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Nonlinear ARX Model Plots

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About Nonlinear ARX Plots How to Plot Nonlinear ARX Plots Using the GUI Configuring the Nonlinear ARX Plot Axis Limits, Legend, and 3-D Rotation How to Plot Nonlinear ARX Plots at the Command Line

About Nonlinear ARX Plots

The Nonlinear ARX plot displays the characteristics of model nonlinearities as a function of one or two regressors. For more information about estimating nonlinear ARX models, see Identifying Nonlinear ARX Models.

Examining a nonlinear ARX plot can help you gain insight into which regressors have the strongest effect on the model output. Understanding the relative importance of the regressors on the output can help you decide which regressors should be included in the nonlinear function.

Furthermore, you can create several nonlinear models for the same data set using different nonlinearity estimators, such a wavelet network and tree partition, and then compare the nonlinear surfaces of these models. Agreement between nonlinear surfaces increases the confidence that these nonlinear models capture the true dynamics of the system.

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How to Plot Nonlinear ARX Plots Using the GUI

To create a nonlinear ARX plot in the System Identification Tool GUI, select the Nonlinear ARX check box in the Model Views area. For general information about creating and working with plots, see Working with Plots in the System Identification Tool GUI.

Note   The Nonlinear ARX check box is unavailable if you do not have a nonlinear ARX model in the Model Board.

The following figure shows a sample nonlinear ARX plot.

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Configuring the Nonlinear ARX Plot

To include or exclude a model on the plot, click the corresponding model icon in the System Identification Tool GUI. Active models display a thick line inside the Model Board icon.

To configure the plot:

1. If your model contains multiple output, select the output channel in the Select nonlinearity at output list. Selecting the output channel displays the nonlinearity values that correspond to this output channel.

2. If the regressor selection options are not visible, click to expand the Nonlinear ARX Model Plot window.

3. Select Regressor 1 from the list of available regressors. In the Range field, enter the range of values to include on the plot for this regressor. The regressor values are plotted on the Reg1 axis.

4. Specify a second regressor for a 3-D plot by selecting one of the following types of options:

   • Select Regressor 2 to display three axes. In the Range field, enter the range of values to include on the plot for this regressor. The regressor values are plotted on the Reg2 axis.

   • Select <none> in the Regressor 2 list to display only two axes.

5. To fix the values of the regressor that are not displayed, click Fix Values. In the Fix Regressor Values dialog box, double-click the Value cell to edit the constant value of the corresponding regressor. The default values are determined during model estimation. Click OK.

6. In the Nonlinear ARX Model Plot window, click Apply to update the plot.

7. To change the grid of the regressor space along each axis, Options > Set number of samples, and enter the number of samples to use for each regressor. Click Apply and then Close.

   For example, if the number of samples is 20, each regressor variable contains 20 points in its specified range. For a 3-D plots, this results in evaluating the nonlinearity at 20 x 20 = 400 points.

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Axis Limits, Legend, and 3-D Rotation

The following table summarizes the commands to modify the appearance of the Nonlinear ARX plot.

Changing Appearance of the Nonlinear ARX Plot

Action	Command
Change axis limits.	Select Options > Set axis limits to open the Axis Limits dialog box, and edit the limits. Click Apply.
Hide or show the legend.	Select Style > Legend. Select this option again to show the legend.
(Three axes only) Rotate in three dimensions. Note   Available only when you have selected two regressors as independent variables.	Select Style > 3D Rotate and drag the axes on the plot to a new orientation. To disable three-dimensional rotation, select Style > 3D Rotate again.

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How to Plot Nonlinear ARX Plots at the Command Line

You can plot the nonlinearity shape of nonlinear ARX models using the following syntax:

plot(model)

model must be an idnlarx model object. You can use additional plot arguments to specify the following information:

• Include multiple nonlinear ARX models on the plot.

• Configure the regressor values for computing the nonlinearity values.

The plot command opens the Nonlinear ARX Model Plot window. For more information about working with this plot window, see Configuring the Nonlinear ARX Plot and Axis Limits, Legend, and 3-D Rotation.

For detailed information about plot, type the following command at the prompt:

help idnlarx/plot

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