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S+T=1 sensitivity of a control system

  1. Dec 9, 2012 #1


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    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
  2. jcsd
  3. Dec 9, 2012 #2

    jim hardy

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    I gather you're talking about feedback systems here....

    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.

    old jim
    Last edited: Dec 9, 2012
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