
A general approach to deriving the z-domain transfer function H(z) for a discrete-time system
intended to approximate a linear continuous-time system with transfer function H(s) is now given.
Starting with a simulation diagram of the continuous-time system, each integrator block with
transfer function H
I
(s) ¼1=s is replaced by a discrete-time transfer function block H
I
(z) correspond-
ing to a specific numerical integrator. For example, replacing H
I
(s)byH
I
(z) for explicit Euler
integration,
1
s
H
I
(z) ¼
T
z 1
) s
1
H
I
(z)
¼
z 1
T
(4:495)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
t (s)
y
k
, k = 0, 2, 4, 6, ..., 200
y(t), 0 ≤ t ≤5
Explicit ...