Closed-Loop Responses with a PID Controller 

Plot the output and control responses for different exogenous inputs.

In[1]:=

X pid = PIDTune[ TransferFunctionModel[ Unevaluated[{{1/((0.4 s + 1) (0.5 s + 1)^2)}}], s, SamplingPeriod ->None, SystemsModelLabels -> None], "PID", "PIDData"];

The output and and control responses for a SquareWave process disturbance.

In[2]:=

X d = SquareWave[t]; yres1 = OutputResponse[pid["DisturbanceOutput"], d, {t, 0, 5}]; ures1 = OutputResponse[pid["DisturbanceControl"], d, {t, 0, 5}];

In[3]:=

X {Plot[yres1, {t, 0, 5}, PlotRange -> All], Plot[ures1, {t, 0, 5}, PlotRange -> All]}

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The output and control responses for a UnitBox reference.

In[4]:=

X r = UnitBox[t]; yres2 = OutputResponse[pid["ReferenceOutput"], r, {t, 0, 5}]; ures2 = OutputResponse[pid["ReferenceControl"], r, {t, 0, 5}];

In[5]:=

X {Plot[yres2, {t, 0, 5}, PlotRange -> All], Plot[ures2, {t, 0, 5}, PlotRange -> All]}

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The output and control responses for a ramp sensor noise.

In[6]:=

X m = 0.2 t; yres3 = OutputResponse[pid["SensorOutput"], m, {t, 0, 5}]; ures3 = OutputResponse[pid["SensorControl"], m, {t, 0, 5}];

In[7]:=

X {Plot[yres3, {t, 0, 5}, PlotRange -> All], Plot[ures3, {t, 0, 5}, PlotRange -> All]}

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