WOLFRAM

Wolfram Language & System Documentation Center

Closed-Loop Responses with a PID Controller

Plot the output and control responses for different exogenous inputs:
Wolfram Language code: pid = PIDTune[TransferFunctionModel[Unevaluated[{{(1/(0.4s + 1)(0.5s + 1)^2)}}], s, SamplingPeriod -> None, SystemsModelLabels -> None], "PID", "PIDData"];
The output and and control responses for a SquareWave process disturbance:
Wolfram Language code: d = SquareWave[t]; yres1 = OutputResponse[pid["DisturbanceOutput"], d, {t, 0, 5}]; ures1 = OutputResponse[pid["DisturbanceControl"], d, {t, 0, 5}];
Wolfram Language code: {Plot[yres1, {t, 0, 5}, PlotRange -> All], Plot[ures1, {t, 0, 5}, PlotRange -> All]}
The output and control responses for a UnitBox reference:
Wolfram Language code: r = UnitBox[t]; yres2 = OutputResponse[pid["ReferenceOutput"], r, {t, 0, 5}]; ures2 = OutputResponse[pid["ReferenceControl"], r, {t, 0, 5}];
Wolfram Language code: {Plot[yres2, {t, 0, 5}, PlotRange -> All], Plot[ures2, {t, 0, 5}, PlotRange -> All]}
The output and control responses for a ramp sensor noise:
Wolfram Language code: m = 0.2t; yres3 = OutputResponse[pid["SensorOutput"], m, {t, 0, 5}]; ures3 = OutputResponse[pid["SensorControl"], m, {t, 0, 5}];
Wolfram Language code: {Plot[yres3, {t, 0, 5}, PlotRange -> All], Plot[ures3, {t, 0, 5}, PlotRange -> All]}