Mark Signals of Interest for Control System Analysis and Design

Specify Analysis Points for MATLAB Models

Consider an LTI model of the simpleFeedback system.

G = tf(10,[1 3 10]);
C = pid(0.2,1.5);
T = feedback(G*C,1);

With this model, you can obtain the closed-loop response from r to y. However, you cannot analyze the open-loop response at the plant input or simulate the rejection of a step disturbance at the plant input. To enable such analysis, mark the signal u as an analysis point by inserting an AnalysisPoint block between the plant and controller.

AP = AnalysisPoint("u");
T = feedback(G*AP*C,1);
T.OutputName = "y";

The plant input, u, is now available for analysis.

In creating the model T, you manually created the analysis point block AP and explicitly included it in the feedback loop. When you combine models using the connect command, you can instruct the software to insert analysis points automatically at the locations you specify. For more information, see connect.

Specify Analysis Points for Simulink Models

In Simulink, you can mark analysis points either explicitly in the block diagram, or programmatically using the addPoint command for slLinearizer or slTuner interfaces.

To specify analysis points directly in your Simulink model, first open the Linearization tab. To do so, in the Apps gallery, click Linearization Manager.

To specify an analysis point:

You can select any of the following closed-loop analysis point types, which are equivalent within an slLinearizer or slTuner interface; that is, they are treated the same way by analysis functions, such as getIOTransfer, and tuning goals, such as TuningGoal.StepTracking.

If you want to introduce a permanent loop opening at a signal as well, select one of the following open-loop analysis point types:

When you define a signal as an open-loop point, analysis functions such as getIOTransfer always enforce a loop break at that signal during linearization. All open-loop analysis point types are equivalent within an slLinearizer or slTuner interface. For more information on how the software treats loop openings during linearization, see How the Software Treats Loop Openings.

When you create an slLinearizer or slTuner interface for a model, any analysis points defined in the model are automatically added to the interface. If you defined an analysis point using:

To mark analysis points programmatically, use the addPoint command. For example, consider the scdcascade model.

open_system("scdcascade")

To mark analysis points, first create an slTuner interface.

ST = slTuner("scdcascade");

To add a signal as an analysis point, use the addPoint command, specifying the source block and port number for the signal.

addPoint(ST,"scdcascade/C1",1);

If the source block has a single output port, you can omit the port number.

addPoint(ST,"scdcascade/G2");

For convenience, you can also mark analysis points using the:

addPoint(ST,"y2");

addPoint(ST,"scdcascade/C1/1")

addPoint(ST,"G1/1")

You can also add permanent openings to an slLinearizer or slTuner interface using the addOpening command, and specifying signals in the same way as for addPoint. For more information on how the software treats loop openings during linearization, see How the Software Treats Loop Openings.

addOpening(ST,"y1m");

You can also define analysis points by creating linearization I/O objects using the linio command.

io(1) = linio("scdcascade/C1",1,"input");
io(2) = linio("scdcascade/G1",1,"output");
addPoint(ST,io);

As when you define analysis points directly in your model, if you specify a linearization I/O object with:

When you specify response I/Os in a tool such as Model Linearizer or Control System Tuner, the software creates analysis points as needed.

Refer to Analysis Points for Analysis and Tuning

Once you have marked analysis points, you can analyze the response at any of these points using the following analysis functions:

You can also create tuning goals that constrain the system response at these points. The tools to perform these operations operate in a similar manner for models created at the command line and models created in Simulink.

To view the available analysis points, use the getPoints function. You can view the analysis for models created:

getPoints(T)

ans = 1x1 cell array
    {'u'}

getPoints(ST)

ans = 3x1 cell
    {'scdcascade/C1/1[u1]'}
    {'scdcascade/G2/1[y2]'}
    {'scdcascade/G1/1[y1]'}

For closed-loop models created at the command line, you can also use the model input and output names when:

ioSys = getIOTransfer(T,"u","y");
stepplot(ioSys)

loopSys = getLoopTransfer(T,"u",-1);
bodeplot(loopSys)

R = TuningGoal.Margins("u",10,60);

Use the same method to refer to analysis points for models created in Simulink. In Simulink models, for convenience, you can use any unambiguous abbreviation of the analysis point names returned by getPoints.

ioSys = getIOTransfer(ST,"u1","y1");
sensG2 = getSensitivity(ST,"G2");
R = TuningGoal.Margins("u1",10,60);

Finally, if some analysis points are vector-valued signals or multichannel locations, you can use indices to select particular entries or channels. For example, suppose u is a two-entry vector in a closed-loop MIMO model.

G = ss([-1 0.2;0 -2],[1 0;0.3 1],eye(2),0);
C = pid(0.2,0.5);
AP = AnalysisPoint("u",2);
T = feedback(G*AP*C,eye(2));
T.OutputName = "y";

You can compute the open-loop response of the second channel and measure the impact of a disturbance on the first channel.

L = getLoopTransfer(T,"u(2)",-1);
stepplot(getIOTransfer(T,"u(1)","y"))

When you create tuning goals in Control System Tuner, the software creates analysis points as needed.