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Advanced Hybrid and Differential Algebraic Equations
ProportionalDerivative Controller
Model the position of a moving body with 1 kg mass and use a sampled proportionalderivative (PD) controller to keep the position at a constant reference value.
In[1]:=
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system = {x''[t] == u[t], x'[0] == x[0] == 0, u[0] == 1}; control = WhenEvent[Mod[t, \[Tau]], u[t] > kp (xref  x[t]  td x'[t])]; params = {kp > 1, td > 1, \[Tau] > 1, xref > 1};
In[2]:=
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sol = NDSolve[{system, control} /. params, {x, u}, {t, 0, 12}, DiscreteVariables > u];
In[3]:=
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Plot[Evaluate[{xref /. params, x[t], u[t]} /. sol], {t, 0, 12}, PlotLegends > {"xref", "x(t)", "u(t)"}, ImageSize > Medium]
Out[3]=