User`s guide

3 Operations on LTI Models
3-22
and you get back the original discrete-time system (up to canceling the
pole/zero pair at z=–0.5):
Zero/pole/gain:
(z+0.5)
---------
(z+0.5)^2
Sampling time: 0.1
First-Order Hold
First-order hold (FOH) differs from ZOH by t he underlying hold mechanism.
To turn the input samples into a continuous input , FOH uses linear
interpolation between samples.
This method i s generally more accurate t han ZOH for systems driven by
smooth inpu ts . D ue t o causality constraints, this opt io n is only a vailable for
c2d conversions, and not d2c conversions.
Note: This FOH method differs from standard causal FOH and is more
appropriately called triangle approximation (see [2], p. 151). It is also known
as ramp-invariant approximation be c ause it is disto r tio n -free f or ra mp inputs.
Tustin Approximation
The Tustin or bilinear approximation uses the approximation
to relate s-domain and z-domain transfer functions. In
c2d conversions, the
discretization of a continuous transfer function is derived by
uk
[]
ut
()
ut() uk[]
tkT
s
–
T
s
------------------
uk 1+[]uk[]–(),+= kT
s
tk1+()T
s
≤≤
ze
sT
s
1 sT
s
2
⁄+
1 sT
s
2⁄–
--------------------------
≈=
H
d
z
()
Hs
()