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Finding Impulse Transfer Function with Impulse Invariant Method

  1. May 27, 2012 #1
    1. The problem statement, all variables and given/known data
    Transfer functions of the continuous compensation links are given as follows. Find the impulse transfer functions of the digital compensation links using the impulse invariant method.

    [itex]\frac{a}{s+a}[/itex]

    I don't know how to solve the problem correctly :cry:


    2. Relevant equations
    D(z)=Z[D(s)]


    3. The attempt at a solution
    d(t) = ae-at
    D(z)=[itex]\frac{az}{z-e^(-at)}[/itex]
     
  2. jcsd
  3. May 27, 2012 #2
    The idea behidn impulse invariant method is to compute a discrete impulse response, h[n], from the continuous impulse response, h(t), by sampling h(t) every T units of time.
    [tex]h[n] = Th(Tn)[/tex]
    The discrete impulse response is the z-transform of this quantity. It's troubling that the problem statement doesn't give you a sampling time. I suppose you will have to keep it symbolic as T.
     
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