Integral Op-amp Model

Model of an Integral (I) controller op-amp circuit

Examples

Basic Examples (2)

Retrieve the model:

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$ResourceData[\!$\* TagBox["\"\<Integral Op-amp Model\>\"", #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$]$

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The icon:

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$ResourceData[\!$\* TagBox["\"\<Integral Op-amp Model\>\"", #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$, "Icon"]$

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Scope & Additional Elements (6)

Available content elements:

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$\!$\* TagBox[ RowBox[{"ResourceObject", "[", "\"\<Integral Op-amp Model\>\"", "]"}], #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$["ContentElements"]$

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The state space model:

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$ResourceData[\!$\* TagBox["\"\<Integral Op-amp Model\>\"", #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$, "StateSpaceModel"]$

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The input variables:

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$ResourceData[\!$\* TagBox["\"\<Integral Op-amp Model\>\"", #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$, "InputVariables"]$

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The output variables:

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$ResourceData[\!$\* TagBox["\"\<Integral Op-amp Model\>\"", #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$, "OutputVariables"]$

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The complex variable:

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$ResourceData[\!$\* TagBox["\"\<Integral Op-amp Model\>\"", #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$, "ComplexVariable"]$

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The model parameters:

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$ResourceData[\!$\* TagBox["\"\<Integral Op-amp Model\>\"", #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$, "Parameters"]$

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Visualizations (1)

The integral action for various input frequencies and component values:

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$Manipulate[ Plot[{Sin[\[Omega] t], Evaluate@OutputResponse[ResourceData[\!$\* TagBox["\"\<Integral Op-amp Model\>\"", #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$] /. {Subscript[\[ScriptCapitalR], 1] -> r1, Subscript[\[ScriptCapitalR], 3] -> r3, Subscript[\[ScriptCapitalR], 4] -> r4, Subscript[\[ScriptCapitalC], 2] -> c2}, Sin[\[Omega] t], {t, 0, 10}]}, {t, 0, 10}, Sequence[ PlotLegends -> Placed[{"input", "output"}, Below], Frame -> True]], Sequence[{{\[Omega], 1}, 0.1, 10, ImageSize -> 75}, Delimiter, {{r1, 100, Subscript[\[ScriptCapitalR], 1]}, {100, 330, 500, 1000}}, {{r3, 330, Subscript[\[ScriptCapitalR], 3]}, {100, 330, 500, 1000}}, {{r4, 330, Subscript[\[ScriptCapitalR], 4]}, {100, 330, 500, 1000}}, {{c2, 0.01, "\!$\*SubscriptBox[\(\[ScriptCapitalC]$, $2$]\)"}, {0.005, 0.01, 0.025, 0.1}}], Sequence[ ControlPlacement -> Left, SaveDefinitions -> True]]$

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Analysis (1)

The magnitude decreases 20 dB every decade and the phase lag is a constant 90 °:

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$Manipulate[BodePlot[ResourceData[\!$\* TagBox["\"\<Integral Op-amp Model\>\"", #& , BoxID -> "ResourceTag-Integral Op-amp Model-Input", AutoDelete->True]$] /. {Subscript[\[ScriptCapitalR], 1] -> r1, Subscript[\[ScriptCapitalR], 3] -> r3, Subscript[\[ScriptCapitalR], 4] -> r4, Subscript[\[ScriptCapitalC], 2] -> c2}, Sequence[ ImageSize -> Small, PlotLayout -> "HorizontalGrid", PlotLabel -> {"magnitude", "phase"}]], Grid[{{ Control[{{r1, 100, Subscript[\[ScriptCapitalR], 1]}, {100, 330, 500, 1000}}], Control[{{r4, 330, Subscript[\[ScriptCapitalR], 4]}, {100, 330, 500, 1000}}]}, { Control[{{r3, 330, Subscript[\[ScriptCapitalR], 3]}, {100, 330, 500, 1000}}], Control[{{c2, 0.01, "\!$\*SubscriptBox[\(\[ScriptCapitalC]$, $2$]\)"}, {0.005, 0.01, 0.025, 0.1}}]}}, Spacings -> 2], SaveDefinitions -> True]$

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Bibliographic Citation

Suba Thomas, "Integral Op-amp Model" from the Wolfram Data Repository (2025)

Data Resource History

Date Created: 15 May 2025

Source Metadata

Citation: K. Ogata, "Modern Control Engineering", 5th ed. Upper Saddle River, NJ, USA: Pearson, 2010.

Publisher Information

Prepared for the Wolfram Data Repository By: Maher Kuzbari, Suba Thomas
Publisher of Record: Suba Thomas