thd2thc (System Identification Toolbox)

Convert a model from discrete to continuous time.

thc = thd2thc(thd)
thc = thd2thc(thd,delay,NoP)

Description

The discrete-time model thd, given in the theta format, is converted to a continuous-time counterpart thc. The covariance matrix of the parameters in the model is also translated using 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 NoP = 1.

If the discrete-time model contains pure time delays, i.e.,

, then these are first removed before the transformation is made. These delays should then be appended as pure time-delay (deadtime) to the continuous-time model. This is done automatically by th2ff. To have the time delay approximated by a finite-dimensional continuous system, enter delay = 'del'. The default is delay = 'nodel'.

If the innovations variance is

in thd, and its sampling interval is T, then the continuous-time model has an indicated level of innovations spectral density equal to T *

Important: The transformation from discrete to continuous time is not unique. thd2thc 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 may 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:

gd = th2ff(th);
thc = thd2thc(th);
gc = th2ff(thc);
bodeplot([gd, gc],3)