Specifications

3 Operations on LTI Models
3-22
---------
(z+0.5)^2
Sampling time: 0.1
First-Order Hold
First-order hold (FOH) differs from ZOH by the underlying hold mechanism.
To turn the input samples into acontinuous input , FOH uses linear
interpolation between samples.
This method is generally more accurate than ZOH for systems driven by
smooth inputs. Due to causality constraints, this option is only available 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 because it is distortion-free for ramp 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
Similarly, the
d2c conversion relies on the inverse correspondence
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
()
H
d
z
()
Hs
'()
,where= s
'
2
T
s
------
z 1–
z 1+
------------
=