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Linearizing the Model

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Linearizing at an Operating Point Creating Other Types of Linear Models Linearizing Discrete-Time and Multirate Models

Linearizing at an Operating Point

You can use linearize around operating points. Refer to What Are Operating Points? for more information on the role of operating points in linearization.

This section contains the following topics:

• Linearizing at a Simulink Model Operating Point

• Linearizing at Captured Operating Points

• Linearizing at Specified Simulation Times

• Linearizing at Simulation Events

Tip   To automatically generate MATLAB code that linearizes your model as specified in the Control and Estimation Tools Manager, click or select File > Generate MATLAB Code.

Linearizing at a Simulink Model Operating Point

To linearize around the operating point in the Simulink model:

1. Select the Operating Points tab in the Linearization Task node.

2. Select the Linearize at the operating point currently specified in the Simulink model option button. This button is selected by default.

   

3. Click Linearize Model. The software does the following:

   • Simulates the model

   • Computes the operating point of the model, including the nontrimmable states

   • Linearizes around that operating point

   • Adds the linearization result, labeled Model, to the Linearization Task node

Linearizing at Captured Operating Points

You can linearize around operating points that you captured in the Operating Points node.

This section continues the example from Inspecting Analysis I/Os. At this stage in the example, a linearization task has been created, operating points have been specified, and linearization points have been inserted.

In this step of the linearization task, you linearize the model using one of the operating points that you created in the project workspace. For information about additional linearization option, see Linearizing the Model.

Click the Operating Points tab in the Linearization Task node to select one or more operating points for the linearization. To linearize the magnetic ball model around the operating point computed from partial specifications, first select the Linearize at one or more of the following operating points option button. Then, select Operating Point in the list, as shown in the following figure.

To compute the linearized model:

1. In the menu to the right of the Linearize Model button, select from one of the nine options for displaying the results of the linearization. Clear the check box next to this menu when you do not want to display the results.

2. Click the Linearize Model button at the bottom of the pane. The linearized model is computed and displayed in the LTI Viewer.

The following figure shows the step response for the linearized magball model.

Linearizing at Specified Simulation Times

You can linearize around operating points extracted from a simulation of your model at specified times, such as when the simulation reaches a steady state solution.

To linearize around one or more simulation times:

1. Select the Operating Points tab in the Linearization Task node.

2. From the Select operating point type list, select Simulation snapshot.

   

3. Enter a vector of one or more times in the Simulation snapshot times (sec.) field. For example, enter [1,10] to compute operating points at t=1 and t=10.

4. Click Linearize Model. The software does the following:

   • Simulates the model

   • Extracts the specified operating points

   • Linearizes around these operating points

   • Adds the linearization result, labeled Model, to the Linearization Task node

Linearizing at Simulation Events

You can linearize around operating points extracted from a simulation of your model at one or more of the following simulation events:

• Trigger-based events

• Function-call events

For more information about modeling events in Simulink, see Creating Conditional Subsystems in the Simulink User's Guide.

The Simulink Control Designn software linearizes around the operating points of all simulation events within a specified simulation time. The linearization takes into account all states in the model operating point.

To linearize around one or more simulation events:

1. Add a Trigger-Based Operating Point Snapshot block to your model.

   This block is in the Simulink Control Design block library. The model in the Trigger-Based Operating Point Snapshot demo shows the use of this block.

2. Select the Operating Points tab in the Linearization Task node.

3. From the Select operating point type list, select Simulation snapshot.

4. Enter a scalar value that specifies the simulation end time in the Simulation snapshot times (sec.) field.

   

5. Click Linearize Model. The software does the following:

   • Simulates the model for the specified duration

   • Extracts the operating points at each simulation event

   • Linearizes around these operating points

   • Adds the linearization result, labeled Model, to the Linearization Task node

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Creating Other Types of Linear Models

In addition to creating simple transfer functions using the input and output points, you can create more sophisticated linearized models using some of the other options in the Linearization Points menu.

• Input-Output Point, an input point immediately followed by an output point. This is useful for measuring sensitivity to output disturbances

• Output-Input Point, an output point immediately followed by an input point. This is useful for robust control. Use the resulting transfer function in mu analysis of your system.

• Open Loop, discussed in Performing Open-Loop Analysis

• Output Constraint, discussed in Constraining Outputs

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Linearizing Discrete-Time and Multirate Models

The linearization method is the same for models containing discrete-time states or several different sample times. However, you can choose to adjust the Linearization sample time in the Linearization options pane. By default, this parameter is set to -1, in which case the software linearizes at the slowest sample rate in the model. To create a linearized model with a different sample time, enter a new value in the dialog box. A value of 0 gives a continuous-time model.

To change the method that Simulink Control Design software uses for converting a multirate model to a single-rate model, change the Rate conversion method in the Options dialog box.

For more information, and examples, on methods and algorithms for rate conversions and linearization of multirate models, see the "Linearization of Multi-Rate Models" and "Rate Conversion Method Selection for Linearization" demos listed under the Simulink Control Design Demos in the demos browser.

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Linearizing a Block

Viewing Linearization Results

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