Specifications

Continuous/Discrete Conversions of LTI Models
3-23
Tustin with Frequency Prewarping
This variation of the Tustin approximation uses the correspondence
This change of variable ensures the matching of the continuous- and
discrete-time frequency responses at the frequency .
Matched Poles and Zeros
The matched pole-zero method applies only to SISO systems. The continuous
and discretized systems have matching DC gains and their poles and zeros
correspond in the transformation
See [2], p. 147 for more details.
Discretization of Systems with Delays
Youcan alsousec2dto discretizeSISO or MIMO continuous-timemodels with
time delays. If
Ts is the sampling period used for discretization:
•A delay of
tau seconds in the continuous-time model is mapped to a delay of
k sampling periods in the discretized model, where k = fix(tau/Ts).
•The residual fractional delay
tau – k*Ts is absorbed into the coefficients of
the discretized model (for the zero-order-hold and first-order-hold methods
only).
For example, to discretize the transfer function
Hs
()
H
d
z
'()
,where= z
'
1 sT
s
2
⁄
+
1 sT
s
2
⁄
–
--------------------------
=
H
d
z
()
Hs
'()
,= s
'
ω
ω
T
s
2
⁄()
tan
---------------------------------
z 1–
z 1+
------------
=
ω
Hj
ω()
H
d
e
j
ω
T
s
()
=
ze
sT
s
=
Hs() e
0.25s– 10
s
2
3s 10++
-------------------------------
=