User`s guide

4 Nonlinear Black-Box Model Identification
Identifying Nonlinear ARX Models
In this section...
“Supported Data for Nonlinear AR X M o dels” on pag e 4-4
“Denition of the N o nlinear ARX Model” on page 4-4
“Using Regressors” on page 4-6
“Nonlinearity Estimators for Nonlinear ARX Models” on page 4-9
“How to Estimate Nonlinear A RX Models in the G UI” on page 4-10
“How to Estimate Nonlinear AR X Models at the Command Line” on page
4-11
Supported Data for Nonlinear ARX Models
You can estimate discrete-time nonlinear ARX models from data w ith the
following characteristics:
Time-domain input-output data or time-series data
Single-output or multiple-output data
For m ore information about representing your data for system identication,
see Chapter 1, “Data Processing”.
Definition of the Nonlinear ARX Model
Nonline ar ARX models descri be nonl in ear stru ctures usin g a parallel
combination of non li near an d linear blocks. T h e nonl in ear and linear
functions are ex presse d in term s of variables called regressors.
The System Identication Toolbox product computes regressors by performing
transformations of the measured input u(t) and output y(t) signals based
on the model order you specify . For example, regressors can be delayed
inputs and outputs, such as u(t-1) and y(t-3). Regressors can also b e nonlinear
functions o f inputs and outputs, such as tan(u(t-1)) or u(t-1)y(t-3).Youcan
either use d efault regressors, or specify your own custom functions of input
and output signals.
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