<Bob Clark (940427.1543 EDT)>
Bill Powers (940422.0600 MDT) Subject: predictions; DME
This was the third topic in your post. To simplify the discussion, I
am experimenting with trying to keep each post to a single topic.
Rate Feedback. Bob Clark (940421.2155) Subject:RE: CONFLICTS - RKC.
In response to my questions:
_where_ is the ability to "predict" included in PCT? And _who_, or
_what_ does the "predicting?"
You point out:
In control theory the general term for predictive or anticipatory
control is rate feedback.
To me, equating "predictive or anticipatory control" with rate
feedback is questionable. "Rate feedback" includes time derivatives
of current signals within the feedback function. Commonly, they are
added to those same signals: f = a * x + b * dx/dt, where a and b are
weighting factors. This has some resemblance to anticipation since
the feedback signal, f, is affected by the rate of change of the
variable, x. But this does not become "anticipation" or "prediction"
until some form of extrapolation is applied.
Your reference to excessive sensitivity to first derivatives is an
important part of the situation. I had an experience in flying
somewhat similar to yours. The first time I flew to North Carolina I
wore myself out trying to hold my altitude going over the mountains.
Only my problem was not "rate sensitivity," it was simply trying too
hard to hold my altitude too precisely. It never changed very fast,
but I tried to keep it at a specific value. This was "perfectionism"
in controlling altitude. [No doubt you recall my tendency to
perfectionism?]
You also comment on excessive attention to long-term predictions. I
agree, but it is hard to determine in advance what might be
"excessive." "Long-term" is defined in terms of some time scale.
Beginning to plan for a college education soon after the birth of a
child may be looking too far ahead. But a modified form of such
planning may contribute favorably to retirement income. In addition,
long-term goals can provide perspective for short-term decision
making. Indeed, any theory provides a long term perspective for the
design and interpretation of short-term analysis and experiment.
Time integrals are another form of temporal perception. Because more
time is needed for the signal to reach a significant magnitude,
integration of the feedback signal results in a slower response. The
form of the integrated signal is quite different from that of a
delayed signal. A delayed signal approximates the original wave
form, but at a later time.
Excessive attention to time integrals can create other problems. It
can resemble depression, with a generally "sluggish" response. This
response contrasts with the "quick and nervous" types you suggest for
those with excessive attention to time derivatives.
Derivatives and integrals tend to compensate for each other -- one
delays, the other accelerates. If an individual shifts his attention
back and forth from one to the other, a form of oscillation can
result. Depending on the time scale, this can look like a form of
"manic-depression." It seems to me that we, including MacFarland,
discussed this way back when. In such an oscillation, the damping
term needs to be increased. Give more attention to the current value
of the variable -- "Get Real!"
Again we find perception of temporal variables plays an important
part in the operation of control systems.
Regards, Bob Clark