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Control system doubt

  1. Mar 20, 2016 #1

    cnh1995

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    Consider the following circuit with Vs=1V,
    R=1Ω and C=1F.
    upload_2016-3-20_16-49-34.png
    The voltage transfer function of the resistor can be written as
    Vr(s)/Vs(s)=s/(s+1).
    Now I understand s is complex frequency and at s=∞
    the transfer function becomes unity since capacitor acts as a short and Vs=Vr. What I don't understand is at s=-1, the TF becomes infinity.
    If s=-1 and s=σ+jω, σ=-1 gives TF=∞. What is the meaning of this? What is the general significance of σ? I know jω represents the oscillations in the system but what does the real part σ represent?
     
  2. jcsd
  3. Mar 20, 2016 #2

    BvU

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  4. Mar 20, 2016 #3
    σ is for an exponential voltage (or current) proportional to exp(σt).
    Consider the current I=exp(-t).
    It gives voltages exp(-t) and -exp(-t)+const passing through the resistor and capacitor - so the sum is constant (1 in your case) which means infinite "AC" gain of your circuit.

    (but of course it's only in mathematics where a current can be infinite in the past))
     
    Last edited: Mar 20, 2016
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