Design a PID Liquid Level Controller for a Boiler 

Compute a two-degree-of-freedom PID controller that can maintain a desired liquid level for a drum boiler.

Enter the models.

In[1]:=

X {valve, boiler} = {TransferFunctionModel[ Unevaluated[{{1.2/(0.8 s + 1)}}], s, SamplingPeriod ->None, SystemsModelLabels -> {{None}, {None}}], TransferFunctionModel[ Unevaluated[{{(0.1 (1 - 2 s))/(s (5 s + 1))}}], s, SamplingPeriod ->None, SystemsModelLabels -> {{None}, {None}}]};

Obtain the two-degree-of-freedom controller.

In[2]:=

X pid2dof = PIDTune[SystemsModelSeriesConnect[valve, boiler], "PID", "PIDData", PIDFeedforward -> 0.5];

The response of the closed-loop system to a set point change of 5.

In[3]:=

X level = OutputResponse[pid2dof["ReferenceOutput"], 5 UnitStep[t], {t, 0, 65}];

In[4]:=

X Plot[{level, 5 UnitStep[t]}, {t, 0, 65}, PlotRange -> All]

Out[4]=