From: jeff@DRETOR.DCIEM.DND.CA ((Jeffrey C. Hunter))
Newsgroups: bit.listserv.csg-l
Subject: Re: Jeff's Loose control system
Date: 7 Nov 92 00:48:34 GMT
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
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              at Nov 5, 92 3:45 pm

[From Jeff Hunter (921106-A)]

>  Re: Bill Powers (921105.1430)

	Great. I was afraid when I posted that you would either agree,
or disagree with the post. Since you've done both I can be happy :-)
	I'll try and state my points again more carefully. If I do it
right you should reply "yeah. that's trivially obvious".

	First your comments on the "wavers" program. (Which by-the-way
are pretty perceptive.)

>  I've got your program to run, and think I understand it now. By the
>  way, Turbo C doesn't like long integers as indexes to arrays

	Ta. That bin stuff didn't need to be "long" anyways.

>  The environmental part of the loop is a simple integrator.

	Yup. It's just one-dimensional brownian motion. Fortuitously
Hans Blom is also into the topic.
	The default change-per-tick is +-4 (just to be greater than 2).

> The perceptual function and comparator are in "if (cont_tot > 0)"...

	Yup. Reference is zero. Linear input function. No delay.
	The comparator is actually *trinary* since it can produce <0, >0,
or =0. This point is obscured by the code, and it makes an analysis
of the beast a little tricky.

>  The steady-state loop gain of these control systems is nominally
>  infinite.
	Great. Glad you agree.

>  ... The reason is the integration in the environmental part of
>  the loop.
	Not exactly. The reason is that the long term average of the
disturbances is zero. If I had biassed the random numbers so that
there were 3 increases for each decrease then the control would
disappear.

	This is the main point of "wavers". The effective loop
gain of the control can be varied wildly merely by applying
a different "pattern of disturbances". For example in the
"bias" case the disturbances were +5,-3 rather than +4,-4.

>  ... It is
>  impossible to estimate the effective loop gain except for the biased
>  case, where a constant of 1 was added on each iteration. Over 10,000
>  iterations, this should have added 10,000 to the value of bias_tot
>  (and a lot more to the squared error); instead, bias_tot changed by
>  only 104, or about 1% of the expected value. This yields an effective
>  loop gain of about 100.


	Forgive me if this point (effective loop gain depends on the
disturbances) is obvious. However a lot of discussion on the group
appears to ignore this.
	I think that the one of the points of the "leaning on the
environment" posts was that a perfectly valid control system in one
setup could fail spectacularly if the disturbances changed in
pattern even if they stayed the same in magnitude.


> If you intended to portray a loose (low-loop-gain) control system,
>  you didn't succeed.
	I actually wanted to emphasise the difference between
moment-by-moment gain (in which "cont" is totally swamped by
almost every disturbance) and the long-term gain (in which "cont"
has infinite gain).

				... Jeff
--
De apibus semper dubitandum est - Winni Ille Pu
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU