noise2meas
Noise component of linear identified model
Description
returns the noise component of a linear identified model, noiseModel
= noise2meas(sys
)sys
.
Use noise2meas
to convert a time-series model (no inputs) to an
input/output model. You can use the converted model for linear analysis, including
viewing pole/zero maps and plotting the step response.
specifies the noise variance normalization method.noiseModel
= noise2meas(sys
,noise
)
Examples
Convert Noise Component of Linear Identified Model into Input/Output Model
Convert a time-series model to an input/output model that may be used by linear analysis tools.
Identify a time-series model.
load iddata9 z9 sys = ar(z9,4,'ls');
sys
is an idpoly
model with no inputs.
Convert sys
to a measured model.
noise_model = noise2meas(sys);
noise_model
is an idpoly
model with one input.
You can use noise_model
for linear analysis functions such as step
, iopzmap
, etc.
Normalizing Noise Variance
Convert an identified linear model to an input/output model, and normalize its noise variance.
Identify a linear model using data.
load twotankdata;
z = iddata(y,u,0.2);
sys = ssest(z,4);
sys
is an idss
model, with a noise variance of 6.6211e-06. The value of is sqrt(sys.NoiseVariance)
, which is 0.0026.
View the disturbance matrix.
sys.K
ans = 4×1
0.2719
1.6570
0.6318
0.2877
Obtain a model that absorbs the noise variance of sys
.
noise_model_normalize = noise2meas(sys,'normalize');
noise_model_normalize
is an idpoly
model.
View the matrix for noise_model_normalize
.
noise_model_normalize.B
ans = 4×1
0.0007
0.0043
0.0016
0.0007
As expected, noise_model_normalize.B
is equal to L*sys.K
.
Compare the bode response with a model that ignores the noise variance of sys
.
noise_model_innovation = noise2meas(sys,'innovations'); bodemag(noise_model_normalize,noise_model_innovation); legend('Normalized noise variance','Ignored noise variance');
The difference between the bode magnitudes of the noise_model_innovation
and noise_model_normalized
is approximately 51 dB. As expected, the magnitude difference is approximately equal to 20*log10(L)
.
Input Arguments
sys
— Identified linear model
idss
| idtf
| idproc
| idpoly
| idfrd
| idgrey
Identified linear model, specified as one of the following model objects.
sys
represents the system:
G is the transfer function between the measured input, u(t), and the output, y(t). H is the noise model and describes the effect of the disturbance, e(t), on the model response.
An equivalent state-space representation of sys
is
v(t) is white noise with independent
channels and unit variances. The white-noise signal
e(t) represents the model
innovations and has variance
LLT. The noise-variance
data is stored using the NoiseVariance
property of
sys
.
noise
— Noise variance normalization method
'innovations'
(default) | 'normalize'
Noise variance normalization method, specified as one of the following values.
'innovations'
— Noise sources are not normalized and remain as the innovations process.'normalize'
— Noise sources are normalized to be independent with unit variance.
Output Arguments
noiseModel
— Noise component of identified model
idss
| idtf
| idpoly
| idfrd
Noise component of identified model, returned as an idss
,
idtf
, idpoly
, or
idfrd
object.
The model type of noiseModel
depends on the model
type of sys
.
noiseModel
is anidtf
model ifsys
is anidproc
model.noiseModel
is anidss
model ifsys
is anidgrey
model.noiseModel
is the same type of model assys
for all other model types.
To obtain the model coefficients of noiseModel
in
state-space form, use ssdata
. Similarly, to obtain
the model coefficients in transfer-function form, use tfdata
.
Noise Sources Not Normalized
If noise
is 'innovations'
,
then noise2meas
returns H and
noiseModel
represents the system
An equivalent state-space representation of
noiseModel
is
noise2meas
returns the noise channels of
sys
as the input channels of
noiseModel
. The input channels are named using
the format 'e@yk'
, where yk
corresponds to the OutputName
property of an output.
The measured input channels of sys
are discarded
and the noise variance is set to zero.
Noise Sources Normalized
If noise
is 'normalize'
, then
noise2meas
first normalizes
noiseModel
represents the system
or, equivalently, in state-space representation
The input channels are named using the format
'v@yk'
, where yk
corresponds
to the OutputName
property of an output.
Version History
Introduced in R2012a
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