Specifications

3 Operations on LTI Models
3-20
Continuous/Discrete Conversions of LTI Models
The function c2d discretizes continuous-time TF, SS, or ZPK models.
Conversely,
d2c converts discrete-time TF, SS, or ZPK models to continuous
time. Several discretization/interpolation methods are supported, including
zero-order hold (ZOH), first-order hold (FOH), Tustin approximation with or
without frequency prewarping, and matched poles and zeros.
The syntax
sysd = c2d(sysc,Ts); % Ts = sampling period in seconds
sysc = d2c(sysd);
performs ZOH conversions by default. To use alternative conversion schemes,
specifythedesiredmethodasanextrastringinput:
sysd = c2d(sysc,Ts,'foh');% use first-order hold
sysc = d2c(sysd,'tustin');% use Tustin approximation
The conversion methods and their limitations are discussed next.
Zero-Order Hold
Zero-order hold (ZOH) devices convert sampled signals to continuous-time
signals for analyzing sampled continuous-time systems. The zero-order-hold
discretization of a continuous-time LTI model is depicted in the
following block diagram.
The ZOH device generates a continuous input signal u(t) by holding each
sample value u[k] constant over one sample period.
H
d
z
()
Hs
()
Hs
()
uk
[]
yk
[]
ut
()
yt
()
ZOH
T
s
H
d
z
()
ut() uk[],= kT
s
tk1+()T
s
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