Specifications

2 LTI Models
2-50
Specifying Delays in Discrete-Time Models
You can also use the ioDelay, InputDelay,andOutputDelay properties to
specify delays in discrete-time LTI models. You specify time delays in
discrete-timemodels with integer multiples ofthesampling period.Theinteger
k you supply for the time delay of a discrete-time model specifies a time delay
of k sampling periods. Such a delay contributes a factor to the transfer
function.
For example,
h = tf(1,[1 0.5 0.2],0.1,'inputdelay',3)
produces the discrete-time transfer function
Transfer function:
1
z^(–3) * -----------------
z^2 + 0.5 z + 0.2
Sampling time: 0.1
Notice the z^(–3) factor reflecting the three-sampling-period delay on the
input.
Mapping Discrete-Time Delays to Poles at the Origin
Since discrete-time delays are equivalent to additional poles at ,they can
be easily absorbed into the transfer function denominator or the state-space
equations. For example, the transfer function of the delayed integrator
is
α
1
β
1
+
α
2
β
1
+ ...
α
m
β
1
+
α
1
β
2
+
α
2
β
2
+
α
m
β
2
+
:: :
α
1
β
p
+
α
2
β
p
+ ...
α
m
β
p
+
z
k–
z 0=
yk 1+[]yk[] uk 2–[]+=