Deducing the disturbance

[From Rick Marken (950122.1630 PST)]

While doing some tracking research with my daughter as the subject
(as usual, being her dad, I gave her terrible instructions -- but
she still did extremely well, just as Tom predicted, and just as she
always does -- adorable little control system that she is) I thought
of a way for Bruce and Bill to get a lighter sentence on the "deducing
the disturbance" rap. It is, indeed, not in general as easy to deduce
the disturbance as Tom and I might have suggested.

If all you know about a subject's performace is the state of
the controlled variable, c, over time, then, of course, there
is no way to deduce the disturbance that was acting at the time
c was being kept under control. This, as we all know, is the situation
that the control system itself is in; all it knows is the state of
c (as a perceptual signal); it responds "as though" it knew the
disturbance (because it is generating outputs that counteract
the effects of the disturbance(s) on c) but, of course, the control
system cannot (and does not) deduce d.

If you know both c and h (the output) you STILL don't know enough
to deduce the disturbance. You also need to know the nature of
the feedback function, g(), that relates h to c. In our tracking
experiments we know that g() is typically a multiplier of 1.0
so g() is linear and it can be written as c=h. But it is often the
case in real world control situations that the relationship between
output, h, and controlled variable, c, is not linear. In this case,
if we deduced that d is c-h we would be wrong; d is actually c-g(h).
We have to know g() before we can make the corerct deduction of d
(actually the effect of d, h(d)) on c.

So, in general, in order to be able to deduce d we have to know
not only the output variable that affects c but we also have to know
HOW it affects c -- linearly, non-linearly or, even, changing
over time. Note, however, that we never have to know the reference
level for the controlled variable, c, in order to deduce d.

Happy deducing

Rick