# Electronics metaphors and PCT

[From Bill Powers (940225.1030 MST)]

Bill Leach (940224 etc.) --

Bill, I'm glad to know you're an old electroniker. So have I been
since the early 1950s (actually since 1946 as a Navy "electronic
technician's mate" if you can accept that term without jumping to
conclusions). We ought to be able to work out this problem about
feedback with no difficulty.

The basic problem is that you're using electronics metaphors that
need to be expanded and adjusted to fit PCT.

One metaphor is "feeding back a portion of the output to the
input." If you consider this idea carefully, you will realize
that what is fed back is not a "portion of the output," but a
signal that is proportional to the output. The fed-back signal
doesn't have to be in the same form as the output.

For example, the output could be a voltage, and the input could
be a current going into the base of a transistor. You can't feed
back a portion of the output voltage to achieve feedback, because
the transistor is current-sensitive, not voltage-sensitive. So
what do you do? You insert a device into the feedback path that
converts the output _voltage_ into a proportional input
_current_: a resistor. The fed-back current now subtracts (for
negative feedback) from the signal input current at the same base
junction.

Now go slightly further afield. Suppose we want to make a super
hi-fi audio system. Rather than feeding a voltage or current back
from the output transformer secondary to get the feedback we
want, let's mount a high-quality capacitor microphone right in
front of the speaker, very close to the diaphragm (less than half
the highest wavelength). This microphone is used to pick up the
air pressure caused by the speaker and convert it to a voltage
instantaneously proportional to air pressure. We use that voltage
as the feedback signal to an earlier stage of the power amplifier
(using a resistor to convert it to current if necessary). By this
means we make the feedback signal proportional to the actual
momentary air pressure, which is really what we want to control
(who cares what the diaphragm movements are, if the air pressure
fluctuates exactly as the input signal does?). The gain of the
system makes the feedback signal match the input signal, which
now means that the air pressure fluctuations match the electrical
fluctuations in the input signal. Perfect hole-in-the-wall hi-fi.

The metaphor of taking a portion of the output to feed back is
now converted to something more realistic: we are using a
feedback path that creates a signal proportional to the output
effect we want to control. By using the output to make that
signal track the input, we thereby make the output effect also
track the input.

One more step is needed: to get away from the idea that it is the
output of the system that is controlled. Suppose that instead of
making music, we use the same amplifier to position a load (in
the early days, I actually used a commercial 100-watt audio power
amplifier with response to DC in servomechanisms -- very handy).
Now the output of the electronic system is a torque applied to a
motor armature.

We don't want to control the torque, but something that is
affected by that torque. The armature turns a shaft, the shaft
turns a gear train, the gear train turns a screw, and the screw
moves the load. So the position of the load is a rather remote
effect of generating an output torque.

What we need now is to turn the position of the load into an
electrical signal. We do this by mounting a linear potentiometer
on the load, long enough to span all desired positions. We apply
a fixed voltage across the pot. The load moves the wiper, and the
wiper then picks off a voltage proportional to position. We can
now feed back this position voltage, which is really a perceptual
signal in PCT terms, to the input of the amplifier. If there is
high enough gain, the fed-back voltage will be made to track the
input voltage. Since that fed-back voltage is determined by the
load position, the result is to make the load position track the
input voltage, too. We now have a system in which a physical
output (a torque) is mechanically converted into a different
variable in different physical units (a position), and in which
the feedback effects are converted again into still another
physical form (a voltage analogous to position).

One last set of adjustments to the electronic metaphors needs to
be made. We have to change a bunch of labels around to meet the
needs of modeling the behavior of an organism.

First off, we actually have two "inputs" to the control system.
One is the input signal that is used to specify the desired load
position (or that is the electronic signal input to the audio
amplifier). The other is the electronic signal generated by the
position-measuring potentiometer (or the signal representing the
state of the output in the audio amplifier). One (or both) of
these signals has to be renamed so we know what is meant when we
refer to the "input."

In PCT we rename the input that is driving the whole system; we
call it the "reference signal," which is compatible with normal
engineering usage. The other signal, the one that represents the
state of the controlled variable (load position or air pressure),
we call the "perceptual signal" because it is an internal
representation of the external variable that is to be controlled.
The device that actually generates the perceptual signal as a
function of the state of the controlled variable (the
potentiometer) is called the "input function" (surprise!). Servo
engineers often call it the "sensor."

On the output side, we call the output of the control system the
actual physical effect produced by the electronic (or neural)
signals at the electronics-environment boundary: the torque in
the servo motor, or the force created by the voice-coil. We call
this the "output quantity" because it is a measurable physical
quantity that is the first possible measure of the macroscopic
physical effects of the system on its environment.

There is one last label. The output quantity (torque or force) is
connected to the controlled quantity (load position or air
pressure) through physical linkages of some sort (gears or laws
of air compression and wave propagation). These linkages make up
what we call in PCT the _feedback function_.

So to sum up for the load position servomechanism and add a few
remaining terms:

A reference signal enters the system at one input, along with a
feedback or perceptual signal. The difference or error signal
(computed by a comparator or differential amplifier) is highly
amplified to create a macroscopic physical output effect, a
torque, which we call the output quantity. This torque feeds back
through mechanical linkages to affect the state of a controlled
quantity located at the _input_ to the control system: the
position of a load which is sensed by a potentiometer, the input
function. The resulting input or perceptual signal which
represents the state of the controlled variable connects back to
the place where the reference signal came in, at the comparator,
and we have completed the loop. If the amplifications are large
enough, and dynamic stability is achieved (not usually
difficult), the result will be that varying the reference signal
will result in varying the load position so the perceptual signal
representing load position almost exactly tracks the reference
signal.

Kind of makes you want to go out and build one, doesn't it?
Building one is exactly as simple as it sounds, nearly.

Now we need to orient this diagram in a standard way and decide
where to put the system boundaries.

First, tilt the system 90 degrees so the reference signal comes
in from above instead of (as usually) from the left. Draw the
boundary between the control system and its environment as a (now
horizontal) line that passes through the output actuator (motor)
and the input sensor (potentiometer). The only input from the
environment is the sensory input representing the state of the
controlled quantity. The only output to the environment is the
output of the actuator, the output quantity. In the environment,
draw a path from the output quantity to the controlled quantity,
which is placed just below the sensor. This path is the
environmental feedback connection through which the output
quantity affects the controlled variable at the input.

The reference signal comes from higher up inside the overall
system in which we find this control system. It comes from inside
the organism, not from its environment. This is a break with
engineering tradition, because when engineers build a
servomechanism, they make its reference input accessible to
adjustment by external agencies in the environment -- users. In
organisms there is no external user, and reference signals are
generated by higher organizations inside the organism. The only
inputs from environment to organisms are _sensory_ inputs, which
simply report the current state of the controlled variable.

I just don't feel like going through the tedium of making an
ASCII diagram of all this. You'll find the standard diagram in
nearly all PCT publications, in some form or other. If the above
is too confusing I'll byte the bullet.

Incidentally, you are quite right to reject the implication that
a disturbance is "feedback." A disturbance is an independent
influence applied to the controlled variable (directly or through
effects anywhere else in the loop). It would be friction in the
screw moving the load, or someone pushing on the load. That is
simply a disturbance, which is automatically countered by
variations in the control system's output quantity.

The term "feedback" itself is almost always misused if you want
to be a purist. Feedback is a property of an entire loop; the
effect of a variable in the loop _on itself_. When I call the
output-to-input connection the "feedback function" I am speaking
loosely; it is really the external connection that makes feedback
possible. If we understand the organization of a control loop
clearly, we can be a little loose sometimes, although it's

ยทยทยท

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Best,

Bill P.

<[Bill Leach 940225.21:23 EST(EDT)]

[Bill Powers (940225.1030 MST)]

"Electronic Technicians Mate" should have been the forerunner to the
"Electronics Techinican", yes? Hummm, 1946... probably not involved in
equipment.

Bill, thanks! Your lucid explaination did a great deal for me, I think.

I really don't think that I ever did have a problem with the reference
signal. Even in "regular control theory" I have always "sorta"
considered changes to set-points as a change in "purpose". The idea that
the "set-point" "setter" is wholey internal doesn't bother me a bit.

Just to make sure that I do have this straight though:

The entire perception signal is considered feedback, yes? A disturbance
then, if perceived becomes a _part_ of the feedback, yes?

Thus, in the skater example: If we assume that the coach's words are a
significant factor in the perception of the subject, then calling what
the coach is doing "feedback" is NOT really out of line.

Now then calling it "postive" or "negative" feedback would be wrong as
far as PCT is concerned BECAUSE the in the sense that such modifiers are
typically used the paradigm is not PCT. If I think that I am "giving
positive feedback" to support a behaviour, that is ok but from a PCT
standpoint, the "feedback" still results in a perception and that
perception is still a part of a negative feedback control loop?

-bill