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exo1.py

Created by raph-couvert

Created on June 13, 2023

640 Bytes

Essayez-le maint...Redemander plus tardNe plus afficher
On a :
sk = 0,5ek−1 − 0,6sk−1
Calculer la fonction de transfert en z 
lim k->+inf sk lorsque le signal d’entrée est un échelon unité.
On prend la transformée en z de la relation de récurrence, on obtient alors :
S(z) = 0,5E(z) − 0,6z^(−1)S(z)
d’où l’on déduit :

G(z) = S(z)/E(z)= 0, 5 / z + 0, 6

Si en entrée, on a un échelon unité, alors :

E(z) = z / z − 1

et le théorème de la valeur finale s’écrit :
s(inf) = lim z->1 de (1 − z^(−1))S(z) 
= lim z->1 de (1 − z^(−1))G(z)E(z)
= lim z->1 de  (z − 1 / z)(0, 5 / z + 0, 6z)(z / z − 1)
=0, 5 / 1, 6
= 0, 3125

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