Specifications

Continuous/Discrete Conversions of LTI Models
3-21
The signal is then fed to the continuous system , and the resulting
output is sampled every seconds to produce .
Conversely, given a discrete system , the
d2c conversion produces a
continuous system whose ZOH discretization coincides with . This
inverse operation has the following limitations:
•
d2c cannotoperate onLTImodels withpolesat whenthe ZOH isused.
•Negative real poles in the domain are mapped to pairs of complex poles in
the domain. As a result, the
d2c conversion of a discrete system with
negative real poles produces a continuous system with higher order.
The next example illustrates the behavior of
d2c with real negative poles.
Consider the following discrete-time ZPK model.
hd = zpk([],–0.5,1,0.1)
Zero/pole/gain:
1
-------
(z+0.5)
Sampling time: 0.1
Use d2c to convert this model to continuous-time
hc = d2c(hd)
and you get a second-order model.
Zero/pole/gain:
4.621 (s+149.3)
---------------------
(s^2 + 13.86s + 1035)
Discretize the model again
c2d(hc,0.1)
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)
ut
()
Hs
()
yt
()
T
s
yk
[]
H
d
z
()
Hs
()
H
d
z
()
z 0=
z
s