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| Contents | Index |
| Learn more about System Identification Toolbox |
| On this page… |
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About Hammerstein-Wiener Plots How to Create Hammerstein-Wiener Plots in the GUI How to Plot Hammerstein-Wiener Plots at the Command Line |
Hammerstein-Wiener model plot lets you explore the characteristics of the linear block and the static nonlinearities of the Hammerstein-Wiener model. For more information about estimating nonlinear Hammerstein-Wiener models, see Identifying Hammerstein-Wiener Models.
Examining a Hammerstein-Wiener plot can help you determine whether you chose an unnecessarily complicated nonlinearity for modeling your system. For example, if you chose a piece-wise-linear nonlinearity (which is very general), but the plot indicates saturation behavior, then you can estimate a new model using the simpler saturation nonlinearity instead.
For multivariable systems, you can use the Hammerstein-Wiener plot to determine whether to exclude nonlinearities for specific channels. If the nonlinearity for a specific input or output channel does not exhibit strong nonlinear behavior, you can estimate a new model after setting the nonlinearity at that channel to unit gain.
To create a Hammerstein-Wiener plot in the System Identification Tool GUI, select the Hamm-Wiener 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 Hamm-Wiener check box is unavailable if you do not have a Hammerstein-Wiener model in the Model Board. |
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 icon, as shown in the following figure.
After you generate a plot, you can learn more about your model by:
You can plot input and output nonlinearity and linear responses for Hammerstein-Wiener models using the following syntax:
plot(model)
model must be an idnlhw model object. You can use additional plot arguments to specify the following information:
Include several Hammerstein-Wiener models on the plot.
Configure how to evaluate the nonlinearity at each input and output channel.
Specify the time or frequency values for computing transient and frequency response plots of the linear block.
The plot command opens the Hammerstein-Wiener Model Plot window. For more information about working with this plot window, see Plotting Nonlinear Block Characteristics and Plotting Linear Block Characteristics.
For detailed information about plot, type the following command at the prompt:
help idnlhw/plot
The Hammerstein-Wiener model can contain up to two nonlinear blocks. The nonlinearity at the input to the Linear Block is labeled uNL and is called the input nonlinearity. The nonlinearity at the output of the Linear Block is labeled yNL and is called the output nonlinearity.
To configure the plot, perform the following steps:
If the top pane is not visible, click
to expand the Hammerstein-Wiener
Model Plot window.
Select the nonlinear block you want to plot:
To plot uNL as a command of the input data, click the uNL block.
To plot yNL as a command of its inputs, click the yNL block.
The selected block is highlighted in green.
If your model contains multiple variables, select the channel in the Select nonlinearity at channel list. Selecting the channel updates the plot and displays the nonlinearity values versus the corresponding input to this nonlinear block.
To change the range of the horizontal axis, select Options > Set input range to open the Range for Input to Nonlinearity dialog box. Enter the range using the format [MinValue MaxValue]. Click Apply and then Close to update the plot.
The Hammerstein-Wiener model contains one Linear Block that represents the embedded linear model.
To configure the plot:
If the top pane is not visible, click
to expand the Hammerstein-Wiener
Model Plot window.
Click the Linear Block to select it. The Linear Block is highlighted in green.
In the Select I/O pair list, select the input and output data pair for which to view the response.
In the Choose plot type list, select the linear plot from the following options:
Step
Impulse
Bode
Pole-Zero Map
If you selected to plot step or impulse response, you can set the time span. Select Options > Time span and enter a new time span in units of time you specified for the model.
For a time span T, the resulting response is plotted from -T/4 to T. The default time span is 10.
Click Apply and then Close.
If you selected to plot a Bode plot, you can set the frequency range.
The default frequency vector is 128 linearly distributed values, greater than zero and less than or equal to the Nyquist frequency. To change the range, select Options > Frequency range, and specify a new frequency vector in units of rad per model time units.
Enter the frequency vector using any one of following methods:
MATLAB expression, such as [1:100]*pi/100 or logspace(-3,-1,200). Cannot contain variables in the MATLAB workspace.
Row vector of values, such as [1:.1:100].
Click Apply and then Close.
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