Powers on (not so) Slow feedback

[from Gary Cziko 930130.0430 GMT]

Bill Powers (930128.2200) elucidated:

Imagine a control system that has a time-constant of 40
milliseconds (we don't actually have to imagine it; the Little
Man models it). This control system can control the position of
an arm, so that one or more perceived joint angles follows a
smoothly varying reference signal, moving the arm under complete
control at all times.

But now take this very same control system, and instead of giving
it a reference signal that passes smoothly from one magnitude to
another, make the reference signal jump instantaneously -- in,
say ten milliseconds -- from a frequency of 200 impulses per
second to a frequency of 500 impulses per second, with no passage
through intermediate frequencies. . . .

During this maximum-speed movement, there is naturally no
control. The control system is already producing the largest
output it can consistent with stopping in the new position. Any
disturbance that came and went during the approach would simply
cause a deviation from the nominal path. So, paradoxically it may
seem, the control system's control action is uncontrolled after a
step-change in the reference signal -- although the final
position is as controlled as ever.

Wouldn't research to show this be quite easy to do? Simply apply
disturbances (big rubber band like I used at Durango) during an action that
was performed at various speeds. If the HPCT model is right, then for
slower actions the path of the limb will be controlled as well as its final
position. At higher speeds, the path will be less well-controlled but the
final position will still be. While at the highest speeds, only the final
position will be controlled.

Might it take only a big rubber band and a well-place video camera to do
this research? (A more sophisticated way of introducing disturbances would
be a knee or elbow brace with the physical resistance of the joint
manipulable by remote control--in your spare time, Bill).

But for some reason I have the intuition that at the very highest speeds
even the final position will not be well-controlled, at least not without
some patch-up correction at the end of the movement. But I want my
inuitions to be wrong here.

Looks like a good project for a master's thesis.--Gary

P.S. It's possible that my College of Education might in the near future
inherit our campus's Department of Kinesiology. Could be fun.


Gary Cziko Telephone: 217-333-8527
Educational Psychology FAX: 217-244-7620
University of Illinois E-mail: g-cziko@uiuc.edu
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Champaign, Illinois 61820-6990