Loose control

]From Jeff Hunter (921026-1)

Bill Powers (921013.0930)
> Greg Williams (921012-2) --

>In principle, there is no difference between this sort of control
>and the control of a cursor subject to a "hidden" disturbance -- in
>both cases, what is tending to thwart control cannot be "seen."

Qualitatively, perhaps not. But control is not just a qualitative
matter -- control or no control. A control system that can cancel only
10 percent of a disturbance isn't much of a control system. In a
tracking situation, 98 percent of the disturbance is cancelled.

  Ok. Here's where we disagree strongly. You say, "A control system
that can cancel only 10 percent of a disturbance isn't much of a
control system." Here's an everyday counter-example.

  During fall a squirrel can find lots of food. It stores (say) 30
grams of body fat as "insurance" for the winter. During winter it can
find little food (except what it has hidden) and burns 0.3 grams per day.
After 100 days winter had better be over. (Can you tell I'm Canadian?)

  If the squirrel can reduce "fat burned today" by 10% (from
.3 g to .27 g) it will stretch its fat reserves an extra 11 days.
This could be the margin between life and death. (Now can you tell I'm
Canadian? :slight_smile:

  During winter the squirrel has great incentive to reduce
"amount of fat burned today" to zero or even negative levels.
  It presumably does this by fluffing its fur, sleeping during
really cold patches, prospecting for nuts during warm spells, etc.
  (We could test the reference levels of "fat burned" and
"fat stored" by providing the squirrel with peanut butter, and
finding how much the squirrel will eat when there is no cost or
risk to gathering food.)

  At any rate we have a control system (the squirrel) trying to
control a disturbance (winter famine) in a CEV (fat burned per day)
and not reducing the error (0.3 g) to zero, but still having a useful
result (it survives till spring).

  We get the same sort of thing in concert halls. The air
conditioning cannot handle the heat output of 40,000 sweaty rock fans.
However the management pre-cools the building, and keeps the conditioning
running during and after the concert. Given that the hall is only used
4 hours out of every day the air conditioning (a classic control
system) can keep the temperature acceptable even though it can
only compensate for a fraction of the momentary disturbance.

>Today my son Evan was having a problem with his new birthday
>present, a radio- controlled truck. He asked me to help him figure
>out what was wrong with the transmitter. Some experiments guided by
>me showed a weak battery. Next time he'll be able to cure the
>malady himself. No, he didn't hold a gun to MY head, either. We
>BOTH got to where we wanted to be.

See how easy it is when nobody is trying to figure out how to control
someone else?

  See why it seems that your definition of control is not:
  - getting someone else to do what you want
but
  - getting someone to do what they don't want to

>This is the crux of our dispute. I claim that this is truly
>CONTROLLING FOR, not just "wishes to see." B arranges A's
>environment so as to encourage a class of actions by A which B
>wants to see. If A doesn't perform actions in the class defined by
>B, then B RE-arranges A's environment. And so on, until A does
>actions in the class defined by B, or B gives up.

If this is the crux of our dispute, then our dispute seems to come
down to a quantitative question: loop gain. I guess I automatically
dismiss examples in which the loop gain is so low that disturbances
can't be significantly resisted. A model of the sort of situation you
propose just above would, I imagine, have a loop gain very much less
than -1; the degree of control possible would be very low. For
significant control, I use a rough rule of thumb of a loop gain of at
least -5 or -10. Only when the loop gain becomes that large do you
begin to see the typical properties of a control system -- action
opposing disturbance, controlled variable remaining near the reference
level.

  And I contend that you are blinding yourself to the possibility
that loop-gain should be measured over a longer period if the
disturbance is predictable (cyclic or following a known growth pattern).

  In the case of Gary's son he is following a technique (involving
yourself in your child's education) which has a high correlation with
academic achievement. He may only be able to change Evan from a "B"
to an "A" rather than an "A+" student. Nevertheless he is applying
control, and it is useful.

      ... Jeff

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