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SystemsModelStateFeedbackConnect[sys,con]

连接系统模型 sys 的状态到控制器 con ，并连接 con 的输出到反馈中给 sys 的输入.

SystemsModelStateFeedbackConnect[sys,con,{s1,…},{{in1,ftype1},…}]

连接 sys 的 si 状态到 con 的第 i^(th) 个输入，并连接 con 的第 j^(th) 个输出到有 ftypej 反馈类型的 sys 的输入 inj

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SystemsModelStateFeedbackConnect

SystemsModelStateFeedbackConnect[sys,con]

连接系统模型 sys 的状态到控制器 con ，并连接 con 的输出到反馈中给 sys 的输入.

SystemsModelStateFeedbackConnect[sys,con,{s1,…},{{in1,ftype1},…}]

连接 sys 的 si 状态到 con 的第 i^(th) 个输入，并连接 con 的第 j^(th) 个输出到有 ftypej 反馈类型的 sys 的输入 inj

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范例

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基本范例  (3)

决定状态反馈系统的闭环模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{Subscript[a, 1], Subscript[a, 2]}, {Subscript[a, 3], Subscript[a, 4]}}, {{Subscript[b, 1]}, {Subscript[b, 2]}}, {{Subscript[c, 1], Subscript[c, 2]}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], {{Subscript[k, 1], Subscript[k, 2]}}]

对离散时间系统，计算反馈增益用以放置 z1 和 z2 处的极点：

Wolfram Language code: ssm = StateSpaceModel[{{{1, T}, {0, 1}}, {{T^2/2}, {T}}, {{1, 0}}, {{0}}}, SamplingPeriod -> T, SystemsModelLabels -> None]; k = StateFeedbackGains[ssm, {Subscript[z, 1], Subscript[z, 2]}]

决定闭环模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[ssm, k]

验证极点位置：

Wolfram Language code: Eigenvalues[Normal[%][[1]]]

决定具有一组最优状态反馈增益的闭环模型：

Wolfram Language code: Subscript[ssm, d] = StateSpaceModel[{{{0.4725, 0.2376, 0.0589, 0.1971}, {0.1451, 0.5669, 0.2311, 0.0439}, {0.0932, 0.119, 0.5752, 0.2319}, {0.2628, 0.0757, 0.1406, 0.4465}}, {{0.5711}, {-0.3999}, {0.6899}, {0.8156}}, {{0.11, 0, 0, 0.05}, {0, 0, 0.03, 1.1}}, {{0}, {0}}}, SamplingPeriod -> 0.01, SystemsModelLabels -> None]; q = DiagonalMatrix[{0.5, 0.8, 2, 4}];r = {{1}}; k = LQRegulatorGains[Subscript[ssm, d], {q, r}]; SystemsModelStateFeedbackConnect[Subscript[ssm, d], k]

范围  (15)

基本用途  (10)

具有状态反馈的系统的闭环模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], {{k}}]

有正状态反馈：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], {{k}}, "Positive"]

将状态反馈增益指定为传递函数模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{8, 6}, {-4, -2}}, {{-4}, {3}}, {{2, 3}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], TransferFunctionModel[{{{-95/2, -60}}, 1}, ]]

将增益指定为状态空间模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{8, 6}, {-4, -2}}, {{-4}, {3}}, {{2, 3}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{}, {}, {}, {{-95/2, -60}}}, SamplingPeriod -> None, SystemsModelLabels -> None]]

一个有在向量中指定的反馈的仿射状态空间模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[AffineStateSpaceModel[{{a[Subscript[x, 1]]}, {{b[Subscript[x, 1]]}}, {c[Subscript[x, 1]]}, {{0}}}, {Subscript[x, 1]}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], {k[Subscript[x, 1]]}]

一个有在向量中指定的反馈的非线性状态空间模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[NonlinearStateSpaceModel[{{f[x, u]}, {h[x, u]}}, {x}, {u}, {Automatic}, Automatic, SamplingPeriod -> None], {k[x, u]}]

正状态反馈增益：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{27.5, 24.6}, {-30, -26.5}}, {{-1}, {1}}, {{-5, -4}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], {{4.59, -6.42}}, "Positive"]

只反馈第一个输入：

Wolfram Language code: ssm = StateSpaceModel[{{{0, -1, -2}, {-2, -1, 0}, {2, 2, 3}}, {{0, -2}, {0, 1}, {1, 1}}, {{1, 2, 1}}, {{0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None];
Wolfram Language code: SystemsModelStateFeedbackConnect[ssm, (⁠-(67/2) (127/4) 18⁠), {1, 2, 3}, {1}]

只反馈第二个输入：

Wolfram Language code: ssm = StateSpaceModel[{{{0, -1, -2}, {-2, -1, 0}, {2, 2, 3}}, {{0, -2}, {0, 1}, {1, 1}}, {{1, 2, 1}}, {{0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None];
Wolfram Language code: SystemsModelStateFeedbackConnect[ssm, (⁠364 (467/2) (1025/2)⁠), {1, 2, 3}, {2}]

通过反馈系统，将第二个状态域第一个输入相连：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{Subscript[a, 11], Subscript[a, 12]}, {Subscript[a, 21], Subscript[a, 22]}}, {{Subscript[b, 11], Subscript[b, 12]}, {Subscript[b, 21], Subscript[b, 22]}}, {{Subscript[c, 11], Subscript[c, 12]}, {Subscript[c, 21], Subscript[c, 22]}}, {{0, 0}, {0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{Subscript[α, 11], Subscript[α, 12]}, {Subscript[α, 21], Subscript[α, 22]}}, {{Subscript[β, 11], Subscript[β, 12]}, {Subscript[β, 21], Subscript[β, 22]}}, {{Subscript[γ, 11], Subscript[γ, 12]}}, {{0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None], {2}, {1}]

多输入系统的闭环模型：

Wolfram Language code: ssm = StateSpaceModel[{{{0, -1, -2}, {-2, -1, 0}, {2, 2, 3}}, {{0, -2}, {0, 1}, {1, 1}}, {{1, 2, 1}}, {{0, 0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]; k = StateFeedbackGains[ssm, {-4. + 2 I, -4. - 2 I, -8.}]
Wolfram Language code: SystemsModelStateFeedbackConnect[ssm, k]

系统类型  (5)

连接两个 StateSpaceModel 系统：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{α}}, {{β}}, {{γ}}, {{ρ}}}, SamplingPeriod -> None, SystemsModelLabels -> None]]

具有延迟：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{a + SystemsModelDelay[Subscript[τ, 1]]}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{α + SystemsModelDelay[Subscript[τ, 2]]}}, {{β}}, {{γ}}, {{ρ}}}, SamplingPeriod -> None, SystemsModelLabels -> None]]

使用描述器状态空间模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}, {{e}}}, SamplingPeriod -> None, SystemsModelLabels -> None], StateSpaceModel[{{{α}}, {{β}}, {{γ}}, {{ρ}}, {{η}}}, SamplingPeriod -> None, SystemsModelLabels -> None]]

输入线性 AffineStateSpaceModel 系统：

Wolfram Language code: SystemsModelStateFeedbackConnect[AffineStateSpaceModel[{{a[Subscript[x, 1]]}, {{b[Subscript[x, 1]]}}, {c[Subscript[x, 1]]}, {{0}}}, {Subscript[x, 1]}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], AffineStateSpaceModel[{{α[Subscript[x, 2]]}, {{β[Subscript[x, 2]]}}, {γ[Subscript[x, 2]]}, {{0}}}, {Subscript[x, 2]}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None]]

一般非线性 NonlinearStateSpaceModel 系统：

Wolfram Language code: SystemsModelStateFeedbackConnect[NonlinearStateSpaceModel[{{Subscript[f, 1][Subscript[x, 1], Subscript[u, 1]]}, {Subscript[h, 1][Subscript[x, 1], Subscript[u, 1]]}}, {Subscript[x, 1]}, {Subscript[u, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], NonlinearStateSpaceModel[{{Subscript[f, 2][Subscript[x, 2], Subscript[u, 2]]}, {Subscript[x, 2]}}, {Subscript[x, 2]}, {Subscript[u, 2]}, {Automatic}, Automatic, SamplingPeriod -> None]]

连接标准线性系统和输入线性系统将给出一个仿射模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], AffineStateSpaceModel[{{α[x]}, {{β[x]}}, {γ[x]}, {{0}}}, {x}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None]]

连接非线性系统和标准线性或仿射系统将给出一个非线性模型：

Wolfram Language code: SystemsModelStateFeedbackConnect[StateSpaceModel[{{{a}}, {{b}}, {{c}}, {{d}}}, SamplingPeriod -> None, SystemsModelLabels -> None], NonlinearStateSpaceModel[{{f[x, u]}, {h[x, u]}}, {x}, {u}, {Automatic}, Automatic, SamplingPeriod -> None]]
Wolfram Language code: SystemsModelStateFeedbackConnect[AffineStateSpaceModel[{{a[x]}, {{b[x]}}, {c[x]}, {{d[x]}}}, {x}, {Subscript[, 1]}, {Automatic}, Automatic, SamplingPeriod -> None], NonlinearStateSpaceModel[{{f[x, u]}, {h[x, u]}}, {x}, {u}, {Automatic}, Automatic, SamplingPeriod -> None]]

应用  (3)

线性可逆钟摆模型是不稳定：

Wolfram Language code: pendulum = StateSpaceModel[{{{0, 1, 0, 0}, {(g*(m + M))/ (l*M), 0, 0, 0}, {0, 0, 0, 1}, {(-g)*(m/M), 0, 0, 0}}, {{0}, {-l^(-1)/M}, {0}, {M^(-1)}}, {{1, 0, 0, 0}, {0, 0, 1, 0}}, {{0}, {0}}}, SamplingPeriod -> None, SystemsModelLabels -> None] /. {g -> 9.8, m -> 1, M -> 10, l -> 5};

A plot of its unstable response:

Wolfram Language code: StateResponse[{pendulum, {.01, 0, 0, 0}}, 0, {t, 0, 5}]; Plot[%, {t, 0, 5}]

计算增益矩阵以把闭环极点放在左半平面中：

Wolfram Language code: k = StateFeedbackGains[pendulum, {-0.2, -0.5, -5, -8.67}]

求闭环系统：

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

闭环响应是稳定的：

Wolfram Language code: StateResponse[{csys, {.01, 0, 0, 0}}, 0, {t, 0, 15}]; Plot[%, {t, 0, 15}, PlotLayout -> "Column", PlotRange -> All]

计算增益矩阵来最优化输入和状态的二次代价函数：

Wolfram Language code: ssm = StateSpaceModel[{{{0, 1, 0}, {0, 0, 1}, {0, -2, -3}}, {{0}, {0}, {1}}, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0}, {0}, {0}}}, SamplingPeriod -> None, SystemsModelLabels -> None]; k = LQRegulatorGains[ssm, {(⁠| | | | | --- | - | - | | 100 | 0 | 0 | | 0 | 1 | 0 | | 0 | 0 | 1 |⁠), (⁠0.01⁠)}]

求闭环系统：

Wolfram Language code: SystemsModelStateFeedbackConnect[ssm, k]

计算增益系统来最优化输入和输出的二次代价函数：

Wolfram Language code: ssm = StateSpaceModel[{{{0, 0, 1, 0}, {0, 0, 0, 1}, {-0.12, 0, -0.8, 0}, {0, -0.12, 0, -0.8}}, {{0, 0}, {0, 0}, {1, 0}, {0, 1}}, {{-0.54, 0.6, -2.7, 1}}, {{3, 0}}}, SamplingPeriod -> 0.5, SystemsModelLabels -> None]; k = LQOutputRegulatorGains[ssm, {{{0.05}}, DiagonalMatrix[{2, 2}]}];

求闭环系统：

Wolfram Language code: SystemsModelStateFeedbackConnect[ssm, k]

属性和关系  (1)

模型中的输出矩阵是恒等的，并且直接传递矩阵是零：

Wolfram Language code: ssm = StateSpaceModel[{RandomReal[5, {2, 2}], RandomReal[5, {2, 1}], IdentityMatrix[2]}]

SystemsModelStateFeedbackConnect 和 SystemsModelFeedbackConnect 是等价的：

Wolfram Language code: {SystemsModelStateFeedbackConnect[ssm, {{Subscript[k, 1], Subscript[k, 2]}}], SystemsModelFeedbackConnect[ssm, TransferFunctionModel[{{Subscript[k, 1], Subscript[k, 2]}}]]}
Wolfram Language code: Subtract@@(Normal /@ %)
Wolfram Research (2010)，SystemsModelStateFeedbackConnect，Wolfram 语言函数，https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html （更新于 2014 年）.

文本

Wolfram Research (2010)，SystemsModelStateFeedbackConnect，Wolfram 语言函数，https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html （更新于 2014 年）.

CMS

Wolfram 语言. 2010. "SystemsModelStateFeedbackConnect." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2014. https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html.

APA

Wolfram 语言. (2010). SystemsModelStateFeedbackConnect. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html 年

BibTeX

@misc{reference.wolfram_2026_systemsmodelstatefeedbackconnect, author="Wolfram Research", title="{SystemsModelStateFeedbackConnect}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html}", note=[Accessed: 12-July-2026]}

BibLaTeX

@online{reference.wolfram_2026_systemsmodelstatefeedbackconnect, organization={Wolfram Research}, title={SystemsModelStateFeedbackConnect}, year={2014}, url={https://reference.wolfram.com/language/ref/SystemsModelStateFeedbackConnect.html}, note=[Accessed: 12-July-2026]}