d2c - Transform linear model from discrete to continuous time
Syntax
mc = d2c(md)
mc = d2c(md,method)
mc = d2c(md,'CovarianceMatrix',cov,'InputDelay',inpd)
Description
The discrete-time model md, given as any idmodel object,
is converted to a continuous-time counterpart mc.
The covariance matrix of the parameters in the model is also translated
using the Gauss approximation formula and numerical derivatives of
the transformation. The step sizes in the numerical derivatives are
determined by the function nuderst. To inhibit
the translation of the covariance matrix and save time, enter among
the input arguments (...,'CovarianceMatrix,'None,....))
(any abbreviations will do).
method is one of the input intersample behaviors 'zoh' (zero-order
hold) or 'foh' (first-order hold). If method is
not specified, the InterSample behavior of the
data from which md was estimated is used.
When you haveControl System Toolbox installed, the following
methods are also supported: 'tustin', 'prewarp',
and 'matched'. In these cases no translation of
the covariance matrix takes place.
If the discrete-time model contains pure time delays, that is,
,
then these are first removed before the transformation is made. These
delays are appended as pure time delay (dead time) to the continuous-time
model as the property InputDelay. To have the time
delay approximated by a finite-dimensional continuous system, enter
among the input arguments (...,'InputDelay',0,...).
If the noise variance is
in md, and its
sampling interval is T, then the continuous-time
model has an indicated level of noise spectral density equal to T
.
While idpoly and idss models
are returned in the same format, idarx models are
returned as idss models mc.
The reason is that the transformation does not preserve the special
structure of idarx. The idgrey structures
are preserved if their CDMfile property is equal
to cd. Otherwise they are transformed to idss objects.
Note
The transformation from discrete to continuous time is not unique. d2c selects
the continuous-time counterpart with the slowest time constants consistent
with the discrete-time model. The lack of uniqueness also means that
the transformation can be ill-conditioned or even singular. In particular,
poles on the negative real axis, in the origin, or in the point 1,
are likely to cause problems. Interpret the results with care. |
Examples
Transform an identified model to continuous time and compare
the frequency responses of the two models.
m = n4sid(data,3)
mc = d2c(m);
bode(m,mc,'sd',3)
Note that you can include the transformation to continuous time
in the n4sid command by specifying the model to
be continuous time.
mc = n4sid(data,3,'Ts',0)
See Also
 | diff | | EstimationInfo |  |
Includes the most popular MATLAB recorded presentations with Q&A sessions led by MATLAB experts.
Get the Interactive Kit
Store 
