[From Bill Powers (2010.02.13.0818 MST)]
Gavin Ritz 2010.02.13.15.20NZT –
BP earlier: bp:
I think we’re using different
definitions for these terms. Would you describe what your meanings are
for reference signal and reference
level?
GR: The reference
signal as I understand it is the signal inside the control system (r) the
specifies the error state (e) and hence determines what the reference
level of the controlled quantity is.
BP: That may be the problem. Here is a lesson about signals and
analog computing which may clarify matters.
The reference signal is a signal that enters the control system
from outside (from above, as shown in the standard PCT diagram). It
specifies how much perceptual signal the control system is to create by
acting on the environment – more specifically, by acting through
environment on a physical input quantity that it is sensing. The
reference signal is simply a neural signal that sets the way the
perceptual signal will be made to look – not because the reference
signal causes this match, but because of the action of the rest of the
control loop. The perceptual signal represents the state of that input
quantity, so the control system is really acting on its own perceptual
signal. The net effect of this feedback is that the perceptual signal is
altered until it nearly matches the magnitude of the reference signal.
When the perceptual signal matches the reference signal in terms of
impulses per second, the input quantity outside the control system will
necessarily be in a corresponding state - the state that produces an
amount of perceptual signal equal to the reference signal. That state of
the input quantity is observable from outside; when the perceptual signal
matches the reference signal, we call the magnitude of the input quantity
the “reference level”. Of course the input quantity is at the
reference level only when the perceptual signal matches the
reference signal.
The error signal is produced by subtracting the magnitude of the
perceptual signal from the magnitude of the reference signal. So the
error signal is not determined by the reference signal, but is also
influenced just as much by the perceptual signal. The subtraction is done
by inhibition of the reference signal by the perceptual signal; it’s the
kind of computation that goes on continuously, an analog
computation.
The error signal is amplified by the output function to generate the
output quantity. The output quantity, acting through a feedback link in
the environment, affects the input quantity being sensed – but external
disturbances also add to the effects of the output on the input quantity.
Nevertheless, the control system is able to keep the perceptual signal
matching the reference signal.
The meaning of the term “signal” in PCT, and engineering in
general, is not the common-sense meaning of a coded message or a
starter’s gun. It means the magnitude of a physical quantity like a
voltage or the frequency firing of a neuron. It is called a signal
because the physical variable involved is very weak, not able by itself
to caused any significant physical consequences, but its magnitude
carries information about the magnitude of some other variable that does
have significant physical effects. At some point in a network of signals,
there is an amplifier (like a muscle) that transforms the weak signal
into a large physical effect, as the signal from a motor neuron is
transformed into a muscle tension that, in the biceps for example, can
exert a pull of over a quarter of a ton. That, by the way, is the primary
place where metabolic energy is used – in the transformation from
signals to physical effects.
In the control system, signals are combined by being added to or
subtracted from other signals – in terms of their magnitudes. The
reference signal, set to some steady number of impulses per second (a
neural signal, that is), enters a neural comparator, which also receives
a perceptual signal that is variable in magnitude and represents the
state of some external variable in the environment. The perceptual
signal is inhibitory, so its effects in the comparator subtract from the
effects of the reference signal. This is an “analog
computation”: the result of the computation is a continuous error
signal with a magnitude equal to the difference in magnitudes between the
reference and perceptual signals. It is another neural signal, still
small and weak in terms of physical effects. That small signal gets
amplified and otherwise processed to produce a larger (in magnitude, but
still physically weak) signal that goes into the output transducer where
now its effects are made a million times larger in terms of energy usage,
to create a macroscopic effect on the environment.
It’s crucial to read the Live Block Diagram with these descriptions in
mind. The blocks do not represent events that happen one after another as
you move your eye around the closed loop. They are places where variables
are transformed continually into the states of other continuous
variables, all the blocks being active at the same time as you can see by
watching the Live Block Diagram after you change the disturbance or
reference signal.
I hope that somewhere in that discussion is something that will help our
communications.
Best,
Bill P.