tfestOptions
Option set for tfest
Description
Use a tfestOptions
object to specify options for estimating
transfer function models using the tfest
function. You can specify options such as
the estimation objective, the handling of initial conditions, and the numerical search method
to be used in estimation.
Creation
Description
creates the default
option set for estimating a transfer function model using opt
= tfestOptionstfest
. To modify the properties of this option set for your specific
application, use dot notation.
creates an option set with properties specified using one or more name-value
arguments.opt
= tfestOptions(Name,Value
)
Properties
InitializeMethod
— Algorithm used to initialize numerator and denominator
'iv'
(default) | 'svf'
| 'gpmf'
| 'n4sid'
| 'all'
Algorithm used to initialize the values of the numerator and denominator of the
output of tfest
, specified as one of the following values:
'iv'
— Instrument Variable approach.'svf'
— State Variable Filters approach.'gpmf'
— Generalized Poisson Moment Functions approach.'n4sid'
— Subspace state-space estimation approach.'all'
— Combination of all of the preceding approaches. The software tries all these methods and selects the method that yields the smallest value of the prediction error norm.
This property is applicable only for estimation of continuous-time transfer functions using time-domain data
InitializeOptions
— Option set for initialization algorithm
structure
Option set for the initialization algorithm used to initialize the values of the
numerator and denominator of the output of tfest
, specified as a
structure with the fields in the following table.
Field Name | Description | Default | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
N4Weight | Calculates the weighting matrices used in the singular-value
decomposition step of the
| 'auto' | ||||||||||
N4Horizon | Determines the forward and backward prediction horizons used by the
See pages 209 and 210 in [1] 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 If | 'auto' | ||||||||||
FilterTimeConstant | Time constant of the differentiating filter used by the
Ts is the sample time of the estimation data. Specify
| 0.1 | ||||||||||
MaxIterations | Maximum number of iterations. Applicable when
InitializeMethod is 'iv' . | 30 | ||||||||||
Tolerance | Convergence tolerance. Applicable when
InitializeMethod is 'iv' . | 0.01 |
InitialCondition
— Handling of initial conditions
'auto'
(default) | 'zero'
| 'estimate'
| 'backcast'
Handling of initial conditions during estimation, specified as one of the following values:
'zero'
— All initial conditions are taken as zero.'estimate'
— The necessary initial conditions are treated as estimation parameters.'backcast'
— The necessary initial conditions are estimated by a backcasting (backward filtering) process, described in [2].'auto'
— An automatic choice among the preceding options is made, guided by the data.
WeightingFilter
— Weighting prefilter
[]
(default) | vector | matrix | cell array | linear system | 'inv'
| 'invsqrt'
Weighting 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 values in the following
table.
Value | Description |
---|---|
[] | 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, specify
Passbands are expressed in
rad/ |
SISO filter | Specify a single-input-single-output (SISO) linear filter in one of the following ways:
|
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, |
'inv' | Applicable for estimation using frequency-response data only. Use as the weighting filter, where G(ω) is the complex frequency-response data. Use this option for capturing relatively low amplitude dynamics in data, or for fitting data with high modal density. This option also makes it easier to specify channel-dependent weighting filters for MIMO frequency-response data. |
'invsqrt' | Applicable for estimation using frequency-response data only. Use as the weighting filter. Use this option for capturing relatively low amplitude dynamics in data, or for fitting data with high modal density. This option also makes it easier to specify channel-dependent weighting filters for MIMO frequency-response data. |
EnforceStability
— Option to enforce stability of model
false
(default) |
true
Option to enforce stability of the estimated model, specified as
true
or false
.
Use this option when estimating models using frequency-domain data. Models estimated using time-domain data are always stable.
EstimateCovariance
— Option to generate parameter covariance data
true
(default) | false
Option to generate parameter covariance data, specified as true
or
false
.
If EstimateCovariance
is true
, then use
getcov
to fetch the covariance matrix
from the estimated model.
Display
— Option to display estimation progress
'off'
(default) | 'on'
Option 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.
InputInterSample
— Input-channel intersample behavior
'auto'
| 'zoh'
| 'foh'
| 'bl'
Input-channel intersample behavior for transformations between discrete time and continuous time, specified as 'auto'
, 'zoh'
,'foh'
, or 'bl'
.
The definitions of the three behavior values are as follows:
'zoh'
— Zero-order hold maintains a piecewise-constant input signal between samples.'foh'
— First-order hold maintains a piecewise-linear input signal between samples.'bl'
— Band-limited behavior specifies that the continuous-time input signal has zero power above the Nyquist frequency.
iddata
objects have a similar property,
data.InterSample
, that contains the same behavior value options.
When the InputInterSample
value is 'auto'
and
the estimation data is in an iddata
object data
, the
software uses the data.InterSample
value. When the estimation data
is instead contained in a timetable or a matrix pair, with the 'auto'
option, the software uses 'zoh'
.
The software applies the same option value to all channels and all experiments.
InputOffset
— Removal of offset from time-domain input data during estimation
[]
(default) | vector of positive integers | matrix
Removal of offset from time-domain input data during estimation, specified as 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 | matrix
Removal of offset from time-domain output data during estimation, specified as 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 matrix
Weighting of prediction errors in multi-output estimations, specified as one of the following values:
'noise'
— Minimize , where E represents the prediction error andN
is the number of data samples. This choice is optimal in a statistical sense and leads to maximum likelihood estimates if nothing is known about the variance of the noise. It uses the inverse of the estimated noise variance as the weighting function.Note
OutputWeight
must not be'noise'
ifSearchMethod
is'lsqnonlin'
.Positive semidefinite symmetric matrix (
W
) — Minimize the trace of the weighted prediction error matrixtrace(E'*E*W/N)
, where:E is the matrix of prediction errors, with one column for each output, and 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'noise'
and using the identity matrix forW
.
This option is relevant for only multi-output models.
Regularization
— Options for regularized estimation of model parameters
structure
Options for regularized estimation of model parameters, specified as a structure with the fields in the following table. For more information on regularization, see Regularized Estimates of Model Parameters.
Field Name | Description | Default |
---|---|---|
Lambda | Constant that determines the bias versus variance tradeoff. Specify a positive scalar to add the regularization term to the estimation cost. The default value of 0 implies no regularization. | 0 |
R | Weighting matrix. Specify a vector of nonnegative numbers or a square positive semi-definite matrix. The length must be equal to the number of free parameters of the model. For black-box models, using the default value is
recommended. For structured and grey-box models, you can also
specify a vector of The default value of 1 implies a value of
| 1 |
Nominal | The nominal value towards which the free parameters are pulled during estimation. The default value of 0 implies that
the parameter values are pulled towards zero. If you are refining a
model, you can set the value to | 0 |
SearchMethod
— Numerical search method used for iterative parameter estimation
'auto'
(default) | 'gn'
| 'gna'
| 'lm'
| 'grad'
| 'lsqnonlin'
| 'fmincon'
Numerical search method used for iterative parameter estimation, specified as the one of the values in the following table.
SearchMethod | Description |
---|---|
'auto' | Automatic method selection A combination of the
line search algorithms, |
'gn' | Subspace Gauss-Newton least-squares search Singular
values of the Jacobian matrix less than
|
'gna' | Adaptive subspace Gauss-Newton search Eigenvalues
less than |
'lm' | Levenberg-Marquardt least squares search Each
parameter value is |
'grad' | Steepest descent least-squares search |
'lsqnonlin' | Trust-region-reflective algorithm of This algorithm requires Optimization Toolbox™ software. |
'fmincon' | Constrained nonlinear solvers You can use the
sequential quadratic programming (SQP) and trust-region-reflective
algorithms of the
|
SearchOptions
— Option set for search algorithm
search option set
Option set for the search algorithm, specified as a search option set with fields that
depend on the value of SearchMethod
.
SearchOptions
Structure When SearchMethod
Is Specified
as 'gn'
, 'gna'
, 'lm'
,
'grad'
, or 'auto'
Field Name | Description | Default | ||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Tolerance | Minimum percentage difference between the current value
of the loss function and its expected improvement after the next iteration,
specified as a positive scalar. When the percentage of expected improvement
is less than | 0.01 | ||||||||||||||||||||||||||||||
MaxIterations | Maximum number of iterations during loss-function minimization, specified as a positive
integer. The iterations stop when Setting
Use
| 20 | ||||||||||||||||||||||||||||||
Advanced | Advanced search settings, specified as a structure with the following fields.
|
SearchOptions
Structure When SearchMethod
Is Specified
as 'lsqnonlin'
Field Name | Description | Default |
---|---|---|
FunctionTolerance | Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar. The
value of | 1e-5 |
StepTolerance | Termination tolerance on the estimated parameter values, specified as a positive scalar. The value of | 1e-6 |
MaxIterations | Maximum number of iterations during loss-function minimization, specified as a positive
integer. The iterations stop when The value of
| 20 |
SearchOptions
Structure When SearchMethod
Is Specified
as 'fmincon'
Field Name | Description | Default |
---|---|---|
Algorithm |
For more information about the algorithms, see Constrained Nonlinear Optimization Algorithms (Optimization Toolbox) and Choosing the Algorithm (Optimization Toolbox). | 'sqp' |
FunctionTolerance | Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar. | 1e-6 |
StepTolerance | Termination tolerance on the estimated parameter values, specified as a positive scalar. | 1e-6 |
MaxIterations | Maximum number of iterations during loss function minimization, specified as a positive
integer. The iterations stop when | 100 |
Advanced
— Additional advanced options
structure
Additional advanced options, specified as a structure with the fields in the following table.
Field Name | Description | Default | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
ErrorThreshold | Error threshold at which to adjust the weight of large errors from quadratic to linear. Errors larger than
An | 0 | |||||||||
MaxSize | Maximum number of elements in a segment when input-output data is split into segments.
| 250000 | |||||||||
StabilityThreshold | Threshold for stability tests.
| ||||||||||
AutoInitThreshold | Threshold at which to automatically estimate initial conditions. The software estimates the initial conditions when: | 1.05 |
Examples
Create Default Options Set for Transfer Function Estimation
opt = tfestOptions;
Specify Options for Transfer Function Estimation
Create an options set for tfest
using the 'n4sid'
initialization algorithm and set the Display
to 'on'
.
opt = tfestOptions('InitializeMethod','n4sid','Display','on');
Alternatively, use dot notation to set the values of opt
.
opt = tfestOptions; opt.InitializeMethod = 'n4sid'; opt.Display = 'on';
References
[1] Ljung, Lennart. System Identification: Theory for the User. 2nd Ed. Upper Saddle River, NJ: Prentice-Hall PTR, 1999.
[2] Knudsen, T. "A New method for estimating ARMAX models," IFAC Proceedings Volumes 27, no. 8 (July 1994): 895–901. https://doi.org/10.1016/S1474-6670(17)47823-2.
[3] Wills, Adrian, B. Ninness, and S. Gibson. “On Gradient-Based Search for Multivariable System Estimates.” IFAC Proceedings Volumes 38, No 1 (2005): 832–837. https://doi.org/10.3182/20050703-6-CZ-1902.00140.
[4] Garnier, H., M. Mensler, and A. Richard. “Continuous-time Model Identification From Sampled Data: Implementation Issues and Performance Evaluation” International Journal of Control 76, no 13 (January 2003): 1337–57. https://doi.org/10.1080/0020717031000149636.
[5] Ljung, Lennart. “Experiments With Identification of Continuous-Time Models.” IFAC Proceedings Volumes 42, no. 10 (2009):1175–80. https://doi.org/10.3182/20090706-3-FR-2004.00195.
[6] Jansson, Magnus. “Subspace identification and ARX modeling.” IFAC Proceedings Volumes 36 no. 16 (September 2003): 1585–90. https://doi.org/10.1016/S1474-6670(17)34986-8
Version History
Introduced in R2012bR2022b: InputInterSample
option allows intersample behavior specification for continuous models estimated from timetables or matrices.
iddata
objects contain an InterSample
property that
describes the behavior of the signal between sample points. The
InputInterSample
option implements a version of that property in
tfestOptions
so that intersample behavior can be specified also when
estimation data is stored in timetables or matrices.
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