Finding Impulse Transfer Function with Impulse Invariant Method

1. May 27, 2012

maxiking

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.

$\frac{a}{s+a}$

I don't know how to solve the problem correctly

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

3. The attempt at a solution
d(t) = ae-at
D(z)=$\frac{az}{z-e^(-at)}$

2. May 27, 2012

RoshanBBQ

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.
$$h[n] = Th(Tn)$$
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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