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Design a Smith Predictor for a Tank Reactor

    
An isothermal continuous stirred-tank reactor (CSTR) can be modeled by a first-order-plus-time-delay system:
Wolfram Language code: reactor = TransferFunctionModel[Unevaluated[{{(E^-δ s/1 + s)}}], s, SamplingPeriod -> None, SystemsModelLabels -> None];
Designing a PI controller with the delay set to zero results in an unstable closed-loop system:
Wolfram Language code: pi = PIDTune[reactor /. δ -> 0, "PI"]; closedloop = SystemsModelFeedbackConnect[SystemsModelSeriesConnect[pi, reactor]]
Wolfram Language code: OutputResponse[closedloop /. δ -> 2, UnitStep[t - 1], {t, 0, 12}]; Plot[%, {t, 0, 12}, PlotRange -> All, ImageSize -> Medium]
Use SmithDelayCompensator to create a stabilizing controller for the time-delay system:
Wolfram Language code: smith = SmithDelayCompensator[reactor, pi]; closedloopSmith = SystemsModelFeedbackConnect[SystemsModelSeriesConnect[smith, reactor]]
Wolfram Language code: OutputResponse[closedloopSmith /. δ -> 2, UnitStep[t - 1], {t, 0, 12}]; Plot[%, {t, 0, 12}, PlotRange -> All, ImageSize -> Medium]