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Visualize Reduced-Order Models in Model Reducer App

The plotting tools in the Model Reducer app let you examine and compare time-domain and frequency-domain responses of the original model and the reduced models you create in the app. Use these tools to help verify that the reduced-order model you choose to work with preserves the system behaviors that are important for your application.

For more general information about model reduction, see Model Reduction Basics.

Comparison Plots

By default, for any model reduction method, Model Reducer shows a frequency-response plot of both the original and reduced models. This plot is a Bode plot for SISO models, and a singular-value plot for MIMO models.

To more closely examine the differences between an original model and a reduced model, you can use absolute error or relative error plots. On any model reduction tab, click Absolute error plot or Relative error plot to view these plots.

  • Absolute error plot — Shows the singular values of G-Gr, where G is the original model and Gr is the current reduced model.

  • Relative error plot — Shows the singular values of (G-Gr)/G. This plot is useful when the model has very high or very low gain in the region that is important to your application. In such regions, absolute error can be misleading.

For SISO models, the singular-value plot is the magnitude of the frequency response.

For Modal Truncation, the app provides an additional comparison plot Mode locations to compare mode locations of original and reduced models.

Analysis plots

For Balanced Truncation and Modal Truncation methods, the app also provides plots to analyze the model and select a model order reduction criteria.

  • Balanced Truncation analysis plots:

    • Hankel singular values — Bar chart of Hankel singular values and associated error bounds. This is the default plot type.

    • State energies — Bar chart of normalized state energies.

  • Modal Truncation analysis plots:

    • DC contributions — Bar chart of normalized DC contributions. This is the default plot type.

    • Mode locations — Location of the poles.

    • Mode damping and natural frequency — Damping and natural frequencies of the poles.

Response Plots

After you click Save Reduced Model to add one or more reduced models to the data browser, compare additional responses of the original and reduced models using the Plots tab.

Create New Response Plot

In the data browser, select one or more models to plot. (Ctrl-click to select multiple models.) Then, on the Plots tab, click the type of plot you want to create.

Model Reducer creates the plot.

Add Model to Existing Plot

In the data browser, select the model to add. Then, on the Plots tab, click the icon corresponding to the plot you want to update. Plots you have created appear on the left side of the plot gallery.

Model Reducer updates the plot with the new model.


To expand the gallery view, click .

Plot Characteristics

On any plot in Model Reducer:

  • To see response information and data values, click a line on the plot.

  • To view system characteristics, right-click anywhere on the plot.

Plot Tools

Mouse over any plot to access plot tools at the upper right corner of the plot.

  • and — Zoom in and zoom out. Click to activate, and drag the cursor over the region to zoom. The zoom icon turns dark when zoom is active. Right-click while zoom is active select Restore View. Click the icon again to deactivate.

  • — Pan. Click to activate, and drag the cursor across the plot area to pan. The pan icon turns dark when pan is active. Right-click while pan is active to access additional pan options. Click the icon again to deactivate.

  • — Legend. By default, the plot legend is active. To toggle the legend off and on, click this icon. To move the legend, drag it to a new location on the plot.

To change the way plots are tiled or sorted, click on the arrow icon at the end of the plot tabs and select one of the options from Tile All.

See Also

Related Topics