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Linear Model Identification Basics

Essential information for identifying linear models, selecting suitable model structures, constructing and modifying model object structures, and using regularized estimation

Linear models are the simplest models you can identify using System Identification Toolbox™. Use linear model identification when a linear model is sufficient to completely capture your system dynamics. To identify linear models, you start with time-domain or frequency domain input-output data and a model structure, such as a state-space or transfer function model. The software iteratively adjusts the free model parameters in order to minimize the difference between the measured output and the simulated model response to the input data. The toolbox allows you to perform tasks such as the following:

  • Estimate linear models using a specific model structure.

  • Use a black-box modeling approach and explore which model structure best suits your data.

  • Construct a preliminary linear model and use it to initialize the parameters of the model you want to estimate.

  • Incorporate system knowledge into your model by fixing known parameters to specific values.

  • Use regularized estimation to reduce the uncertainty in your model by constraining model flexibility.


Identify Linear Models

Identify Linear Models Using System Identification App

Identify linear black-box models from single-input/single-output (SISO) data using the System Identification app.

Identify Linear Models Using the Command Line

Identify linear models from multiple-input/single-output (MISO) data using System Identification Toolbox commands.

Frequency Domain Identification: Estimating Models Using Frequency Domain Data

This example shows how to estimate models using frequency domain data.

Estimation Report

The estimation report contains information about the results and options used for a model estimation.

Select Model Structure

About Identified Linear Models

System Identification Toolbox software uses objects to represent a variety of linear and nonlinear model structures.

Available Linear Models

Summary of linear model types that you can use for system identification.

Black-Box Modeling

Black-box modeling is useful when your primary interest is in fitting the data regardless of a particular mathematical structure of the model.

Model Structure Selection: Determining Model Order and Input Delay

This example shows some methods for choosing and configuring the model structure.

Modeling Multiple-Output Systems

Use a multiple-output modeling technique that suits the complexity and internal input-output coupling of your system.

Types of Model Objects

Model object types include numeric models, for representing systems with fixed coefficients, and generalized models for systems with tunable or uncertain coefficients.

Model Object Structures and Constraints

Linear Model Structures

Linear models in System Identification Toolbox take the form of model objects that are linear model structures. You can construct model objects directly or use estimation commands to both construct and estimate models. You can also modify the properties of existing model objects.

Imposing Constraints on Model Parameter Values

Constrain the adjustments that the estimation algorithm can make to individual model parameters by using the Structure property of the mode object.


Regularized Identification of Dynamic Systems

This example shows the benefits of regularization for identification of linear and nonlinear models.

Estimate Regularized ARX Model Using System Identification App

This example shows how to estimate regularized ARX models using automatically generated regularization constants in the System Identification app.

Regularized Estimates of Model Parameters

Regularization is the technique for specifying constraints on the flexibility of a model, thereby reducing uncertainty in the estimated parameter values.

Additional topics

Loss Function and Model Quality Metrics

Configure the loss function that is minimized during parameter estimation. After estimation, use model quality metrics to assess the quality of identified models.

Effect of Input Intersample Behavior on Continuous-Time Models

The intersample behavior of the input signals influences the estimation, simulation and prediction of continuous-time models.

Featured Examples