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Linear Model Structures

About System Identification Toolbox Model Objects

Objects are instances of model classes. Each class is a blueprint that defines the following information about your model:

  • How the object stores data

  • Which operations you can perform on the object

This toolbox includes nine classes for representing models. For example, idss represents linear state-space models and idnlarx represents nonlinear ARX models. For a complete list of available model objects, see Available Linear Models and Available Nonlinear Models.

Model properties define how a model object stores information. Model objects store information about a model, such as the mathematical form of a model, names of input and output channels, units, names and values of estimated parameters, parameter uncertainties, and estimation report. For example, an idss model has an InputName property for storing one or more input channel names.

The allowed operations on an object are called methods. In System Identification Toolbox™ software, some methods have the same name but apply to multiple model objects. For example, step creates a step response plot for all dynamic system objects. However, other methods are unique to a specific model object. For example, canon is unique to state-space idss models and linearize to nonlinear black-box models.

Every class has a special method, called the constructor, for creating objects of that class. Using a constructor creates an instance of the corresponding class or instantiates the object. The constructor name is the same as the class name. For example, idss and idnlarx are both the name of the class and the name of the constructor for instantiating the linear state-space models and nonlinear ARX models, respectively.

When to Construct a Model Structure Independently of Estimation

You use model constructors to create a model object at the command line by specifying all required model properties explicitly.

You must construct the model object independently of estimation when you want to:

  • Simulate or analyze the effect of model parameters on its response, independent of estimation.

  • Specify an initial guess for specific model parameter values before estimation. You can specify bounds on parameter values, or set up the auxiliary model information in advance, or both. Auxiliary model information includes specifying input/output names, units, notes, user data, and so on.

In most cases, you can use the estimation commands to both construct and estimate the model—without having to construct the model object independently. For example, the estimation command tfest creates a transfer function model using data and the number of poles and zeros of the model. Similarly, nlarx creates a nonlinear ARX model using data and model orders and delays that define the regressor configuration. For information about how to both construct and estimate models with a single command, see Model Estimation Commands.

In case of grey-box models, you must always construct the model object first and then estimate the parameters of the ordinary differential or difference equation.

Commands for Constructing Linear Model Structures

The following table summarizes the model constructors available in the System Identification Toolbox product for representing various types of linear models.

After model estimation, you can recognize the corresponding model objects in the MATLAB® Workspace browser by their class names. The name of the constructor matches the name of the object it creates.

For information about how to both construct and estimate models with a single command, see Model Estimation Commands.

Summary of Model Constructors

Model ConstructorResulting Model Class
idfrdNonparametric frequency-response model.
idprocContinuous-time, low-order transfer functions (process models).

Linear input-output polynomial models:

  • ARX


  • Output-Error

  • Box-Jenkins


Linear state-space models.


Linear transfer function models.

idgreyLinear ordinary differential or difference equations (grey-box models). You write a function that translates user parameters to state-space matrices. Can also be viewed as state-space models with user-specified parameterization.

For more information about when to use these commands, see When to Construct a Model Structure Independently of Estimation.

Model Properties

Categories of Model Properties

The way a model object stores information is defined by the properties of the corresponding model class.

Each model object has properties for storing information that are relevant only to that specific model type. The idtf, idgrey, idpoly, idproc, and idss model objects are based on the idlti superclass and inherit all idlti properties.

In general, all model objects have properties that belong to the following categories:

  • Names of input and output channels, such as InputName and OutputName

  • Sample time of the model, such as Ts

  • Units for time or frequency

  • Model order and mathematical structure (for example, ODE or nonlinearities)

  • Properties that store estimation results (Report)

  • User comments, such as Notes and Userdata

For information about getting help on object properties, see the model reference pages.

Viewing Model Properties and Estimated Parameters

The following table summarizes the commands for viewing and changing model property values. Property names are not case sensitive. You do not need to type the entire property name if the first few letters uniquely identify the property.

View all model properties and their valuesget

Load sample data, compute an ARX model, and list the model properties:

load iddata8
m_arx=arx(z8,[4 3 2 3 0 0 0]);
Access a specific model propertyUse dot notation

View the A matrix containing the estimated parameters in the previous model:

For properties, such as Report, that are configured like structures, use dot notation of the form model.PropertyName.FieldName.
FieldName is the name of any field of the property.

View the method used in ARX model estimation:

Change model property valuesdot notation

Change the input delays for all three input channels to [1 1 1] for an ARX model:

m_arx.InputDelay = [1 1 1]
Access model parameter values and uncertainty informationUse getpar, getpvec and getcov
See Also: polydata, idssdata, tfdata, zpkdata
  • View a table of all parameter attributes:


  • View the A polynomial and 1 standard uncertainty of an ARX model:

    [a,~,~,~,~,da] = polydata(m_arx)

Set model property values and uncertainty informationUse setpar, setpvec and setcov
  • Set default parameter labels:

    m_arx = setpar(m_arx,'label','default')

  • Set parameter covariance data:
    m_arx = setcov(m_arx,cov)

Get number of parametersUse nparams

Get the number of parameters:


See Also

Validate each model directly after estimation to help fine-tune your modeling strategy. When you do not achieve a satisfactory model, you can try a different model structure and order, or try another identification algorithm. For more information about validating and troubleshooting models, see Validating Models After Estimation.