System Identification Toolbox™

c2d - Convert model from continuous to discrete time

Syntax

md = c2d(mc,T)
md = c2d(mc,T,method)
[md,G] = c2d(mc,T,method)

Description

mc is a continuous-time model such as any idmodel object (idgrey, idproc, idpoly, or idss). md is the model that is obtained when it is sampled with sampling interval T.

method = 'zoh' (default) makes the translation to discrete time under the assumption that the input is piecewise constant (zero-order hold).

method = 'foh' assumes the input to be piecewise linear between the sampling instants (first-order hold).

When you have the Control System Toolbox™ product installed, the following methods are also supported: 'tustin', 'prewarp', and 'matched'. In these cases the covariance matrix is not transformed.

Note that the innovations variance of the continuous-time model is interpreted as the intensity of the spectral density of the noise spectrum. The noise variance in md is thus given as /T.

idpoly and idss models are returned in the same format. idgrey structures are preserved if their CDMfile property is equal to 'cd'. Otherwise they are transformed to idss objects. idproc models are returned as idgrey objects.

For idpoly models, the covariance matrix is translated by the use of numerical derivatives. The step sizes used for the differentiation are given by the function nuderst. For idss, idproc, and idgrey models, the covariance matrix is not translated, but covariance information about the input-output properties is included in md. To inhibit the translation of covariance information (which may take some time), use c2d(mc,T,'covariance','none').

The output argument G is a matrix that transforms the initial state x0 of mc to the initial state of md as

X0d=G * [X0; u(0)],

where u(0) is the input at time 0. For idproc models, the state variables correspond to those of idgrey(mc). For idpoly models, G is returned as the empty matrix.

Examples

Define a continuous-time system and study the poles and zeros of the sampled counterpart.

mc = idpoly(1,1,1,1,[1 1 0],'Ts',0);
md = c2d(mc,0.5);
pzmap(md)

See Also

customreg

data2state(idnlarx)