Challenge, Control and Purpose -Reply

[Hans Blom, 950918c]

(Rick Marken (950916.915))

Are things clearer now?

Sort of. Your model definitely controls.

Thank you! That coming from you I take as the grandest compliment I
could possibly get! ;-).

But there are some funny little problems. For example, in the
calculation of dpre (dpre = 2*dnew-dold) the 2 is crucial; a value
other than 2 leads to loss of control rather abruptly.

Explanation: draw two points, x[i-2] and x[i-1], and connect them by
a straight line. Extrapolate upto time i by continuing the straight
line "into the future". You get

          * x[i] --- we need a prediction of this value
       * x[i-1] --- based on this value
   * x[i-2] --- and on this value

The best prediction of the value of x[i] from this extrapolation is

  x[i-1] + {x[i-1] - x[i-2]}

which is simply the value of the last point plus the previous incre-
ment. This extrapolation is based on the assumption that the
derivative of the signal does not change between time i-2 and time i.
That is only an assumption, of course, but it works well with low
frequency signals. If you change the factor 2 into something else,
you base your prediction on a different assumption. Obviously an
incorrect one, and one that leads to loss of control.

The feedback function (k) is also limited to values <=1. Any gain
from environmental feedback seems to lead to loss of control.

I can think of no reason why this could be so except a programming
error. So it cannot be true ;-).

your control system must have a precise measure of its own output

Yes. Doesn't yours?

and it must be able to store previous values of the estimates of
disturbance (dold)

Yes. My controller needs some extra memory in order to be able to
calculate a first derivative.

and it must do this storage precisely (while the integration done by
the control model can be relatively sloppy -- leaky).

Yes. But see what you gain by some precision...

Rick, are you satisfied too?

Somewhat, yes. I'm sure glad you provided that model; I still need
to study it to see what's going on; even though it is simple it is
very puzzling.

I like puzzles. Don't you?

If we take the model at face value as a reasonable model of control,
I guess the next question is whether we can do an experiment with
people to see which of the two models (PCT vs model based control)
gives the best representation of their controlling.

We can start to study ANTICIPATION.