User`s guide

Identifying Nonlinear ARX Models
Example – Relationship Between Regressors, Model Orders,
and Delays
This example describes how the model orders and delays you specify relate
to computing the regressors.
Suppose that you specify a nonlinear ARX model with a minimum of a
two-sample input delay and the number of input terms is n
b
=2. The toolbox
computes the following standard regressors from the input signal:
• u(t-2)
• u(t-3)
If you specify that the number of output terms is n
a
=4, the toolbox com putes
the f ollowing standard regressors from the output signals:
• y(t-1)
• y(t-2)
• y(t-3)
• y(t-4)
Note The minimum output delay is fixed at 1 because the prediction of
an output requires the delayed versions of itself and all other outputs.
To use past outputs for predicting the current value, you must include
past output samples, starting with the m ost rece nt at
t=-1.Inthecase
of decoupled outputs, the delay for output signals corresponding to the
prediction horizon. To use greater output delay values (for example,
2), y ou
must explicitly exclude the regressors that correspond to a delay of 1 (such
as
y_i(t-1)) for the nonlinear block during estimation by configuring the
NonlinearRegressors model property. However, all regressors are used in
the linear bl ock if the linear b lock i s included in your model.
If you have physical insight that your current output depends on specific
delayed inputs and outputs, select the appropriate model orders to compute
the required regressors.
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