Open-Loop Response of Control System for Stability Margin Analysis

This example shows how to analyze the open-loop response of a control system using the Linear Analysis Tool.

This example shows how to compute a linear model of the combined controller-plant system without the effects of the feedback signal. You can analyze the resulting linear model using, for example, a Bode plot.

Open Simulink® model.

sys = 'watertank';
open_system(sys)

The Water-Tank System block represents the plant in this control system and contains all of the system nonlinearities.

In the Simulink model window, specify the portion of the model to linearize. For this example, specify the loop opening using open-loop output analysis point.

  1. Open the Linearization tab. To do so, in the Apps gallery, click Linearization Manager.

  2. To specify an analysis point for a signal, click the signal in the model. Then, on the Linearization tab, in the Insert Analysis Points gallery, select the type of analysis point.

    • Configure the input signal of the PID Controller block as an Input Perturbation.

    • Configure the output signal of the Water-Tank System block as an Open-loop Output.

Annotations appear in the model indicating which signals are designated as analysis points.

Tip

If you do not want to introduce changes to the Simulink model, you can specify the analysis points in the Linear Analysis Tool. For more information, see Specify Portion of Model to Linearize in Linear Analysis Tool.

Open the Linear Analysis Tool for the model. In the Simulink model window, in the Apps gallery, click Model Linearizer.

By default, the analysis points you specified in the model are selected for linearization, as displayed in the Analysis I/Os drop-down list.

To linearize the model using the specified analysis points and generate a Bode plot of the linearized model, click Bode.

By default, the Linear Analysis Tool linearizes the model at the model initial conditions, as shown in the Operating Point drop-down list. For examples of linearizing a model at a different operating point, see Linearize at Trimmed Operating Point and Linearize at Simulation Snapshot.

Tip

To generate response types other than a Bode plot, click the corresponding button in the plot gallery.

To view the minimum stability margins for the model, right-click the Bode plot, and select Characteristics > Minimum Stability Margins.

The Bode plot displays the phase margin marker. To show a data tip that contains the phase margin value, click the marker.

For this system, the phase margin is 90 degrees at a crossover frequency of 0.4 rad/s.

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