It seems as if the environment of the person is more intelligent than the person. This is based at looking at the equations for the different variables.
Will you please explain the choice you made for which variables are level, which auxillary?
If you were able to think of another way of modeling this, what are the considerations for choosing this one over other ways?
From: David Goldstein
Subject: the exact model
Date: 9/20/98
[From Bill Powers (980920.0743 MDT)]
David Goldstein Subject: the exact model Date: 9/20/98
It seems
as if the environment of the person is more intelligent than the person.
I suppose it is, since it consists of all the people who can run a
production line, repair bad items, and so forth. All the controller has to
do in this case is to control the right perceptual variable relative to the
reference value given (presumably) by higher management. The controlled
perception is simple -- the sum of two quantities -- so if someone would
key those values into a computer every day, a program could do it.
This is based at looking at the equations for the different variables.
Will you please explain the choice you made for which variables are level,
which auxillary?
I wasn't too sure about that myself. I experimented with accumulating the
output of the production line into a "produced items" level variable (
which is just an accumulation, an integral), then running those items
through an inspection station as a flow which would branch into good,
to-be-reworked, and to-be-discarded level variables, and so on, but decided
that involved too much detail and anyway would put two level variables in
series into the control loop, which would make stabilization hard ...
Anyway, I ended up assuming that inspection and division of the flow into
three channels could take place on the fly, so everything would remain a
flow type of variable until the accumumation of good items and
to-be-reworked items, which would be level variables. The auxiliary
variables following the flow off the production line remain flow-type
variables until they get integrated into a level-type variable.
If you were able to think of another way of modeling
this, what are the considerations for choosing this one over other ways?
I tried lots of ways, most of which I can't remember since they all had
something wrong with them when I imagined how they would work. For example,
I ended up making the speed of reworking increase as the backlog of items
to be reworked (level variable) increased. I tried making the reworking
speed constant, but this meant either that there was no accumulation of
items to be reworked (all items repaired in one day) or the backlog just
kept increasing until the error was low enough to slow the production line
-- and then it took a long time to get rid of the backlog and reach the
desired number of items. With a fast enough constant rework rate, I might
as well have omitted the reworked-item loop, which wasn't very interesting.
So I decided that management would assign workers to the reworking shop
according to the size of the backlog, and the number of workers assigned
would be the "speed of repair" variable. To be even more realistic, I could
have stolen those people from the production line ...
This wasn't a real modeling problem ( as far as I know), so there were no
data to dictate the details and I made up my own, trying to make them
realistic. The main thing I was trying to show was how a control system
could be superimposed on an otherwise open-loop process to give it a
specific goal and make it stop when it reached that goal. The "reworking"
loop was suggested by Bob, and makes the problem somewhat less trivial.
Best,
Bill P.