Wolfram Data Repository
Immediate Computable Access to Curated Contributed Data
Proportional-Integral-Derivative Op-amp Model
Model of a Proportional-Integral-Derivative (PID) controller op-amp circuit
Examples
Basic Examples (2)
Retrieve the model:
| In[1]:= | ![ResourceData[\!\(\*
TagBox["\"\<Proportional-Integral-Derivative Op-amp Model\>\"",
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\)]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/1525d13d91f284e7.png){kind=small} |
| Out[1]= |  |
The icon:
| In[2]:= | ![ResourceData[\!\(\*
TagBox["\"\<Proportional-Integral-Derivative Op-amp Model\>\"",
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\), "Icon"]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/6aef0a78f1ab90d3.png){kind=small} |
| Out[2]= |  |
Scope & Additional Elements (6)
Available content elements:
| In[3]:= | ![\!\(\*
TagBox[
RowBox[{"ResourceObject", "[", "\"\<Proportional-Integral-Derivative Op-amp Model\>\"", "]"}],
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\)["ContentElements"]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/6f83e349e1a0a200.png){kind=small} |
| Out[3]= |  |
The state space model:
| In[4]:= | ![ResourceData[\!\(\*
TagBox["\"\<Proportional-Integral-Derivative Op-amp Model\>\"",
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\), "StateSpaceModel"]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/73d3d9b67fde128d.png){kind=small} |
| Out[4]= |  |
The input variables:
| In[5]:= | ![ResourceData[\!\(\*
TagBox["\"\<Proportional-Integral-Derivative Op-amp Model\>\"",
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\), "InputVariables"]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/7b2332f7ac8ace89.png){kind=small} |
| Out[5]= |  |
The output variables:
| In[6]:= | ![ResourceData[\!\(\*
TagBox["\"\<Proportional-Integral-Derivative Op-amp Model\>\"",
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\), "OutputVariables"]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/0cd0c5332d4d971a.png){kind=small} |
| Out[6]= |  |
The complex variable:
| In[7]:= | ![ResourceData[\!\(\*
TagBox["\"\<Proportional-Integral-Derivative Op-amp Model\>\"",
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\), "ComplexVariable"]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/3e435e93ee16523a.png){kind=small} |
| Out[7]= |  |
The model parameters:
| In[8]:= | ![ResourceData[\!\(\*
TagBox["\"\<Proportional-Integral-Derivative Op-amp Model\>\"",
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\), "Parameters"]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/278e76cd510b0482.png){kind=small} |
| Out[8]= |  |
Visualizations (1)
The proportional, integral and derivative action for various input frequencies and component values:| In[9]:= | ![Manipulate[
Plot[{Sin[\[Omega] t], Evaluate@OutputResponse[ResourceData[\!\(\*
TagBox["\"\<Proportional-Integral-Derivative Op-amp Model\>\"",
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\)] /. {Subscript[\[ScriptCapitalR], 1] -> r1, Subscript[\[ScriptCapitalR], 2] -> r2, Subscript[\[ScriptCapitalR], 3] -> r3, Subscript[\[ScriptCapitalR], 4] -> r4, Subscript[\[ScriptCapitalC], 1] -> c1, 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, 330, "\!\(\*SubscriptBox[\(\[ScriptCapitalR]\), \(1\)]\)"}, {100, 330, 500, 1000}}, {{r2, 100, "\!\(\*SubscriptBox[\(\[ScriptCapitalR]\), \(2\)]\)"}, {100, 330, 500, 1000}}, {{r3, 330, "\!\(\*SubscriptBox[\(\[ScriptCapitalR]\), \(3\)]\)"}, {100, 330, 500, 1000}}, {{r4, 330, "\!\(\*SubscriptBox[\(\[ScriptCapitalR]\), \(4\)]\)"}, {100, 330, 500, 1000}}, {{c1, 0.01, "\!\(\*SubscriptBox[\(\[ScriptCapitalC]\), \(1\)]\)"}, {0.005, 0.01, 0.025, 0.1}}, {{c2, 0.01, "\!\(\*SubscriptBox[\(\[ScriptCapitalC]\), \(2\)]\)"}, {0.005, 0.01, 0.025, 0.1}}], Sequence[
ControlPlacement -> Left, SaveDefinitions -> True]]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/05b975ae8f5ec646.png) |
| Out[9]= |  |
Analysis (1)
The magnitude has a bandstop characteristic and the phase starts at -90 ° and reaches 0 °:| In[10]:= | ![Manipulate[BodePlot[ResourceData[\!\(\*
TagBox["\"\<Proportional-Integral-Derivative Op-amp Model\>\"",
#& ,
BoxID -> "ResourceTag-Proportional-Integral-Derivative Op-amp Model-Input",
AutoDelete->True]\)] /. {Subscript[\[ScriptCapitalR], 1] -> r1, Subscript[\[ScriptCapitalR], 2] -> r2, Subscript[\[ScriptCapitalR], 3] -> r3, Subscript[\[ScriptCapitalR], 4] -> r4, Subscript[\[ScriptCapitalC], 1] -> c1, Subscript[\[ScriptCapitalC], 2] -> c2}, Sequence[
ImageSize -> Small, PlotLayout -> "HorizontalGrid", PlotLabel -> {"magnitude", "phase"}]], Grid[{{
Control[{{r1, 100,
Subscript[\[ScriptCapitalR], 1]}, {100, 330, 500, 1000}}],
Control[{{r3, 330,
Subscript[\[ScriptCapitalR], 3]}, {100, 330, 500, 1000}}],
Control[{{c1, 0.01, "\!\(\*SubscriptBox[\(\[ScriptCapitalC]\), \(1\)]\)"}, {0.005, 0.01, 0.025, 0.1}}]}, {
Control[{{r2, 330,
Subscript[\[ScriptCapitalR], 2]}, {100, 330, 500, 1000}}],
Control[{{r4, 330,
Subscript[\[ScriptCapitalR], 4]}, {100, 330, 500, 1000}}],
Control[{{c2, 0.01, "\!\(\*SubscriptBox[\(\[ScriptCapitalC]\), \(2\)]\)"}, {0.005, 0.01, 0.025, 0.1}}]}}, Spacings -> 2], SaveDefinitions -> True]](https://www.wolframcloud.com/obj/resourcesystem/images/e70/e704a5a4-862e-4849-8d3f-3c9a0cf05f22/62fc9bbfbba65fec.png) |
| Out[10]= |  |
Bibliographic Citation
Suba Thomas, "Proportional-Integral-Derivative Op-amp Model" from the Wolfram Data Repository (2025)