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Homework Help: Final Value Theorem

  1. Jun 13, 2010 #1

    I had a question about the final value theorem:

    lim sF(s)
    S->0

    =

    lim F(t)
    t->infinity


    I was told I can only use this if I know that a final value exists for f, or in other words that f(infinity) exists.

    How can I check if it exists? If I have F(s), the only way I can think to check is to find the inverse Laplace and then see. If I do that, then there is no use of me applying the final value theorem as I will already know what it is.

    Can some explain how one can determine whether or not the final value exists before applying the theorem?

    Thanks!!
     
  2. jcsd
  3. Jun 16, 2010 #2
    anyone?
     
  4. Jun 19, 2010 #3
    Well, if you have the transfer function of a system, by analyzing the poles you can determine whether the system is a stable or an unstable one. Giving an appropriate input to a stable system results in an output response that converges to a particular value as t tends to infinity while for an unstable system the output goes to infinity (i.e. it is not bounded)
     
  5. Jun 20, 2010 #4
    I think you USE the final value theorem to verify IF the time function converges to a real value. Basically you solve lim sF(s) for s->0, and if this value exists then the transfer function is good and works because lim sF(s) for s->0 = lim f(t) for t->infinity. If the transfer function is good you would get the same value when solving either limit(if you know the time function). The difference would be that solving lim sF(s) for s->0 is easier because many terms of the transfer function will cancel out because of the s->0.

    Hope you got it!!
     
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