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Date:         Sun, 16 Aug 1992 08:09:19 -0600
From:         "William T. Powers" <POWERS_W%FLC@VAXF.COLORADO.EDU>
Subject:      Re: amplification, organism vs environment
X-To:         CSG-L@vmd.cso.uiuc.edu

[From Bill Powers (920816.0800)]

Martin Taylor (920816.0130) --

[I haven't received your "Paris paper" -- I think I would have noticed a
50-page package!]

You say

>... but elasticity has much the same perceptual effect as an >interaction
over a physical variable with another controller that has a >different
reference.  At one extreme we have a totally non-resisting >medium, in
which (apart from disturbances) the physical variable is >readily induced
to provide the desired percept.  At the other end of >the scale, we have
crystalline elasticity, in which the controller can >have only a trivial
effect on its percept, because the world resists >strongly any attempt to
deform it. In between, there is a whole range >of impedances, both
resistive and reactive.

I think we're talking at cross-purposes here. I was speaking about
amplification, an input-output property, while you're talking about
resistance to disturbance, a possibly closed-loop property. Amplification
(more properly, power gain, which takes impedances into account) entails a
source of energy, a power supply, that can be tapped so that a variation in
the output signal contains a greater energy flux than a variation in the
input signal does. This means that the output of an amplifier does more
work than is done on the input of the amplifier. If input and output
impedances are equal and resistive, the output amplitude is greater than
the input amplitude (unless the loop is closed). This is an aspect of
"dissipative systems" that doesn't seem to get mentioned much.

When a control system's output meets with "crystalline" resistance, its
power output is dissipated mostly internally. The deflection that does
result (assuming that's the sensed and controlled variable) is small, so
the loop gain of the control system is smaller than it would be for a more
compliant and more easily-sensed environment. The internal power gain of
the control system, however, is still large: a small deflection creates a
small change in perception, involving a few microergs of energy transfer.
The resulting output change may involve many pounds of force, acting
through the distance of the deflection. Even taking impedances into
account, there is a large power gain through the control system. The open-
loop change in force per unit deflection is larger than the open-loop
change in deflection per unit force.

The energy put into the crystalline substance compresses it, storing at
most an amount of energy equal to the force times the deflection. The
largest amount of energy that can come out of the crystalline substance
(pushing back against the disturbance) is the amount put into it. So the
power gain of the non-living substance is at most unity.

Only when some external energy source has put some energy into a non-
controlling part of the environment -- lifting the broomstick and standing
it on end -- can there be any power gain in the non-controlling
environment. A small force applied to the upright broomstick is amplified
as the broomstick leans and begins to lose its stored energy. The end of
the broomstick can, if its motion is resisted, exert a greater and greater
force on something else as the angle departs from vertical, producing much
more power than the initial push put into it. So for the moment at least,
the broomstick can display power amplification.

However, the power amplification of the control system balancing the
broomstick can easily put enough energy back into the broomstick to raise
it to the vertical again. The optical energy taken from the broomstick by
looking at it is negligible; the muscle energy put back into the broomstick
by moving its bottom end is immensely greater. So the control system's
power amplification is incomparably greater than that of the broomstick.

Even if the control system were trying to dent the surface of a crystal by
pushing on it, the same situation would apply. If we supplied a microscope
that magnified the perception of the amount of dent, there would be a range
of deflections over which control would be excellent -- we've raised the
loop gain by using the microscope, which can be thought of as an impedance-
matching device. The power gain has not been changed, but now the control
system can sense the deflections more accurately and vary its output force
to create any deflection in the possible range. The possible range, of
course, is set by the maximum available output force, again a matter of
impedance matching. If the output is applied to a compound lever minifying
the output movements, which does not change the power transfer but does
lower the output impedance, the amount of deflection can now be as large as
the control system wants it to be, up to the point where the crystal
fractures.

I used this principle in fine-controlling the position of the 300-pound
carriage of a grating ruling engine. The input (sensing) impedance was
matched by using a laser interferometer to measure the position of the
carriage; the output device was a voice coil impedance-matched through a
compound lever to bend part of the steel casting. As the required
deflections were only about 0.5 wavelength of light, the voice coil thrust,
multiplied about 10,000 times by the compound lever, was quite sufficient
to achieve the desired deflections. The power gain of this system was
probably on the order of a million, after all losses are taken into
account. The amplitude loop gain was about 1000. The open-loop power gain
would have been -- God knows. Billions and Billions, to quote a famous
person.

I used a similar principle to stabilize the laser, an ordinary $100 helium-
neon laser. The controlled variable was the audio-frequency beat frequency
between the two modes of oscillation of the laser, and the output function
was a ring of resistors that heated the Pyrex tube of the laser.

Once you've played with control on such a microscopic scale, there ain't no
such thing as a "crystalline substance" no more. The world is made of soft
rubber. When you pushed with one finger on that 7-ton engine, just about
anywhere, you could see the output meter swing a little as the control
system adjusted the carriage position to resist the disturbance. And of
course the engine-room was temperature controlled; just walking into the
room could make the meter showing heater power swing full scale. The whole
system was a clutter of control systems. Of course you couldn't see any of
them working: nothing was happening but the ruling strokes. That was the
idea. Absolutely nothing was supposed to happen except that the ruling
diamond moved to the right place and stayed there during the stroke. We
maintained about 0.005 wavelength accuracy for 30 days at a time. The
system is still running, although since I left the rat's nest circuitry has
mostly been replaced by a computer. My control systems tended to look more
like the nervous system than a printed circuit (a mess). My guiding
principle for design is called "reorganization."
-----------------------------------------------------------------------

Best,


Bill P.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU
Subject: (no subject given)