|Dec9-12, 10:40 AM||#1|
S+T=1 sensitivity of a control system
with s being the sensitivity of a transfer function GC/(1+GC) to the parameter G. (1/(1+GC)
I see mathematically how it works out. My question is about the profoundness of the statement. Qualitatively, what does it mean
|Dec9-12, 11:27 AM||#2|
To me it is a demonstration of the profound effect of feedback...
G is the forward gain
and C is the feedback
let C be +1 for simplicity's sake
observe that gain of the feedback loop G/(1 + G) cannot be greater than 1, regardless of forward gain G,,,,
unless you reverse sign of feedback
which creates possibility of a zero denominator (hence infinite closed loop gain) hence oscillation....
And that happens by itself when time lag of feedback amounts to a half cycle(180 degrees) which reverses the sign....
Any physical system with feedback will find that frequency for you; recall from elementary school when the PA microphone gets in front of the speaker you get a pure tone - that's the frequency where transit time at speed of sound from speaker to mike amounts to a half cycle.
Mother Nature is very playful !
Look at earth's feedback system for temperature control - heat transport from surface to stratosphere via water vapor.
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