PID Controller Architectures 

The reference response of a system with the proportional (P) controller.

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "P", "ReferenceOutput"]

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "P", "ReferenceOutput"]; Plot[Evaluate@{OutputResponse[%, UnitStep[t - 5], {t, 0, 50}], UnitStep[t - 5]}, {t, 0, 50}, PlotRange -> All, Exclusions -> None]

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The response with the proportional-integral (PI) controller.

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PI", "ReferenceOutput"]

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PI", "ReferenceOutput"]; Plot[Evaluate@{OutputResponse[%, UnitStep[t - 5], {t, 0, 50}], UnitStep[t - 5]}, {t, 0, 50}, PlotRange -> All, Exclusions -> None]

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The response with the proportional-integral-derivative (PID) controller.

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PID", "ReferenceOutput"]

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PID", "ReferenceOutput"]; Plot[Evaluate@{OutputResponse[%, UnitStep[t - 5], {t, 0, 50}], UnitStep[t - 5]}, {t, 0, 50}, PlotRange -> All, Exclusions -> None]

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The response with the proportional-derivative (PD) controller.

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PD", "ReferenceOutput"]

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PD", "ReferenceOutput"]; Plot[Evaluate@{OutputResponse[%, UnitStep[t - 5], {t, 0, 50}], UnitStep[t - 5]}, {t, 0, 50}, PlotRange -> All, Exclusions -> None]

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The response with the proportional-filtered-derivative (PFD) controller.

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PFD", "ReferenceOutput"]

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PFD", "ReferenceOutput"]; Plot[Evaluate@{OutputResponse[%, UnitStep[t - 5], {t, 0, 50}], UnitStep[t - 5]}, {t, 0, 50}, PlotRange -> All, Exclusions -> None]

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The response with the proportional-integral-filtered-derivative (PIFD) controller.

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PIFD", "ReferenceOutput"]

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X PIDTune[TransferFunctionModel[Unevaluated[{{1/(1 + 1.2 s + 3 s^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PIFD", "ReferenceOutput"]; Plot[Evaluate@{OutputResponse[%, UnitStep[t - 5], {t, 0, 50}], UnitStep[t - 5]}, {t, 0, 50}, PlotRange -> All, Exclusions -> None]

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