Specify discretization method for continuous-time to discrete-time conversions
c2dOptions to specify the discretization method and
associated quantities for discretizing models with
returns the default options for
c2d. Customize options by using dot
notation to change the properties of
sets properties using one or more name-value arguments. For example, to use the bilinear
(Tustin) approximation method, set
Method — Discretization method
'zoh' (default) |
Discretization method, specified as one of the following values:
Zero-order hold, where
Triangle approximation (modified first-order hold), where
Bilinear (Tustin) approximation. By default,
Zero-pole matching method. (See , p. 224.) By
|Least-squares method. Minimize the error between the frequency responses of
the continuous-time and discrete-time systems up to the Nyquist frequency. Use
For information about the algorithms for each conversion method, see Continuous-Discrete Conversion Methods.
PrewarpFrequency — Prewarp frequency for
0 (default) | positive scalar
Prewarp frequency for
'tustin' method, specified as 0 or a
positive scalar value. Specify the frequency in
TimeUnit is the time units, specified in the
TimeUnit property, of the discretized system. A value of 0
corresponds to the standard
'tustin' method without prewarp.
FitOrder — Fit order for
'auto' (default) | positive integer
Fit order for
'least-squares' method, specified as
'auto' or an integer. This option specifies the order of the
discrete-time model to be fitted to the continuous-time frequency response with the
'least-squares' method. The default value
to uses the order of the continuous-time model. Specify a model order by changing
FitOrder to a positive integer. Reducing the order can help with
unstable poles or pole/zero cancellations at
z = -1.
FractDelayApproxOrder — Maximum order of Thiran filter for
0 (default) | positive integer
Maximum order of the Thiran filter used to approximate fractional delays in the
'matched' methods. A value of 0
c2d rounds fractional delays to the nearest integer
multiple of the sample time. If you set this property to a positive integer,
thiran to approximate fractional delays before discretizing.
Discretize Two Models Using Tustin Discretization Method
Generate two random continuous-time state-space models.
sys1 = rss(3,2,2); sys2 = rss(4,4,1);
Create an option set for
c2d to use the Tustin discretization method and 3.4 rad/s prewarp frequency.
opt = c2dOptions('Method','tustin','PrewarpFrequency',3.4);
Discretize the models,
sys2, using the same option set, but different sample times.
dsys1 = c2d(sys1,0.1,opt); dsys2 = c2d(sys2,0.2,opt);
 Franklin, G.F., Powell, D.J., and Workman, M.L., Digital Control of Dynamic Systems (3rd Edition), Prentice Hall, 1997.
Version HistoryIntroduced in R2010a
R2021a: Option to specify fit order
FitOrder option specifies the fit order when using the
least-squares method for continuous-discrete conversion.
FitOrder specifies the order of the discrete-time model to be fitted to
the continuous-time frequency response. Reducing the order can help with unstable poles or
pole/zero cancellations at
z = -1.