WOLFRAM

Wolfram 语言与系统参考资料中心

使用延迟反馈减少振荡

时间延迟可以有意加入控制器以改善系统性能. 下面的主动减振器可用延迟状态反馈控制.

Wolfram Language code: {eq1, eq2} = {u[t] + (Subscript[k, 1] + Subscript[k, 2]) Subscript[x, 1][t] - Subscript[k, 2] Subscript[x, 2][t] + (Subscript[b, 1] + Subscript[b, 2]) Derivative[1][Subscript[x, 1]][t] - Subscript[b, 2] Derivative[1][Subscript[x, 2]][t] + Subscript[m, 1]Derivative[2][Subscript[x, 1]][t] == 0, -u[t] + Subscript[k, 2] (-Subscript[x, 1][t] + Subscript[x, 2][t]) + Subscript[b, 2] (-Derivative[1][Subscript[x, 1]][t] + Derivative[1][Subscript[x, 2]][t]) + Subscript[m, 2] Derivative[2][Subscript[x, 2]][t] == 0};
Wolfram Language code: absorber = StateSpaceModel[{eq1, eq2}, {Subscript[x, 1][t], Subscript[x, 1]'[t], Subscript[x, 2][t], Subscript[x, 2]'[t]}, {u[t]}, {Subscript[x, 1][t]}, t];
Wolfram Language code: csys = SystemsModelStateFeedbackConnect[absorber, {{g SystemsModelDelay[τ]}}, {1}, {1}]
带有延迟控制器的比无延迟控制器的闭环减振器在谐振频率处具有更小的振荡：
Wolfram Language code: values = {Subscript[k, 2] -> .1, Subscript[b, 2] -> .02, Subscript[m, 2] -> .1, Subscript[m, 1] -> 1, Subscript[b, 1] -> .05, Subscript[k, 1] -> 1, g -> 0.043};
Wolfram Language code: ynodelay = OutputResponse[csys /. values /. τ -> 0, Sin[ 1.1 t], {t, 0, 80}]; ydelay = OutputResponse[csys /. values /. τ -> 1.82, Sin[1.1t], {t, 0, 80}];
Wolfram Language code: Plot[{ynodelay, ydelay}, {t, 0, 80}, PlotRange -> All, PlotStyle -> {Purple, Thick}, PlotLegends -> {"Delay–Free", "Delayed"}, ImageSize -> Medium]