Open-Loop Response of Control System for Stability Margin Analysis

What Is Open-Loop Response?

Open-loop response is the combined response of the plant and the controller, excluding the effect of the feedback loop. For example, the next block diagram shows a single-loop control system.

Open-loop response corresponds to the linear response of the plant and the controller. If C(s) and P(s) are linear, the corresponding linear systems is C(s)P(s).

In Simulink® Control Design™, the linearization I/O points and the loop opening that correspond to open-loop response look something like this:

However, if there is no loop opening at the output of Water-Tank System block, the resulting linear model is different:

Compute Open-Loop Response

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

Compute a linear model of the combined controller-plant system without the effects of the feedback signal. Use a Bode plot of the resulting linear model to see the open-loop response.

  1. Open Simulink model.

    sys = 'watertank';

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

  2. In the Simulink Editor, define the portion of the model to linearize:

    1. Right-click the PID Controller block input signal (the output of the Sum block). Select Linear Analysis Points > Input Perturbation.

    2. Right-click the Water-Tank System output signal, and select Linear Analysis Points > Open-loop Output.

    Annotations appear in the model indicating which signals are designated as linearization I/O points.

  3. Open the Linear Analysis Tool for the model.

    In the Simulink Editor, select Analysis > Control Design > Linear Analysis.

    By default, the I/O points you specified in the model are the selected Analysis I/Os for linearization, as displayed in the Analysis I/Os menu.

  4. Linearize the model with the specified I/Os, and generate a Bode plot of the linearized model.

    Click Bode. The Bode plot of the linearized plant appears.

      Tip   Instead of a Bode plot, generate other response types by clicking the corresponding button in the plot gallery.

  5. View the minimum stability margins for the model.

    Right-click the plot and select Characteristics > Minimum Stability Margins.

    The Bode plot displays the phase margin marker. Click the marker to show a data tip that contains the phase margin value.

  6. Close Simulink model.


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