Ian, et al,

2010/8/10 Ian Parker <ianpark...@gmail.com>

> A μ sec is nothing even when we are considering time critical functions
> like balance.

Not true!!!

What most people miss are the stability requirements for closed loop control
systems. These are crystal clear in an analog world, but some (many?) people
think that they don't apply in a digital world. They do. While the thing you
are controlling may live in a millisecond world, you can't have a sharp
frequency cutoff point, or the system absolutely WILL oscillate at that
frequency for complex reasons. If you don't understand those reasons, then
you shouldn't be working in this area. So, how sharp is "sharp". The rate of
roll-off must be <12db/octave, as 12db/octave represents a 180 degree phase
shift, and any more makes it positive feedback. This must continue to high
frequencies, at least past the point of "unity gain", meaning that any
positive feedback dampens itself out because there is less than unity gain.

Lets take an example. Suppose your feedback system senses things and
administers corrections, the corrections being, say, at a gain of 1000 times
the error, and you want the feedback to work >1kHz. Rolling off at
6db/octave to stay away from the 12db/octave unstable point, means that the
permissible unity gain point is 1MHz. Of course, for really precise
positioning you might want higher gain and frequency stability, which pushes
you above 1MHz.

Note that delays look just like phase-linear low-pass filters, and indeed
some electronic designs use phase-linear low-pass filters to achieve short
delays. Hopefully you noticed "low pass" here, namely, delays introduce
their own VARIABLE phase shifts so that at higher frequencies, they become
positive feedback and fundamentally unstable.

IMHO the "logic" that does the feedback control MUST NOT incorporate a
network, unless that network is VERY short, e.g. in the same room. Even
then, network protocols will probably delay things too long to run stably.

Hence, while networks may be OK for higher functions, forget them as part of
any real-world feedback loops.

Note in passing that this SAME discussion applies to neurons in complex
feedback configurations (like brains). People now think that neurons are  *S
L O W*  when they may be just "compensated" (using analog terminology,
meaning that their high frequency response rolls off at ~6 db/octave) to
operate in a feedback world. Note that they ARE able to do some things
REALLY FAST (e.g. fast edges, doubled pulses, etc.) so perhaps they are
really running in a world that is ~2 orders of magnitude faster than anyone
(else) has yet thought possible. This would RADICALLY change projections of
how much computer it would take to emulate a brain, perhaps by ~2 orders of


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