0
6.1kviews
Show the mapping from s-plane to z-plane using Impulse Invariant method and explain its limitation. Using this method determine H(z). Assume T= 0.1 sec.
1 Answer
written 5.8 years ago by |
Limitation:
Now,
$H(s)=\frac{3}{((s+2)(s+3))}$ ………………(i)
By using partial fraction,
$\frac{3}{((s+2)(s+3))}$ = $\frac{A}{(S+2)}$+$\frac{B}{(S+3)}$ ………………(ii)
$3=A (s+3)+B (s+2)$
Put s=-3; B=-3
Put s=-2; A=3
Put the value of A and B in equation (i)
$H(s)=\frac{3}{(s+2)}-\frac{3}{(s+3)}$
We have transformation equation
$\frac{1}{(s-P_k )} → \frac{1}{(1-e^{P_k T_S } Z^{-1} }$
$\frac{1}{(s+2} → \frac{1}{1-e^{-2(0.1)} Z^{-1}} = \frac{1}{(1-0.818 Z^{-1} }$
$\frac{1}{(s+3)} → \frac{1}{(1-e^{-3(0.1)} Z^{-1}}= \frac{1}{(1-0.740 Z^{-1}}$
$H(z)=\frac{3Z}{(Z-0.818)}-\frac{3Z}{(Z-0.740)}$