# logical gain

[From Rick Marken (920531)]

Here are some thoughts motivated by an article on the front
page of the Sunday times announcing the development of a
new lightbulb that will last MUCH longer and consume less
energy while putting out the same amount of light. The
improvement is based on logic -- the light is produced by
"signal processing" rather than heating.

This led me to think about loop gain in control systems. I
am thinking of loop gain as all the multiplications that
occur as effects propagate around the control loop. There
are really only two multiplications -- k.o, the organism function
which amplifies input (and is in units of input/output) and k.f,
the feedback function, which amplifies (or reduces) output (and
is in units of output/input). Loop gain, K, is the product k.o*k.f.
K is thus a dimensionless quantity. The bigger K is, the better
control is.

It appears to me that the same level of loop gain (K) can be
achieved in two ways -- by increasing k.o or k.f. Increasing
k.o requires putting energy into the control system (by eating,
etc) and this can be done in only one way -- because the system
can only get "strong" in one way. Increasing k.f can be done in
many ways -- that's where the new light bulb comes in. It seems
to me that one of the advantages of having higher level control
systems is that they can figure out clever ways to make k.f
more efficient (and have fewer undesireable side effects). The
new light bulb let's me control the illumination level in the
room with far less energy input than was required for the old
light bulb. k.o is still the same (I still have to exert the same amount
of energy to turn the rheostat in order to make the lights
brighter or dimmer). The loop gain for controlling illumination
is still the same -- but the amount of energy required to
transform my output (turning the knob) into my input (perceived
brightness) is much less. This is not really an increase in
k.f to offset an decrease in k.o; it's a decrease in the energy
required to produce k.f. There are, however, many examples of higher
level control systems (at the principle level, at least) contributing to
an increase in k.f that increases loop gain dramatically with
no change in k.o; levers and pulleys, for example.

So it seems that higher level systems can serve to increase
the loop gain of lower level systems without necessarily changing
the physical construction of the control system itself. This
might be a way of looking at the evolutionary advantage of having
higher level control systems; its a way to increase loop gain
without too much structural change in the organism. That is,
higher level systems let you increase K by increasing k.f rather
than k.o.

Or maybe not. Just some Sunday musings; now back to the hammock.

Best regards

Rick

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Richard S. Marken USMail: 10459 Holman Ave
The Aerospace Corporation Los Angeles, CA 90024
E-mail: marken@aero.org
(310) 336-6214 (day)
(310) 474-0313 (evening)