Option set for n4sid
opt = n4sidOptions
opt = n4sidOptions(Name,Value)
opt = n4sidOptionsn4sid.
opt = n4sidOptions(Name,Value)Name,Value pair
arguments.
Specify optional
comma-separated pairs of Name,Value arguments. Name is
the argument name and Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN.
'InitialState' — Handling of initial states'estimate' (default) | 'zero'Handling of initial states during estimation, specified as one of the following values:
'zero' — The initial state
is set to zero.
'estimate' — The initial
state is treated as an independent estimation parameter.
'N4Weight' — Weighting scheme used for singular-value decomposition by the N4SID algorithm'auto' (default) | 'MOESP' | 'CVA' | 'SSARX'Weighting scheme used for singular-value decomposition by the N4SID algorithm, specified as one of the following values:
'MOESP' — Uses the MOESP
algorithm by Verhaegen [2].
'CVA' — Uses the Canonical Variate
Algorithm by Larimore [1].
Estimation using frequency-domain data always uses
'CVA'.
'SSARX' — A subspace identification
method that uses an ARX estimation based algorithm to compute the
weighting.
Specifying this option allows unbiased estimates when using data that is collected in closed-loop operation. For more information about the algorithm, see [4].
'auto' — The estimating
function chooses between the MOESP, CVA and SSARX algorithms.
'N4Horizon' — Forward- and backward-prediction horizons used by the N4SID algorithm'auto' (default) | vector [r sy su] | k-by-3 matrixForward- and backward-prediction horizons used by the N4SID algorithm, specified as one of the following values:
A row vector with three elements — [r sy su], where
r is the maximum forward prediction
horizon, using up to r step-ahead predictors.
sy is the number of past outputs, and
su is the number of past inputs that are
used for the predictions. See pages 209 and 210 in [3] for more information. These numbers can have a substantial
influence on the quality of the resulting model, and there are
no simple rules for choosing them. Making
'N4Horizon' a k-by-3
matrix means that each row of 'N4Horizon' is
tried, and the value that gives the best (prediction) fit to
data is selected. k is the number of guesses
of [r sy su] combinations. If
you specify N4Horizon as a single column, r = sy =
su is used.
'auto' — The software uses
an Akaike Information Criterion (AIC) for the selection of sy and su.
'Focus' — Error to be minimized'prediction' (default) | 'simulation'Error to be minimized in the loss function during estimation,
specified as the comma-separated pair consisting of 'Focus' and
one of the following values:
'prediction' — The one-step
ahead prediction error between measured and predicted outputs is minimized
during estimation. As a result, the estimation focuses on producing
a good predictor model.
'simulation' — The simulation
error between measured and simulated outputs is minimized during estimation.
As a result, the estimation focuses on making a good fit for simulation
of model response with the current inputs.
The Focus option can be interpreted as a
weighting filter in the loss function. For more information, see Loss Function and Model Quality Metrics.
'WeightingFilter' — Weighting prefilter[] (default) | vector | matrix | cell array | linear systemWeighting prefilter applied to the loss function to be minimized
during estimation. To understand the effect of WeightingFilter on
the loss function, see Loss Function and Model Quality Metrics.
Specify WeightingFilter as one of the following
values:
[] — No weighting prefilter
is used.
Passbands — Specify a row vector or matrix
containing frequency values that define desired passbands. You select
a frequency band where the fit between estimated model and estimation
data is optimized. For example, [wl,wh] where wl and wh represent
lower and upper limits of a passband. For a matrix with several rows
defining frequency passbands, [w1l,w1h;w2l,w2h;w3l,w3h;...],
the estimation algorithm uses the union of the frequency ranges to
define the estimation passband.
Passbands are expressed in rad/TimeUnit for
time-domain data and in FrequencyUnit for frequency-domain
data, where TimeUnit and FrequencyUnit are
the time and frequency units of the estimation data.
SISO filter — Specify a single-input-single-output (SISO) linear filter in one of the following ways:
A SISO LTI model
{A,B,C,D} format, which specifies
the state-space matrices of a filter with the same sample time as
estimation data.
{numerator,denominator} format,
which specifies the numerator and denominator of the filter as a transfer
function with same sample time as estimation data.
This option calculates the weighting function as a product of the filter and the input spectrum to estimate the transfer function.
Weighting vector — Applicable for frequency-domain
data only. Specify a column vector of weights. This vector must have
the same length as the frequency vector of the data set, Data.Frequency.
Each input and output response in the data is multiplied by the corresponding
weight at that frequency.
'EnforceStability' — Control whether to enforce stability of modelfalse (default) | trueControl whether to enforce stability of estimated model, specified
as the comma-separated pair consisting of 'EnforceStability' and
either true or false.
Data Types: logical
'EstimateCovariance' — Control whether to generate parameter covariance datatrue (default) | falseControls whether parameter covariance data is generated, specified as
true or false.
If EstimateCovariance is true, then use
getcov to fetch the covariance matrix
from the estimated model.
'Display' — Specify whether to display the estimation progress'off' (default) | 'on'Specify whether to display the estimation progress, specified as one of the following values:
'on' — Information on model
structure and estimation results are displayed in a progress-viewer
window.
'off' — No progress or results
information is displayed.
'InputOffset' — Removal of offset from time-domain input data during estimation[] (default) | vector of positive integers | matrixRemoval of offset from time-domain input data during estimation,
specified as the comma-separated pair consisting of 'InputOffset' and
one of the following:
A column vector of positive integers of length Nu, where Nu is the number of inputs.
[] — Indicates no offset.
Nu-by-Ne matrix
— For multi-experiment data, specify InputOffset as
an Nu-by-Ne matrix. Nu is
the number of inputs, and Ne is the number of experiments.
Each entry specified by InputOffset is
subtracted from the corresponding input data.
'OutputOffset' — Removal of offset from time-domain output data during estimation[] (default) | vector | matrixRemoval of offset from time-domain output data during estimation,
specified as the comma-separated pair consisting of 'OutputOffset' and
one of the following:
A column vector of length Ny, where Ny is the number of outputs.
[] — Indicates no offset.
Ny-by-Ne matrix
— For multi-experiment data, specify OutputOffset as
a Ny-by-Ne matrix. Ny is
the number of outputs, and Ne is the number of
experiments.
Each entry specified by OutputOffset is
subtracted from the corresponding output data.
'OutputWeight' — Weighting of prediction errors in multi-output estimations[] (default) | 'noise' | positive semidefinite symmetric matrixWeighting of prediction errors in multi-output estimations, specified as one of the following values:
'noise' — Minimize , where E represents
the prediction error and N is the number of data
samples. This choice is optimal in a statistical sense and leads to
the maximum likelihood estimates in case no data is available about
the variance of the noise. This option uses the inverse of the estimated
noise variance as the weighting function.
Positive semidefinite symmetric matrix (W)
— Minimize the trace of the weighted prediction error matrix trace(E'*E*W/N) where:
E is the matrix of prediction errors,
with one column for each output. W is the positive
semidefinite symmetric matrix of size equal to the number of outputs.
Use W to specify the relative importance of outputs
in multiple-output models, or the reliability of corresponding data.
N is the number of data samples.
[] — The software chooses
between the 'noise' or using the identity matrix
for W.
This option is relevant only for multi-output models.
'Advanced' — Additional advanced optionsAdditional advanced options, specified as a structure with the
field MaxSize. MaxSize specifies
the maximum number of elements in a segment when input-output data
is split into segments.
MaxSize must be a positive integer.
Default: 250000
opt — Option set for n4sidn4sidOptions option setOption set for n4sid,
returned as an n4sidOptions option set.
opt = n4sidOptions;
Create an options set for n4sid using the 'zero' option to initialize the state. Set the Display to 'on'.
opt = n4sidOptions('InitialState','zero','Display','on');
Alternatively, use dot notation to set the values of opt.
opt = n4sidOptions; opt.InitialState = 'zero'; opt.Display = 'on';
The names of some estimation and analysis options were changed in R2018a. Prior names still work. For details, see the R2018a release note Renaming of Estimation and Analysis Options.
[1] Larimore, W.E. “Canonical variate analysis in identification, filtering and adaptive control.” Proceedings of the 29th IEEE Conference on Decision and Control, pp. 596–604, 1990.
[2] Verhaegen, M. “Identification of the deterministic part of MIMO state space models.” Automatica, Vol. 30, 1994, pp. 61–74.
[3] Ljung, L. System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall PTR, 1999.
[4] Jansson, M. “Subspace identification and ARX modeling.” 13th IFAC Symposium on System Identification, Rotterdam, The Netherlands, 2003.
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