d2c (System Identification Toolbox)

Convert a model from discrete to continuous time.

Syntax

mc = d2c(md)
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 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).

If the discrete-time model contains pure time delays, i.e., , then these are first removed before the transformation is made. These delays are appended as pure time-delay (deadtime) 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. idgrey structures will be preserved if their CDMfile property is equal to cd. Otherwise they will be 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 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.

m = n4sid(data,3)
mc = d2c(m);
bode(m.mc,'sd',3)

Note that the transformation to continuous time can be included in the n4sid command by specifying the model to be continuos time.

```
mc = n4sid(data,3,'Ts',0)
```

See Also

c2d, nuderst

References

See Discrete and Continuous Time Models and Spectrum Normalization and the Sampling Interval" in the "Tutorial".

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