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FullInformationOutputRegulator[sys,rspec]

使用指定 rspec 给出 sys 的完整状态信息输出调节器.

FullInformationOutputRegulator[{sys,{out1,…},{in1,…}},…]

指定调节输出 outi 和控制输入 inj.

更多信息和选项
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范例  
基本范例  
范围  
应用  
属性和关系  
参见
相关指南
历史
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FullInformationOutputRegulator

FullInformationOutputRegulator[sys,rspec]

使用指定 rspec 给出 sys 的完整状态信息输出调节器.

FullInformationOutputRegulator[{sys,{out1,…},{in1,…}},…]

指定调节输出 outi 和控制输入 inj.

更多信息和选项

  • FullInformationOutputRegulator 返回一个调节器，驱动 sys 输出为零，并且通常用来抑制或跟踪系统的已知输入.
  • 系统 sys 被视为拥有状态方程 和 及输出 ，其中 是可控输入. 状态 不受输入 的影响，用于模拟抑制或跟踪的信号，如输出函数 所示.
  • 典型的输出函数 ，调节器将驱动至零：
  • 在状态 上抑制 的影响
    导致 跟踪
  • 系统 sys 可以是 StateSpaceModel、AffineStateSpaceModel 或 NonlinearStateSpaceModel.
  • 计算的状态反馈 使用 调节 sys 大约一个工作点.
  • 状态反馈 的形式为 ，其中 ，，且 的计算在 rspec 之后.
  • 可能的调节器指定 rspec：
  • {"Poles",{p1,…}}利用 StateFeedbackGains 计算
    {"Weights",{p,…}}利用 LQRegulatorGains 计算
    {"Gains",κ}显示给定增益
  • 在指定为 {"method",pars,opts} 时，选项 opts 被传递给增益计算函数.
  • 输出 {out1,…} 和输入 {in1,…} 为部分指定，并在默认情况下取 All.

范例

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基本范例  (1)

计算系统的调节反馈，其中恒定干扰为 0.5：

Wolfram Language code: sys = AffineStateSpaceModel[{{w + 2*Subscript[x, 1] + Subscript[x, 2], Subscript[x, 1] - 2*Subscript[x, 2], 0}, {{1}, {0}, {0}}, {Subscript[x, 1] + Subscript[x, 2]}, {{0}}}, {{Subscript[x, 1], 0}, {Subscript[x, 2], 0}, {w, 0.5}}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None];

调节器是状态 和干扰状态 的函数：

Wolfram Language code: k = FullInformationOutputRegulator[sys, {"Poles", {-1, -2}}]

闭环系统：

Wolfram Language code: csys = SystemsModelStateFeedbackConnect[sys, k]

输出被调节至零：

Wolfram Language code: res1 = OutputResponse[{sys, {1, 1, 0.5}}, 0, {t, 0, 5}]; res2 = OutputResponse[{csys, {1, 1, 0.5}}, 0, {t, 0, 5}];
Wolfram Language code: Plot[{res1, res2}, {t, 0, 5}, PlotRange -> {0, 5}, PlotLegends -> {"unregulated", "regulated"}]

范围  (8)

原点处的具有外系统极点的线性系统的调节器：

Wolfram Language code: FullInformationOutputRegulator[ssm = StateSpaceModel[{{{p, r}, {0, 0}}, {{b}, {0}}, {{c, 0}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], {"Poles", {Subscript[p, f]}}]

闭环系统：

Wolfram Language code: SystemsModelStateFeedbackConnect[ssm, %]//Simplify

外系统（exosystem）具有一对复数极点：

Wolfram Language code: ssm = StateSpaceModel[{{{p, Subscript[r, 1], Subscript[r, 2]}, {0, 0, ω}, {0, -ω, 0}}, {{b}, {0}, {0}}, {{c, 0, 0}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None];
Wolfram Language code: Assuming[ω ∈ Reals, FullInformationOutputRegulator[ssm, {"Poles", {Subscript[p, f]}}]]

闭环系统：

Wolfram Language code: SystemsModelStateFeedbackConnect[ssm, %]//Simplify

外系统状态是调节器的一部分：

Wolfram Language code: ssm = StateSpaceModel[{{{p, Subscript[r, 1], Subscript[r, 2]}, {0, 0, ω}, {0, -ω, 0}}, {{b}, {0}, {0}}, {{c, Subscript[c, 1], Subscript[c, 2]}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None];
Wolfram Language code: Assuming[ω ∈ Reals, FullInformationOutputRegulator[ssm, {"Poles", {Subscript[p, f]}}]]

闭环系统：

Wolfram Language code: SystemsModelStateFeedbackConnect[ssm, %]

响应：

Wolfram Language code: OutputResponse[{%, {Subscript[x, 10], Subscript[w, 10], Subscript[w, 20]}}, 0, t]//FullSimplify

如果 pf 是负的，系统是调节好的：

Wolfram Language code: % /. Subscript[p, f] -> -5 /. Thread[{c, Subscript[c, 1], Subscript[c, 2], Subscript[x, 10], Subscript[w, 10], Subscript[w, 20]} -> RandomReal[1, 6]]

调节一个 AffineStateSpaceModel：

Wolfram Language code: Assuming[ω∈Reals, FullInformationOutputRegulator[AffineStateSpaceModel[{{p*x + x^2 + Subscript[c, 1]*Subscript[w, 1] + Subscript[c, 2]* Subscript[w, 2], ω*Subscript[w, 2], (-ω)*Subscript[w, 1]}, {{b}, {0}, {0}}, {x}, {{0}}}, {x, Subscript[w, 1], Subscript[w, 2]}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], {"Poles", {Subscript[p, f]}}]]

调节一个 NonlinearStateSpaceModel:

Wolfram Language code: FullInformationOutputRegulator[NonlinearStateSpaceModel[ {{p*x + w*Subscript[c, 1] + u*Subscript[c, 2] + u*w*x* Subscript[c, 3], 0}, {x}}, {x, w}, {u}, {Automatic}, Automatic, SamplingPeriod -> None], {"Poles", {Subscript[p, f]}}]

指定调节输出和反馈输入：

Wolfram Language code: FullInformationOutputRegulator[{StateSpaceModel[{{{0, 0}, {r, p}}, {{0, Subscript[b, 1]}, {Subscript[b, 2], 0}}, {{1, 0}, {0, 1}}, {{0, 0}, {0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], {2}, {1}}, {"Poles", {Subscript[p, f]}}]

通过指定权值，使用 LQRegulatorGains 计算稳定增益：

Wolfram Language code: FullInformationOutputRegulator[AffineStateSpaceModel[{{w + x, 0}, {{1}, {0}}, {x}, {{0}}}, {x, w}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], {"Weights", {{{1}}, {{1}}}}]

指定使用的增益：

Wolfram Language code: FullInformationOutputRegulator[AffineStateSpaceModel[{{w + x, 0}, {{1}, {0}}, {x}, {{0}}}, {x, w}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], {"Gains", {{k}}}]

应用  (6)

拒绝以 建模的扰动：

Wolfram Language code: dModel = NonlinearStateSpaceModel[w''[t] + w[t] == 0, {{w[t], 0}, {w'[t], 1}}, {}, {}, t];

具有扰动的系统的完整模型：

Wolfram Language code: nsys = NonlinearStateSpaceModel[{{x[t] + Subscript[, 1][t] + v[t]}, {x[t]}}, {{x[t], 0}}, {v[t]}, Automatic, t];
Wolfram Language code: sys = SystemsModelMerge[{dModel, nsys}]

调节器：

Wolfram Language code: k = FullInformationOutputRegulator[sys, {"Poles", {-2}}]

闭环系统：

Wolfram Language code: csys = SystemsModelStateFeedbackConnect[sys, k]

在出现干扰时，调节输出：

Wolfram Language code: OutputResponse[{csys, {0, 1, 1}}, 0, {t, 0, 3}];
Wolfram Language code: Plot[%, {t, 0, 3}, PlotRange -> All]

跟踪以 建模的输入：

Wolfram Language code: iModel = NonlinearStateSpaceModel[w''[t] + w[t] == 0, {{w[t], 0}, {w'[t], 1}}, {}, {}, t];

系统的完整模型和输入模型：

Wolfram Language code: nsys = NonlinearStateSpaceModel[{{x[t] + Subscript[, 1][t] + v[t]}, {x[t], x[t] - Subscript[, 1][t]}}, {{x[t], 0}}, {Subscript[, 1][t], v[t]}, Automatic, t];
Wolfram Language code: sys = SystemsModelMerge[{iModel, nsys}]

调节器：

Wolfram Language code: k = FullInformationOutputRegulator[{sys, 2}, {"Poles", {-2}}]

闭环系统：

Wolfram Language code: csys = SystemsModelExtract[SystemsModelStateFeedbackConnect[sys, k], All, 1]

输出跟踪输入：

Wolfram Language code: or = OutputResponse[{csys, {0, 1, 0.5}}, 0, {t, 0, 10}]; Plot[or, {t, 0, 10}, PlotRange -> All]

同时跟踪一个步阶输入，并且拒绝正弦扰动：

Wolfram Language code: iModel = NonlinearStateSpaceModel[{{0}, {x - r}}, {{r, 1}}, {}]
Wolfram Language code: dModel = NonlinearStateSpaceModel[{{Subscript[w, 2], -Subscript[w, 1]}, {}}, {{Subscript[w, 1], 0}, {Subscript[w, 2], 1}}, {}]

完整系统：

Wolfram Language code: nsys = NonlinearStateSpaceModel[{{x + r + Subscript[w, 1] + v}, {x}}, {{x, 0}}, {r, Subscript[w, 1], v}]
Wolfram Language code: sys = SystemsModelMerge[{nsys, iModel, dModel}]

获取调节器：

Wolfram Language code: k = FullInformationOutputRegulator[{sys, 2}, {"Poles", {-8}}]

闭环系统：

Wolfram Language code: csys = SystemsModelExtract[SystemsModelStateFeedbackConnect[sys, k], All, 1]

仿真显示跟踪步阶信号的输出：

Wolfram Language code: OutputResponse[NonlinearStateSpaceModel[csys, {x -> -1, r -> 1, Subscript[w, 1] -> 0, Subscript[w, 2] -> 1}], 0, {t, 0, 5}]; Plot[%, {t, 0, 5}, PlotRange -> All]

在出现扰动时，调节飞机的纵向动力：»

Wolfram Language code: aircraft = StateSpaceModel[{{{0, 14.3877, 0, -31.5311}, {-0.0012, -0.4217, 1, -0.0284}, {0.0002, -0.3816, -0.4658, 0}, {0, 0, 1, 0}}, {{0.7898, -0.6526, -0.335, 0.4637, 0.9185}, {-0.00588, 0.0049, 0.0025, -0.0035, -0.0068}, {-0.2541, 0.21, 0.1078, -0.1492, -0.2959}, {0, 0, 0, 0, 0}}, {{1, 0, 0, 0}}, {{0, 0, 0, 0, 0}}}, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3], Subscript[x, 4]}, {u, Subscript[w, 1], Subscript[w, 2], Subscript[w, 3], Subscript[w, 4]}, SamplingPeriod -> None, SystemsModelLabels -> None];

扰动包括两个频率分量：

Wolfram Language code: dist = StateSpaceModel[{{{0, -0.1, 0, 0}, {0.1, 0, 0, 0}, {0, 0, 0, -0.2}, {0, 0, 0.2, 0}}, {{}, {}, {}, {}}, {}}, {Subscript[w, 1], Subscript[w, 2], Subscript[w, 3], Subscript[w, 4]}, SamplingPeriod -> None, SystemsModelLabels -> None];

完整系统：

Wolfram Language code: sys = SystemsModelMerge[{aircraft, dist}]

在出现扰动时，调节输出（速度）的控制定律：

Wolfram Language code: fb = FullInformationOutputRegulator[sys, {"Poles", {-1, -2, -2.5 + I, -2.5 - I}}]

闭环系统：

Wolfram Language code: csys = SystemsModelStateFeedbackConnect[sys, fb]

仿真显示获得的调节：

Wolfram Language code: OutputResponse[{csys, {0.1, 0.001, 0, 0, 1, 0, 1, 0}}, 0, {t, 0, 8}]; Plot[%, {t, 0, 8}, PlotRange -> All]

控制工作：

Wolfram Language code: fb.StateResponse[{csys, {0.1, 0.001, 0, 0, 1, 0, 1, 0}}, 0, {t, 0, 150}]; Plot[%, {t, 0, 150}, PlotRange -> All]

调节一个 Rössler 原型 4 系统：»

Wolfram Language code: asys = AffineStateSpaceModel[{{-Subscript[x, 2] - Subscript[x, 3], Subscript[x, 1], 0.5*(Subscript[x, 2] - Subscript[x, 2]^2) - 0.5*Subscript[x, 3]}, {{0}, {0}, {1}}, {-w + Subscript[x, 2]}, {{0}}}, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3]}, Automatic, {Automatic}, Automatic, SamplingPeriod -> None];

混沌行为：

Wolfram Language code: StateResponse[{asys /. w -> 0, RandomReal[{-1, 1}, 3]}, 0, {t, 0, 300}]; ParametricPlot3D[%, {t, 0, 300}]

完整系统，以使得调节状态 ，并且保持常量：

Wolfram Language code: tmodel = NonlinearStateSpaceModel[{{0}, {}}, w, {}]; sys = SystemsModelMerge[{asys, tmodel}]

反馈定律：

Wolfram Language code: fb = FullInformationOutputRegulator[sys, {"Poles", {-1, -1.5 + I, -1.5 - I}}]

闭环系统：

Wolfram Language code: csys = SystemsModelStateFeedbackConnect[sys, fb]

模拟显示调节 ，并且系统没有反馈下的混沌行为：

Wolfram Language code: StateResponse[{csys, Join[RandomReal[{-1, 1}, 3], {1}]}, 0, {t, 0, 8}]; Plot[Evaluate[Most[%]], {t, 0, 8}, PlotLegends -> {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3]}]

调节 Chua 电路中的电压 ，以使其遵循正弦波，而拒绝另一个 Chua 电路的输出的扰动 ：»

Chua 电路的仿射模型，其中非线性是立方多项式：

Wolfram Language code: pars = {Subscript[𝒞, 1] -> 1, Subscript[𝒞, 2] -> 1, ℒ -> 1, ℛ -> 1};
Wolfram Language code: asys = AffineStateSpaceModel[{{(-2*Subscript[𝒱, 1] - Subscript[𝒱, 1]^3 + (-Subscript[𝒱, 1] + Subscript[𝒱, 2])/ℛ)/ Subscript[𝒞, 1], (-𝒾 + (Subscript[𝒱, 1] - Subscript[𝒱, 2])/ ℛ)/Subscript[𝒞, 2], (-Subscript[ℰ, 2] + Subscript[𝒱, 2])/ℒ}, {{-Subscript[𝒞, 1]^(-1)}, {0}, {0}}, {-Subscript[ℰ, 4] + Subscript[𝒱, 2]}, {{0}}}, {Subscript[𝒱, 1], Subscript[𝒱, 2], 𝒾}, Automatic, {Automatic}, Automatic, SamplingPeriod -> None] /. pars;

外系统，其中 ω 是需要跟踪的正弦波的频率：

Wolfram Language code: pars1 = {Subscript[𝒞, 1] -> 1, Subscript[𝒞, 2] -> 1, ℒ -> 1, ℛ -> 1, ω -> 10};
Wolfram Language code: nsys = NonlinearStateSpaceModel[ {{(-Subscript[ℰ, 1] - 2*Subscript[ℰ, 1]^3 + (-Subscript[ℰ, 1] + Subscript[ℰ, 2])/ℛ)/ Subscript[𝒞, 1], ((Subscript[ℰ, 1] - Subscript[ℰ, 2])/ℛ - Subscript[ℰ, 3])/Subscript[𝒞, 2], Subscript[ℰ, 2]/ℒ, ω*Subscript[ℰ, 5], (-ω)*Subscript[ℰ, 4]}, {}}, {Subscript[ℰ, 1], Subscript[ℰ, 2], Subscript[ℰ, 3], Subscript[ℰ, 4], Subscript[ℰ, 5]}, {}, Automatic, Automatic, SamplingPeriod -> None, SystemsModelLabels -> {{}, None}] /.  pars1;

完整系统：

Wolfram Language code: sys = SystemsModelMerge[{asys, nsys}]

干扰模型的极点：

Wolfram Language code: Subscript[poles, d] = Eigenvalues@First@Normal@StateSpaceModel[nsys]//N

系统极点包括三个新极点和可稳定极点：

Wolfram Language code: decays = Join[{-1, -2, -3}, DeleteCases[%, Complex[_ ? PossibleZeroQ, _]]]

调节器：

Wolfram Language code: k = FullInformationOutputRegulator[{sys, All, All, {7, 8}}, {"Poles", decays}]

闭环系统：

Wolfram Language code: csys = SystemsModelStateFeedbackConnect[sys, k]//Simplify

模拟显示已经获得了调节：

Wolfram Language code: OutputResponse[{csys, {10, 0, 0.1, 0, 0, 0, 0, -1}}, 0, {t, 0, 10}]; Plot[%, {t, 0, 10}, PlotRange -> All]

属性和关系  (4)

StateFeedbackGains 是一个特例：

Wolfram Language code: ssm = StateSpaceModel[{{{2, 0, -1}, {0, -2, 1}, {1, -1, 1}}, {{1, 1}, {0, 1}, {1, -1}}, {{1, -1, 0}, {0, 1, -1}}, {{0, 0}, {0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]; poles = {-1, -2, -3};
Wolfram Language code: FullInformationOutputRegulator[ssm, {"Poles", poles}]
Wolfram Language code: StateFeedbackGains[ssm, poles]

LQRegulatorGains 是一个特例：

Wolfram Language code: ssm = StateSpaceModel[{{{2, 0, -1}, {0, -2, 1}, {1, -1, 1}}, {{1, 1}, {0, 1}, {1, -1}}, {{1, -1, 0}, {0, 1, -1}}, {{0, 0}, {0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]; weights = {IdentityMatrix[3], IdentityMatrix[2]};
Wolfram Language code: FullInformationOutputRegulator[N@ssm, {"Weights", weights}]
Wolfram Language code: LQRegulatorGains[N@ssm, weights]

使用 SystemsModelStateFeedbackConnect 获得闭环系统：

Wolfram Language code: sys = NonlinearStateSpaceModel[{{u + w + p*x, 0}, {x}}, {x, w}, {u}, {Automatic}, Automatic, SamplingPeriod -> None];
Wolfram Language code: SystemsModelStateFeedbackConnect[sys, FullInformationOutputRegulator[sys, {"Poles", {Subscript[p, f]}}]]

获得输出调节：

Wolfram Language code: sys = StateSpaceModel[{{{2, 0, -1, 1}, {0, -2, 1, 0}, {1, -1, 1, 0}, {0, 0, 0, 0}}, {{1, 1}, {0, 1}, {1, -1}, {0, 0}}, {{1, -1, 0, 0}, {0, 1, -1, 0}}, {{0, 0}, {0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None];
Wolfram Language code: k = FullInformationOutputRegulator[sys, {"Poles", N@{-1, -2, -3}}]
Wolfram Language code: csys = SystemsModelStateFeedbackConnect[sys, k]
Wolfram Language code: OutputResponse[{csys, RandomReal[2, 4]}, 0, {t, 0, 5}]; Plot[Evaluate[%], {t, 0, 5}, PlotRange -> All]
Wolfram Research (2014)，FullInformationOutputRegulator，Wolfram 语言函数，https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html.

文本

Wolfram Research (2014)，FullInformationOutputRegulator，Wolfram 语言函数，https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html.

CMS

Wolfram 语言. 2014. "FullInformationOutputRegulator." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html.

APA

Wolfram 语言. (2014). FullInformationOutputRegulator. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html 年

BibTeX

@misc{reference.wolfram_2026_fullinformationoutputregulator, author="Wolfram Research", title="{FullInformationOutputRegulator}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html}", note=[Accessed: 03-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_fullinformationoutputregulator, organization={Wolfram Research}, title={FullInformationOutputRegulator}, year={2014}, url={https://reference.wolfram.com/language/ref/FullInformationOutputRegulator.html}, note=[Accessed: 03-November-2026]}