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PID Controller Architectures

    
Wolfram Language code: lsys = TransferFunctionModel[Unevaluated[{{(1/1 + 1.2s + 3s^2)}}], s, SamplingPeriod -> None, SystemsModelLabels -> None]; spResponseTFM[arch_] := PIDTune[lsys, arch, "ReferenceOutput"] spResponsePlot[arch_] := Plot[Evaluate@{OutputResponse[spResponseTFM[arch], UnitStep[t - 5], {t, 0, 50}], UnitStep[t - 5]}, {t, 0, 50}, PlotRange -> All, Exclusions -> None]
The set-point response for a system with a proportional controller:
Wolfram Language code: spResponsePlot["P"]
The response with a proportional-integral controller:
Wolfram Language code: spResponsePlot["PI"]
The response with a proportional-integral-derivative controller:
Wolfram Language code: spResponsePlot["PID"]
The response with a proportional-derivative controller:
Wolfram Language code: spResponsePlot["PD"]
The response with a proportional-filtered-derivative controller:
Wolfram Language code: spResponsePlot["PFD"]
The response with a proportional-integral-filtered-derivative controller:
Wolfram Language code: spResponsePlot["PIFD"]
Wolfram Language code: plot[ctype_, ticks_] := Show[{Plot[UnitStep[t - 5], {t, 0, 50}, Exclusions -> None, PlotStyle -> RandomChoice[ColorData[3, "ColorList"]]], Plot[Evaluate[OutputResponse[PIDTune[lsys, ctype, "ReferenceOutput"], UnitStep[t - 5], {t, 5, 50}]], {t, 0, 50}, PlotRange -> All, PlotStyle -> RandomChoice[ColorData[3, "ColorList"]]]}, PlotRange -> All, PlotLabel -> ctype, Ticks -> ticks]
Wolfram Language code: Grid[Partition[plot[#, None]& /@ {"P", "PI", "PID", "PD", "PFD", "PIFD"}, 3]]