Lecture S12
Muddiest Points
General
Comments
In this lecture,
we continued
our
discussion
of states. We started
with
a
concept
tests on
the
number of states
required
in
modelling a
roller coaster, which
caused
some confusion. We
continued with
a
description
of
a
circuit
in
statespace form, and
found
the eigenvalues of the
system,
which
are the same as
the characteristic values.
Responses
to MuddiestPartoftheLecture
Cards
(44
cards)
1.
The first PRS
question
was
worded
unclearly. (1)
Sorry
if you
found
it
to
be
unclear.
Was
the wording
unclear, or was it
diﬃcult
to
figure out
what
the states are?
2.
In
the PRS
question, no one knew
you
could
assume you
could
assume you
know
the velocity distribution
along the track. (1)
I
don’t
think
I
said
that. I said
that
you
know
that the velocity
vector is along
the track. Is that
what
you
mean?
If so,
that
was
part of
the point of
the problem
—
to
determine what
the minimum
number of
initial
conditions
is.
3.
identifying states
— not sure how
to
do
it
yet. (1)
For circuits, it’s easy
—
it’s all
the capacitor
voltages
and
all
the inductor currents. For other systems, it
takes a
little more
work.
The easiest way
to
identify
them
is to
figure out
what
initial conditions are required.
These correspond
to
states.
4.
The RLC
circuit is
pretty much
analogous
to
the roller
coaster, right?
(1)
Exactly!
In
both
cases,
two
states are needed
to
describe the system.
5.
For
the concept question, the
only states
are
d
and
v
, because both
can
be
determined from
known
parameters
of
s
?
(1)
d
and
v
are states, because they
are
the only
initial
conditions
you
need
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 Fall '05
 MarkDrela
 RLC, Eigenvalues, Eigenvalue, eigenvector and eigenspace, Sx

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