Transform identified linear model with noise channels to model with measured channels only
mod1 = noisecnv(mod)
mod2 = noisecnv(mod,'normalize')
mod1 = noisecnv(mod) and
= noisecnv(mod,'normalize') transform an identified linear
model with noise channels to a model with measured channels only.
mod is any linear identified model,
The noise input channels in
mod are converted as follows: Consider
a model with both measured input channels u
(nu channels) and noise channels e
(ny channels) with covariance matrix
where L is a lower triangular matrix. Note that
mod.NoiseVariance = Λ. The model can also be
described with unit variance, using a normalized noise source
mod1 = noisecnv(mod)converts the model to a representation of the system [G H] with nu+ny inputs and ny outputs. All inputs are treated as measured, and
mod1does not have any noise model. The former noise input channels have names
ynameis the name of the corresponding output.
mod2 = noisecnv(mod,'norm')converts the model to a representation of the system [G HL] with nu+ny inputs and ny outputs. All inputs are treated as measured, and
mod2does not have any noise model. The former noise input channels have names
ynameis the name of the corresponding output. Note that the noise variance matrix factor L typically is uncertain (has a nonzero covariance). This is taken into account in the uncertainty description of
modis a time series, that is, nu
mod1is a model that describes the transfer function H with measured input channels. Analogously,
mod2describes the transfer function HL.
Note the difference with subreferencing:
mod(:,)gives a description of the noise model characteristics as a time-series model, that is, it describes H and also the covariance of e. In contrast,
noise2meas(m)describe just the transfer function H. To obtain a description of the normalized transfer function HL, use
Converting the noise channels to measured inputs is useful to study the properties of the individual transfer functions from noise to output. It is also useful for transforming identified linear models to representations that do not handle disturbance descriptions explicitly.
Identify a model with a measured component (G) and a
non-trivial noise component (H). Compare the amplitude of the
measured component's frequency response to the noise component's spectrum amplitude.
You must convert the noise component into a measured one by using
noisecnv if you want to compare its behavior against a
truly measured component.
load iddata2 z2 sys1 = armax(z2,[2 2 2 1]); % model with noise component sys2 = tfest(z2,3); % model with a trivial noise component sys1 = noisecnv(sys1); sys2 = noisecnv(sys2); bodemag(sys1,sys2)