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.
linear state-space models and
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
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,
unique to state-space
idss models and
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.
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
|Resulting Model Class
|Nonparametric frequency-response model.
|Continuous-time, low-order transfer functions (process models).
Linear input-output polynomial models:
Linear state-space models.
Linear transfer function models.
|Linear 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.
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
objects are based on the
idlti superclass and inherit all
In general, all model objects have properties that belong to the following categories:
Names of input and output channels, such as
Sample time of the model, such as
Units for time or frequency
Model order and mathematical structure (for example, ODE or nonlinearities)
Properties that store estimation results (
User comments, such as
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 values
Load sample data, compute an ARX model, and list the model properties:
m_arx=arx(z8,[4 3 2 3 0 0 0]);
|Access a specific model property
|Use 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
is the name of any field of the property.
View the method used in ARX model estimation:
|Change model property values
Change the input delays for all three input channels to
m_arx.InputDelay = [1 1 1]
|Access model parameter values and uncertainty information
|Set model property values and uncertainty information
|Get number of parameters
Get the number of
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.