Simulink® Control Design™

Viewing Linearization Results

Displaying Linearization Results

This section continues the magball example from Linearizing the Model. At this stage in the example, a linearization task has been created, operating points have been specified, linearization points have been inserted, and a linearized model has been computed.

To display the Linearization Result pane, as shown in the following figure, select the Model node in the project tree. To delete the linearization result, right-click Model and select Delete from the menu. The Linearization Result pane displays a mathematical representation of the linearized model. By default it appears as a state space system and it displays the state space matrices. However, within the pane you can choose to view the model as a zero-pole-gain system or as a transfer function. You can also export the model to the MATLAB workspace.

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Highlighting Blocks in the Linearization

This section continues the magball example from Displaying Linearization Results. At this stage in the example, a linearization task has been created, operating points have been created, linearization points have been inserted, and a linearized model has been computed.

To verify that the correct portion of the model was linearized, you can highlight the blocks in the model that were used in the linearization. To do this, right-click the Model node and select Highlight Blocks in Linearization. The following figure shows that the Magnetic Ball Plant block, including all blocks within it, was used in the linearization.

To remove the highlighting, right-click the Model node and select Remove Highlighting.

Note   You cannot use the Highlight Blocks in Linearization or Remove Highlighting option for models you linearize with numerical-perturbation linearization (when Numerical perturbation is selected as the Linearization Algorithm parameter in the Linearization Task Options window).

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Inspecting the Linearization Results Block by Block

This section continues the example from Displaying Linearization Results. At this stage in the example, a linearization task has been created, operating points have been created, linearization points have been inserted, and a linearized model has been computed.

To verify that blocks of interest linearized as expected, you can inspect linearization results block by block using the Simulink Control Design Linearization Inspector. An example of a block of interest is a block with a sharp discontinuity.

Note   For information on troubleshooting blocks that did not linearize as expected, see Troubleshooting Linearization Results.

To inspect the linearization results for the Current block in the Magnetic Ball Plant:

1. Select the Model node. Then, select the Linearization Inspector tab.

2. In the list of blocks under magball, select the MagneticBall Plant subsystem.

3. In the Subsystems Blocks column, select the Current block.

   Tip   You can filter the Subsystem Blocks list to include only blocks in the linearization path (the blocks between the input and output points). To filter the list, right-click the list, and select Show only blocks in linearization path.

   This action displays the following in the Linearization Inspector pane:

   • State-space matrices A, B, C, and D for the linearized Current block.

   • Sample time Ts, which equals zero and shows that the Magnetic Ball Plant is continuous.

   • A note saying that the block was linearized exactly.

   

You can plot the linearization results for a block. To create a step plot of the Current block linearization results, right-click the Current block in the Subsystems Blocks column and select Plot block > Step Plot.

Note   The Linearization Inspector pane is not available for models that are linearized with numerical-perturbation linearization (when Numerical perturbation is selected as the Linearization Algorithm parameter in the Linearization Task Options window). Such linearizations have no individual block linearizations to inspect.

Disabling the Linearization Inspector

When you do not want diagnostic information for your linearization, you disable the linearization inspector.

To disable the linearization inspector:

1. Select Tools > Options in the Control and Estimation Tools Manager window. Then, click the Linearization tab.

2. Deselect the Store Linearization Diagnostics and Inspector data with linearization option.

Note   You can also disable the linearization inspector globally in the Simulink Control Design tab of the MATLAB preferences dialog box. When you set this global preference, it takes effect in each subsequent creation of linearization tasks and persists from session to session.

For more information on changing linearization options, see Changing Linearization Options.

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Comparing the Results of Multiple Linearizations

This section continues the magball example from Inspecting the Linearization Results Block by Block. At this stage in the example, a linearization task has been created, operating points have been created, linearization points have been inserted, and a linearized model has been computed and inspected.

The LTI Viewer automatically displays a Linearization Quick Plot of the linearization results after the linearization. To create additional, customized plots, especially for comparing multiple linearizations, right-click the Custom Views node under the Linearization Task node and select Add View. A new view, View1, is added to the Custom Views node. Select the View1 node to display the View Setup pane and set up this view.

Example

Before configuring the View Setup pane for the magnetic ball system, run another linearization of this model using the operating point labeled Known Operating Conditions, that you computed in Creating Operating Points from Known Values. This adds Model (2) to the Linearization Task node.

Configure View Setup as shown in the following figure:

Click Display View to display the LTI Viewer, as shown in the following figure:

Before proceeding to Designing Compensators, close the Control and Estimation Tools Manager and the magball model. You do not need to save any projects or any changes to the model.

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Linearizing the Model

Validating and Troubleshooting Linearization Results