Addendum on feedforward

[From Bill Powers (931103.1530 MST)]

Hans Blom (931103) --

A couple more comments on feedforward.

Your use of the term "reference signal" in a completely open-loop
system is somewhat strange to me. Why not just call it the
"input?" Calling it the reference signal makes it difficult to
explain what is different about a reference signal in a negative
feedback system. In the negative feedback system, the perceptual
feedback signal is directly compared with the reference signal,
this comparison being the basis for action. In the open-loop
case, an arbitrary calibration has to exist between the so-called
reference signal and the outcome, because there is no natural
link as there is when the outcome is continually represented by
the perceptual signal.

ยทยทยท

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Greg Williams just sent me (thank you, Greg!) a copy of an
article on H. S. Black, the inventor of feedback theory:

Kline, Ronald; Harold Black and the negative-feedback amplifier;
_Control Systems 13_, #4, p. 82-85.

In 1923, Black had a brilliant notion of how to eliminate
distortion in amplifiers using feedforward. The idea was to
amplify a signal by A, then using passive components divide the
output by a factor of A to produce a sample of the signal with
the same amplitude as the input. Subtracting the input from the
sample would leave a signal representing only the distortions
introduced by the amplifier, scaled down by A. That corrective
signal could then be subtracted from the output (after being
amplified by A again), to leave a distortion-free amplified
output signal. Of course Black found that this didn't actually
work: I presume he realized that in amplifying the corrective
signal he had to use an amplifier with just as much distortion as
the original amplifier had (if an amplifier with less distortion
was available, why not use it for the first amplifier, too?).
Some reduction in distortion was possible, but not the kind that
Black was trying to produce. Also, I am sure, Black realized that
the first amplifier had to retain the same gain to match the
passive division factor as it aged, which was one of the problems
he was trying to solve.

At any rate, the key idea was using a passive network to divide
the amplified signal down. This became the essential feature, in
1927, of the true solution that Black was after: the gain of the
feedback system was the inverse of the passive division factor,
and was as stable and linear as the passive components were.

So Black considered feedforward first, and found it wanting.
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Best,

Bill P.