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比例微分控制器

    
模拟质量为1公斤移动物体的位置，并使用采样比例微分（PD） 控制器保持位置在恒定的基准值上：
Wolfram Language code: system = {x''[t] == u[t], x'[0] == x[0] == 0, u[0] == 1}; control = WhenEvent[Mod[t, τ], u[t] -> kp(xref - x[t] - td x'[t])]; params = {kp -> 1, td -> 1, τ -> 1, xref -> 1};
Wolfram Language code: sol = NDSolve[{system, control} /. params, {x, u}, {t, 0, 12}, DiscreteVariables -> u];
Wolfram Language code: Plot[Evaluate[{xref /. params, x[t], u[t]} /. sol], {t, 0, 12}, PlotLegends -> {"xref", "x(t)", "u(t)"}]