Identifying linear black-box models from single-input/single-output (SISO) data using the System Identification app.
Identifying linear models from multiple-input/single-output (MISO) data using System Identification Toolbox™ commands.
Specify the values and constraints for the numerator, denominator and transport delays.
Specify how initial conditions are handled during model estimation in the app and at the command line.
This example shows some methods for choosing and configuring the model structure. Estimation of a model using measurement data requires selection of a model structure (such as state-space or transfer function) and its order (e.g., number of poles and zeros) in advance. This choice is influenced by prior knowledge about the system being modeled, but can also be motivated by an analysis of data itself. This example describes some options for determining model orders and input delay.
This example shows how to estimate models using frequency domain data. The estimation and validation of models using frequency domain data work the same way as they do with time domain data. This provides a great amount of flexibility in estimation and analysis of models using time and frequency domain as well as spectral (FRF) data. You may simultaneously estimate models using data in both domains, compare and combine these models. A model estimated using time domain data may be validated using spectral data or vice-versa.
This example shows the benefits of regularization for identification of linear and nonlinear models.
This example shows how to estimate regularized ARX models using automatically generated regularization constants in the System Identification app.
Model object types include numeric models, for representing systems with fixed coefficients, and generalized models for systems with tunable or uncertain coefficients.
System Identification Toolbox software uses objects to represent a variety of linear and nonlinear model structures.
A linear model is often sufficient to accurately describe the system dynamics and, in most cases, you should first try to fit linear models. Available linear structures include transfer functions and state-space models, summarized in the following table.
Linear Model Structures
Black-box modeling is useful when your primary interest is in fitting the data regardless of a particular mathematical structure of the model.
Recommended model estimation sequence, from the simplest to the more complex model structures.
All identified linear (IDLTI) models, except
idfrd, contain a
Structure property contains the adjustable
entities (parameters) of the model. Each parameter has attributes
such as value, minimum/maximum bounds, and free/fixed status that
allow you to constrain them to desired values or a range of values
during estimation. You use the
to impose constraints on the values of various model parameters.
Estimation requires you to specify the model order and delay. Many times, these values are not known.
The intersample behavior of the input signals influences the estimation, simulation and prediction of continuous-time models. A sampled signal is characterized only by its values at the sampling instants. However, when you apply a continuous-time input to a continuous-time system, the output values at the sampling instants depend on the inputs at the sampling instants and on the inputs between these points.
Supported models for multiple-output systems.
Configure the loss function that is minimized during parameter estimation. After estimation, use model quality metrics to assess the quality of identified models.
Regularization is the technique for specifying constraints on the flexibility of a model, thereby reducing uncertainty in the estimated parameter values.
The estimation report contains information about the results and
options used for a model estimation. This report is stored in the
property of the estimated model. The exact contents of the report depend on the estimator
function you use to obtain the model.
How you can work with identified models.