load(fullfile(matlabroot,'toolbox','ident','iddemos','data','twotankdata'));
z = iddata(y,u,0.2,'Name','Two tanks');

The data contains 3000 input-output data samples of a two tank system. The input is the voltage applied to a pump, and the output is the liquid level of the lower tank.

Specify file describing the model structure for a two-tank system. The file specifies the state derivatives and model outputs as a function of time, states, inputs, and model parameters.

load(fullfile(matlabroot,'toolbox','ident','iddemos','data','dcmotordata'));
z = iddata(y,u,0.1,'Name','DC-motor');

The data is from a linear DC motor with one input (voltage), and two outputs (angular position and angular velocity). The structure of the model is specified by dcmotor_m.m file.

Time-domain estimation data, specified as an iddata object.
data has the same input and output dimensions as
init_sys.

If you specify the InterSample property of data
as 'bl'(band-limited) and the model is continuous-time, the software treats
data as first-order-hold (foh) interpolated for estimation.

init_sys — Constructed nonlinear grey-box model idnlgrey object

Constructed nonlinear grey-box model that configures the initial parameterization of
sys, specified as an idnlgrey object.
init_sys has the same input and output dimensions as
data. Create init_sys using idnlgrey.

options — Estimation options nlgreyestOptions option set

Estimation options for nonlinear grey-box model identification, specified as an nlgreyestOptions option set.

sys — Estimated nonlinear grey-box model idnlgrey object

Nonlinear grey-box model with the same structure as init_sys,
returned as an idnlgrey object. The parameters of sys
are estimated such that the response of sys matches the output signal in
the estimation data.

Information about the estimation results and options used is stored in the
Report property of the model. Report has the following
fields:

Report Field

Description

Status

Summary of the model status, which indicates whether
the model was created by construction or obtained by estimation.

Method

Name of the simulation solver and the search method used during
estimation.

Fit

Quantitative assessment of the estimation, returned as
a structure. See Loss Function and Model Quality Metrics for more information
on these quality metrics. The structure has the following fields:

Field

Description

FitPercent

Normalized root mean squared error (NRMSE) measure of how well the response of the
model fits the estimation data, expressed as the percentage
fitpercent = 100(1-NRMSE).

LossFcn

Value of the loss function when the estimation completes.

MSE

Mean squared error (MSE) measure of how well the response
of the model fits the estimation data.

FPE

Final prediction error for the model.

AIC

Raw Akaike Information Criteria (AIC) measure of model
quality.

AICc

Small-sample-size corrected AIC.

nAIC

Normalized AIC.

BIC

Bayesian Information Criteria (BIC).

Parameters

Estimated values of the model parameters. Structure with the following
fields:

Field

Description

InitialValues

Structure with values of parameters and initial states before
estimation.

ParVector

Value of parameters after estimation.

Free

Logical vector specifying the fixed or free status of parameters during
estimation

FreeParCovariance

Covariance of the free parameters.

X0

Value of initial states after estimation.

X0Covariance

Covariance of the initial states.

OptionsUsed

Option set used for estimation. If no custom options were configured, this is
a set of default options. See nlgreyestOptions for more
information.

RandState

State of the random number stream at the start of estimation. Empty,
[], if randomization was not used during estimation. For more
information, see rng.

DataUsed

Attributes of the data used for estimation — Structure with the
following fields:

Field

Description

Name

Name of the data set.

Type

Data type — For idnlgrey models, this is set
to 'Time domain data'.

Length

Number of data samples.

Ts

Sample time. This is equivalent to
data.Ts.

InterSample

Input intersample behavior. One of the following values:

'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.

The value of Intersample has no effect on
estimation results for discrete-time models.

InputOffset

Empty, [], for nonlinear estimation
methods.

OutputOffset

Empty, [], for nonlinear estimation
methods.

Termination

Termination conditions for the iterative search used for prediction error minimization,
returned as a structure with the following
fields:

Field

Description

WhyStop

Reason for terminating the numerical search.

Iterations

Number of search iterations performed by the estimation
algorithm.

FirstOrderOptimality

$$\infty $$-norm of the gradient search
vector when the search algorithm terminates.

FcnCount

Number of times the objective function was called.

UpdateNorm

Norm of the gradient search vector in the last iteration.
Omitted when the search method is 'lsqnonlin' or 'fmincon'.

LastImprovement

Criterion improvement in the last iteration, expressed
as a percentage. Omitted when the search method is 'lsqnonlin' or 'fmincon'.

Algorithm

Algorithm used by 'lsqnonlin' or 'fmincon' search
method. Omitted when other search methods are used.

For estimation methods that do not require numerical search optimization,
the Termination field is omitted.

Automatic Parallel Support Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

Parallel computing support is available for estimation using the
lsqnonlin search method (requires Optimization Toolbox™). To enable parallel computing, use nlgreyestOptions, set SearchMethod to
'lsqnonlin', and set SearchOptions.Advanced.UseParallel
to true.

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