Transforming between continuous-time and discrete-time representations is useful, for example, if you have estimated a discrete-time linear model and require a continuous-time model instead for your application.
You can use
d2c to transform any linear identified
model between continuous-time and discrete-time representations.
d2d is useful is you want to change the
sample time of a discrete-time model. All of these operations change
the sample time, which is called resampling the
These commands do not transform the estimated model uncertainty.
If you want to translate the estimated parameter covariance during
the conversion, use
approximate the transformation of the noise model only when the sample
T is small compared to the bandwidth of the
The following table summarizes the commands for transforming between continuous-time and discrete-time model representations.
Converts continuous-time models to discrete-time models.
You cannot use
To transform a continuous-time model
mod_d = c2d(mod_c,T)
Converts parametric discrete-time models to continuous-time models.
You cannot use
To transform a discrete-time model
mod_c = d2c(mod_d)
Resample a linear discrete-time model and produce an equivalent discrete-time model with a new sample time.
You can use the resampled model to simulate or predict output with a specified time interval.
To resample a discrete-time model
mod_d2 = d2d(mod_d1,Ts)
The following commands compare estimated
m and its continuous-time counterpart
a Bode plot:
% Estimate discrete-time ARMAX model % from the data m = armax(data,[2 3 1 2]); % Convert to continuous-time form mc = d2c(m); % Plot bode plot for both models bode(m,mc)
A sampled signal is characterized only by its values at the
sampling instants. However, when you apply a continuous-time input
to a continuous-time system, the output values at the sampling instants
depend on the inputs at the sampling instants and on the inputs between
these points. Thus, the
InterSample data property
describes how the algorithms should handle the input between samples.
For example, you can specify the behavior between the samples to be
piece-wise constant (zero-order hold,
zoh) or linearly
interpolated between the samples (first order hold,
The transformation formulas for
affected by the intersample behavior of the input.
the intersample behavior you assigned to the estimation data. To override
this setting during transformation, add an extra argument in the syntax.
% Set first-order hold intersample behavior mod_d = c2d(mod_c,T,'foh')
the sample time of both the dynamic model and the noise model. Resampling
a model affects the variance of its noise model.
A parametric noise model is a time-series model with the following mathematical description:
The noise spectrum is computed by the following discrete-time equation:
where is the variance of the white noise e(t), and represents the spectral density of e(t). Resampling the noise model preserves the spectral density T . The spectral density T is invariant up to the Nyquist frequency. For more information about spectrum normalization, see Spectrum Normalization.
d2d resampling of the noise model affects
simulations with noise using
sim. If you resample
a model to a faster sampling rate, simulating this model results in
higher noise level. This higher noise level results from the underlying
continuous-time model being subject to continuous-time white noise
disturbances, which have infinite, instantaneous variance. In this
case, the underlying continuous-time model is
the unique representation for discrete-time models. To maintain the
same level of noise after interpolating the noise signal, scale the
noise spectrum by , where Tnew is
the new sample time and Told is
the original sample time. before applying