|
|
|
| R2012a Documentation → Simulink Control Design | |
Learn more about Simulink Control Design |
|
| Contents | Index |
Simulink Control Design lets you specify the subsystem, loop, or block to linearize using linearization input and output points (linearization I/O points).
A linearization input point defines the input signal to the linear model. A linearization output point defines the output signal of the linear model.
You can linearize:
Closed or open loop responses using a linearization input point on the input signal to the portion of the model you want to linearize, and a linearization output point at the output signal of that portion of the model.
Specific subsystem or block.
In this case, linearization I/O points are the input and output signals corresponding to the subsystem or block.
You can define other linear models using additional types of linearization I/O points:
Input-Output Linearization Point—Linearization output point immediately follows a linearization input point. This type of linearization I/O point is useful for measuring sensitivity to output disturbances.
Output-Input Linearization Point—Linearization input point immediately follows a linearization output point. This type of linearization I/O point is useful for robust control. You can use the resulting transfer function in the mu analysis of your system.
Linearization I/O points are pure annotations and do not impact model simulation.
If your model contains one or more feedback loops, you can choose to linearize an open-loop or a closed-loop system.
Simulink Control Design lets you remove the effects of the feedback loop by inserting an open loop point without having to manually break signal lines. In fact, for nonlinear models, do not open the loop by manually removing the feedback signal from the model; this action changes the model operating point and produces a different linear model.
Correct placement of the loop opening is critical to obtaining the right linear model. For example, you might want to linearize only the plant model in a feedback control loop.
To understand the difference between open-loop and closed-loop analysis, consider this single-loop control system.
Suppose you want to linearize the plant, P, about an equilibrium operating point of the model.
To linearize only the plant P, you must
open the loop at the output of the P block. If you do not open the
loop, and if C and P are linear,
the linearized model between U and Y is
.
The loop opening does not need to be in the same location as the linearization input or output point. For example, the next figure shows a loop opening after the gain on the outer feedback loop, which removes the effect of this loop from the linearization. To check whether you correctly excluded the feedback signal, linearize the model and highlight the blocks included in the linearization.
In this example, placing a loop opening at the same location as the linearization output point also removes the effect of the inner loop from the linearization.
There are several ways to specify linearization inputs, outputs, and loop-opening locations (linearization I/O sets). Each method has its own advantages. You can:
Specify linearization I/O points and loop openings directly in the model. An advantage of this method is that the locations of linearization I/O points and loop openings are shown graphically in the model. However, specifying linearization I/O sets this way changes the model.
Interactively define linearization I/O sets using the Linear Analysis Tool. The Create linearization I/O set dialog box in the Linear Analysis Tool allows you to define one or more I/O sets for your model interactively. This approach does not make changes to the model.
Define linearization I/O sets at the command line using linio. This method also allows you to define one or more I/O sets without changing the model.
To specify linearization I/O points and loop openings directly in your Simulink model:
Right-click on the signal you want to define as a linearization input point or output point.
This action opens a context menu on the signal.
Hover the cursor over Linearization Points in the context menu.
A submenu appears listing types of linearization points.
Select the type of linearization point you want to define at the signal. For example, to specify that the signal is a linearization input point, select Input Point.
When you specify a linearization point, a marker appears in your model indicating the linearization point type.
To insert an open loop point at the signal, select Linearization Points > Open Loop from the context menu.
A marker appears in your model indicating the loop opening location.
Repeat steps 2–4 for all signals you want to define as linearization I/O points or open loop points.
Specifying linearization points using the context menu changes the model (makes the model "dirty").
You use linearization inputs, outputs, and loop-opening locations (linearization I/O sets) to specify which portion of the model to linearize. You can specify one or more linearization I/O sets interactively in the Linear Analysis Tool, without introducing changes to the model.
To access the Create linearization I/O set dialog box:
Click the Exact Linearization or Frequency Response Estimation tab.
From the Analysis I/Os drop-down list, select Create new linearization I/Os.
The Create linearization I/O set dialog box opens.
To create a new linearization I/O set:
In your Simulink model, select a signal that you want to define as a linearization input or output point.
The selected signal appears in the Create linearization I/O set dialog box under Currently selected signals.
In the Create linearization I/O set dialog box, click the signal name under Currently selected signals.
Click Add. The signal appears in the list of Analysis I/Os.
Select the linearization point type from the Configuration drop-down list. For example, if you want the selected signal to be a linearization output point, select Output.
If you want the signal to be a loop opening point, click the Open Loop check box.
Repeat steps 1–5 for any other signals you want to define as linearization I/O points.
After you define all the signals for the I/O set, enter a name for the I/O set in the Variable name box.
Click OK.
The Create linearization I/O set dialog box closes. A new linearization I/O set appears in the Linear Analysis Workspace of the Linear Analysis Tool. The new linearization I/O set displays the name you specified.
The newly created linearization I/O set is automatically selected in the Analysis I/Os menu for either the Exact Linearization or Frequency Response Estimation tab, depending on which you selected originally.
Creating linearization I/O sets in the Linear Analysis Tool does not change the Simulink model. You can create multiple I/O sets for a single model.
You can interactively edit a linearization I/O set stored in the Linear Analysis Workspace using the Linear Analysis Tool Edit dialog box.
To open the Edit dialog box for editing a linearization set, either:
In the Linear Analysis Workspace, double-click the I/O set.
Click either the Exact Linearization or Frequency
Response Estimation tab. If the I/O set is selected in the Analysis
I/Os menu, click the edit icon
next to the Analysis
I/Os menu.
Either of these actions opens the I/O set edit dialog box for
the linearization I/O set. You can now edit the I/O set as needed.
When you have finished editing, click
to close the dialog box
and save your changes.
Tip To highlight in the Simulink model the blocks that are included in the linearization specified by the current list of Analysis I/Os, click Highlight. |
To add a linearization input point, output point, or loop opening to the linearization I/O set:
In your Simulink model, select a signal that you want to add to the linearization I/O set.
The selected signal appears in the Create linearization I/O set dialog box under Currently selected signals.
In the Create linearization I/O set dialog box, click the signal name under Currently selected signals.
Click Add. The signal appears in the list of Analysis I/Os.
Select the linearization point type from the Configuration drop-down list. For example, if you want the selected signal to be a linearization output point, select Output.
If you want the signal to be a loop opening point, click the Open Loop check box.
To remove a linearization input point, output point, or loop opening from the linearization I/O set:
Select the signal in the list of Analysis I/Os.
Click Delete to remove the signal from the linearization I/O set.
To change the type of linearization point for a signal, locate the signal in the list of Analysis I/Os. Then, use the Configuration drop-down list and the Open Loop check box for the signal to define the type of linearization point.
For example, if you want the signal to be a linearization output point, select Output from the Configuration drop-down list. If you want the signal not to be an open loop point, verify that the Open Loop check box is cleared.
This example shows how to select individual elements in a bus signal as linearization input/output (I/O) points. Linearization I/O points define the portion of the model to linearize.
Open Simulink model.
sys = 'sldemo_mdlref_bus'; open_system(sys)
In the Simulink model window, define portion of the model to linearize:
Right-click the COUNTERBUS signal, and select Linearization Points > Select Bus Element.
This option appears only if Mux blocks used to create bus signals in the Configuration Parameters > Diagnostics > Connectivity pane is error. Otherwise, right-clicking the bus signal lets you specify all elements in the bus as linearization input or output points.
The Select Linearization Points in the Bus dialog box opens, which shows signals contained in the COUNTERBUS bus signal.
In the Bus Hierarchy area, expand the bus named limits. Then, select upper_saturation_limit.
Tip For large buses, you can enter search text for filtering element names in the Filter by name edit box. The name match is case-sensitive. Additionally, you can enter a MATLAB regular expression. To modify the filtering options, click
|
Click Add.
The selected signal now appears in the Linearization Inputs/Outputs area, and is configured as a linearization input point.
Click OK.
Right-click the OUTPUTBUS signal, and select Linearization Points > Select Bus Element.
In the Bus Hierarchy area, expand the bus named limits, and select upper_saturation_limit.
Click Add to add the selected signal to the Linearization Inputs/Outputs area.
Select Output in the Configuration column.
Click OK.
Tip In the model window, select Format > Port/Signal Displays > Linearization Indicators to view the linearization I/O markers. |
You can select multiple elements in the same bus with different
I/O types. The
marker appears on the bus signal to
indicate multiple bus element selections with different I/O types.
In the Simulink model window, select Tools > Control Design > Linear Analysis.
The Linear Analysis Tool for the model opens.
Click the Exact Linearization tab. Click
adjacent to the Analysis
I/Os list to see the bus elements selected as linearization
I/O points.
In the Exact Linearization tab,
click
to linearize the model using the model initial
condition as the operating point.
 | Linearizing Nonlinear Models | Plant Linearization |  |
Learn more about resources for designing, testing, and implementing control systems.
Get free kit| © 1984-2012- The MathWorks, Inc. - Site Help - Patents - Trademarks - Privacy Policy - Preventing Piracy - RSS |
