Design a Vehicle Crash Controller for an Automated Highway System 

Design a PID controller to maintain the specified relative speed between two automobiles and guide the active vehicle as commanded.

The automobile system model.

In[1]:=

X autoSystem = TransferFunctionModel[Unevaluated[{{1./((s + 2) (8.3 + s))}}], s, SamplingPeriod ->None, SystemsModelLabels -> None];

A PID controller for the system.

In[2]:=

X pid = PIDTune[autoSystem, {"PID", "KappaTau"}, "PIDData"];

Model the prescribed constant relative speed as a step reference and simulate the response of the closed-loop system.

In[3]:=

X OutputResponse[pid["ReferenceOutput"], UnitStep[t], {t, 0, 1.5}];

In[4]:=

X OutputResponse[pid["ReferenceOutput"], UnitStep[t], {t, 0, 1.5}];; Plot[%, {t, 0, 1.5}, PlotRange -> All]

Out[4]=