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PID Tuning Rules

    
Wolfram Language code: lsys = TransferFunctionModel[Unevaluated[{{(1.0/(s + 1)^3)}}], s, SamplingPeriod -> None, SystemsModelLabels -> None]; dResponseTFM[trule_] := PIDTune[lsys, {Automatic, trule}, "DisturbanceOutput"] dResponsePlot[trule_] := Plot[Evaluate@{OutputResponse[dResponseTFM[trule], UnitStep[t - 5], {t, 0, 50}], UnitStep[t - 5]}, {t, 0, 50}, PlotRange -> All, Exclusions -> None]
The process disturbance response using the Ziegler–Nichols tuning rule:
Wolfram Language code: dResponsePlot["ZieglerNichols"]
Use the KappaTau rule:
Wolfram Language code: dResponsePlot["KappaTau"]
Use the AMIGO rule:
Wolfram Language code: dResponsePlot["AMIGO"]
Use the Chien–Hrones–Reswick rule:
Wolfram Language code: dResponsePlot["ChienHronesReswick"]
Use the Cohen–Coon rule:
Wolfram Language code: dResponsePlot["CohenCoon"]
Use the LambdaTuning rule:
Wolfram Language code: dResponsePlot["LambdaTuning"]
Use the SkogestadIMC rule:
Wolfram Language code: dResponsePlot["SkogestadIMC"]
Use the Tyreus–Luyben rule:
Wolfram Language code: dResponsePlot["TyreusLuyben"]
Wolfram Language code: plot[trule_, ticks_] := Show[{Plot[UnitStep[t - 5], {t, 0, 50}, Exclusions -> None, PlotStyle -> RandomChoice[ColorData[3, "ColorList"]]], Plot[Evaluate[OutputResponse[PIDTune[lsys, {Automatic, trule}, "DisturbanceOutput"], UnitStep[t - 5], {t, 5, 50}]], {t, 0, 50}, PlotRange -> All, PlotStyle -> RandomChoice[ColorData[3, "ColorList"]]]}, PlotRange -> All, PlotLabel -> trule, Ticks -> ticks]
Wolfram Language code: plots = plot[#, True]& /@ {"AMIGO", "ChienHronesReswick", "CohenCoon", "LambdaTuning", "SkogestadIMC", "TyreusLuyben"};
Wolfram Language code: Grid[Partition[plot[#, None]& /@ {"ZieglerNichols", "ChienHronesReswick", "CohenCoon", "LambdaTuning", "SkogestadIMC", "TyreusLuyben"}, 3]]