
and
ζ
correspond
to
these
shaded
regions
in
the
s
²plane
Cal
culate
these
exactly
(they
will
be
nonlinear)
and
then
approximate
to
something
more
useful
for
design?
(b)
Let
K
α
=
α
= 2
.
5.
Find
the
values
of
K
and
K
I
so
that
the
poles
of
the
closed²
loop
system
lie
in
the
shaded
region.
(c)
Prove
that,
no
matter
what
the
values
of
K
α
and
α
,
the
controller
provides
suﬃ
cient
ﬂexibility
to
place
the
poles
anywhere
in
the
s
²plane.
2.
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 Spring '04
 EricFeron

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