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Compute Open-Loop Response

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

如果控制器，C(s)和植物，P(s), are linear, the corresponding open-loop transfer function isC(s)P(s).

To remove the effects of the feedback loop, insert a loop opening analysis point without manually breaking the signal line. Manually removing the feedback signal from a nonlinear model changes the model operating point and produces a different linearized model. For more information, seeHow the Software Treats Loop Openings.

If you do not insert a loop opening, the resulting linear model includes the effects of the feedback loop.

To specify the loop opening for this example, you can use either of the following analysis points.

Analysis Point 描述 To computeC(s)P(s)
Open-loop input Specifies a loop opening followed by an input perturbation.

Specify an open-loop input at the input to the controller and an output measurement at the output of the plant.
开环输出 指定输出测量，然后进行循环断裂。

在工厂的输出处指定开环输出，并在控制器的输入处进行输入扰动。

对于某些系统，您无法在与线性化输入或输出点相同的位置指定循环打开。例如，要在以下系统中打开外循环，使用循环断点分析点添加了一个循环的打开点. As a result, only the blue blocks are on the linearization path.

将循环开口放置在与输入或输出信号相同的位置，还将从线性化结果中消除内部环的效果。

您可以直接在Simulink中指定分析点金宝app®model, in the模型线性化器, or at the command line. For more information, about the different types of analysis points and how to define them, seeSpecify Portion of Model to Linearize.

使用使用的开环响应模型线性化器

此示例显示了如何计算组合控制器系统的线性模型，而无需反馈信号的效果。您可以使用例如Bode图分析生成的线性模型。

打开的si金宝appmulink模型。

sys ='水箱';Open_System（SYS）

The水坦克系统块代表该控制系统中的植物，并包含所有系统非线性。

在Simuli金宝appnk模型窗口中，指定要线性化的模型部分。在此示例中，使用开环输出分析点指定循环打开。

  1. Open theLinearizationtab. To do so, in theAppsgallery, clickLinearization Manager.

  2. 要指定信号的分析点，请单击模型中的信号。然后，在Linearization标签，在Insert Analysis Pointsgallery, select the type of analysis point.

    • 配置输入信号PID Controllerblock as anInput Perturbation.

    • Configure the output signal of the水坦克系统block as anOpen-loop Output.

注释出现在模型中，指示哪些信号指定为分析点。

Tip

If you do not want to introduce changes to the Simulink model, you can specify the analysis points in the模型线性化器. For more information, see指定模型的一部分以在模型线性化中线性化.

Open the模型线性化器对于模型。在Simuli金宝appnk模型窗口中Appsgallery, click模型线性化器.

默认情况下，您在模型中指定的分析点是线性化的，如在Analysis I/Osdrop-down list.

要使用指定的分析点线性化模型并生成线性化模型的Bode图，请单击Bode.

By default, the模型线性化器linearizes the model at the model initial conditions, as shown in theOperating Pointdrop-down list. For examples of linearizing a model at a different operating point, seeLinearize at Trimmed Operating Point和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特征>最小稳定性边缘.

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.

Compute Open-Loop Response at the Command Line

打开脚本

此示例显示了如何计算组合控制器系统的线性模型，而无需反馈信号的效果。您可以使用例如Bode图分析生成的线性模型。

打开的si金宝appmulink模型。

sys ='水箱';Open_System（SYS）

Specify the portion of the model to linearize by creating an array of analysis points using theLiniocommand:

  • PID控制器块的输入处的开环输入点。该信号起源于sum1块的输出。

  • 在水坦克系统块的输出处的输出测量。

io(1) = linio('watertank/sum1'，1，'openinput'）；io(2) = linio(“水务/水坦克系统”，1，'output'）；

The open-loop input analysis point includes a loop opening, which breaks the signal flow and removes the effects of the feedback loop.

Linearize the model at the default model operating point using thelinearizecommand.

linsys =线性化（sys，io）;

linsysis the linearized open-loop transfer function of the system. You can now analyze the response by, for example, plotting its frequency response and viewing the gain and phase margins.

margin(linsys)

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

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