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HolderModel[]

表示零阶保持器的单入单出模型.

HolderModel[specs]

表示规范为 specs 的保持器.

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HolderModel

HolderModel[]

表示零阶保持器的单入单出模型.

HolderModel[specs]

表示规范为 specs 的保持器.

更多信息

  • HolderModel 亦称为零阶保持 (ZOH)，一阶保持 (FOH) 和逆采样.
  • HolderModel 通常用于将来自数字微控制器或数字信号处理器的离散时间信号转换为在物理世界或物理世界模型中驱动时使用的连续时间信号.
  • 保持器是一种运算模型，它接受整数定义的离散时间信号 ，生成连续时间信号 f(t)=g(TemplateBox[{{t, /, T}}, Floor])，其中 是采样周期. 使采样点之间的值保持恒定.
  • 规范 spec 是一个关联，可以有以下键：
  • "InputVariables"{u[t]}输入变量
    "Order"0保持器的阶数，为非负整数
    "OutputVariables"{y[t]}输出变量
    "SamplingPeriod"1采样周期
    "SignalCount"1输入和输出的数量
    "TemporalVariable"t时间变量
  • "Order" 属性指定使用的外推的阶数. 阶外推器使用前面 个点来导出 次插值多项式. 然后使用该多项式推断下一个采样周期的值.
  • HolderModel[…]["prop"] 可用于获取模型的各种属性.
  • "prop" 的值可以是 spec 中的任意键及以下内容：
  • "Properties"属性名称列表
    "PropertyAssociation"以关联给出的属性名称和值
    "PropertyDataset"以数据集给出的属性名称和值
    {p1,p2,…}
  • 属性 pi
    • 的值

范例

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基本范例  (2)

零阶保持 (ZOH) 模型：

Wolfram Language code: HolderModel[]

属性：

Wolfram Language code: %["PropertyDataset"]

对 ZOH 对正弦输入的响应进行仿真：

Wolfram Language code: r = InputOutputResponse[HolderModel[], Table[Sin[t], {t, 0, 3π}]]

绘制响应和输入序列：

Wolfram Language code: Show[Plot[r, {, 0, 3π}], ListPlot[Table[{t, Sin[t]}, {t, 0, 3π}], IconizedObject[«opts»]]]

范围  (9)

零阶保持模型：

Wolfram Language code: HolderModel[]

一阶保持：

Wolfram Language code: HolderModel[<|"Order" -> 1|>]

自定义属性的保持器：

Wolfram Language code: HolderModel[<|"InputVariables" -> u[t], "OutputVariables" -> y[t], "TemporalVariable" -> t|>]
Wolfram Language code: %["Dataset"]

列出所有可用属性：

Wolfram Language code: HolderModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript[ ... tion", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "Order", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "Order", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]["Properties"]

获取特定属性：

Wolfram Language code: HolderModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript[ ... tion", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "Order", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "Order", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]["SamplingPeriod"]

获取几个属性：

Wolfram Language code: HolderModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript[ ... tion", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "Order", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "Order", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}][{"Order", "SignalCount"}]

获取关联形式的属性：

Wolfram Language code: HolderModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript[ ... tion", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "Order", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "Order", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]["PropertyAssociation"]

数据集形式的属性：

Wolfram Language code: HolderModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript[ ... tion", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "Order", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "Order", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]["PropertyDataset"]

对一阶保持器对正弦序列的响应进行仿真：

Wolfram Language code: Short[r1 = InputOutputResponse[HolderModel[<|"Order" -> 1|>], Table[Sin[t], {t, 0, 2.5π}]]]

绘制响应和序列：

Wolfram Language code: Show[Plot[r1, {, 0, 2.5π}, PlotRange -> All], ListPlot[Table[{t, Sin[t]}, {t, 0, 2.5π}], IconizedObject[«opts»]]]

缩小采样周期以便更好地近似正弦曲线：

Wolfram Language code: Short[r2 = InputOutputResponse[HolderModel[<|"Order" -> 1, "SamplingPeriod" -> 0.5|>], Table[Sin[t], {t, 0, 2.5π, 0.5}]]]

绘制更好近似情况下的响应和输入序列：

Wolfram Language code: Show[Plot[r2, {, 0, 2.5π}, PlotRange -> All], ListPlot[Table[{t, Sin[t]}, {t, 0, 2.5π, 0.5}], IconizedObject[«opts»]]]

较低的采样周期会产生更好的近似值：

Wolfram Language code: NIntegrate[Abs /@ {Sin[] - r1[[1]], Sin[] - r2[[1]]}, {, 0, 2.5π}]

应用  (1)

保持器模型是采样数据系统的子系统：

Wolfram Language code: csys = SystemsConnectionsModel[{TransferFunctionModel[{{{1.}}, (1 + s)^3}, s], TransferFunctionModel[{{{4.539074548064891 - 9.145098981931369* + 4.606282997931085*^2}}, {{0.23358983848622455 - 0.5071796769724491* + 0.2735898384862246*^2}}}, , ... ummaryItems"}], {"InputVariables", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]}, {{4, 1} -> {3, 1}, {3, 1} -> {2, 1}, {2, 1} -> {5, 1}, {5, 1} -> {1, 1}, {1, 1} -> {6, 1}, {6, 1} -> {3, 2}}, {{4, 1}}, {{1, 1}}];

对系统进行仿真：

Wolfram Language code: r = InputOutputResponse[csys, 1, {t, 0, 10}]

绘制响应：

Wolfram Language code: Plot[r, {t, 0, 10}]

属性和关系  (3)

采样器模型本质上是一个基于时间的动作：

Wolfram Language code: u = Tanh[t]; sp = 0.5;

基于 WhenEvent 的响应：

Wolfram Language code: r1 = NDSolveValue[{WhenEvent@@{Mod[t, sp] == 0, y[t] -> u}, y[0] == 0, Derivative[1][$][t] == 0, $[0] == 0}, y[t], {t, 0, 5}, DiscreteVariables -> {y[t]}]

采样器模型的响应：

Wolfram Language code: r2 = InputOutputResponse[SamplerModel[<|"SamplingPeriod" -> sp|>], u, {t, 0, 5}]

它们是一样的：

Wolfram Language code: Plot[{r1, r2}, {t, 0, 5}, PlotRange -> All]

一阶保持基于当前和之前输入值的线性插值：

Wolfram Language code: u = Tanh[t]; sp = 0.5;

变量 是当前输入的值， 之前输入的值， 是总时长：

Wolfram Language code: action = {Subscript[x, 1][t], Subscript[x, 2][t], 𝒯[t]} -> {u, Subscript[x, 1][t], 𝒯[t] + sp};

离散变量 、 和 在每个采样时刻被更新：

Wolfram Language code: we = WhenEvent@@{Mod[t, sp] == 0, action}

求线性插值的斜率 和截距 ：

Wolfram Language code: sol = Solve[{Subscript[x, 1][t] == m 𝒯[t] + c, Subscript[x, 2][t] == m(𝒯[t] - sp) + c}, {m, c}]

输出表达式：

Wolfram Language code: out = m t + c /. sol//Simplify

求输出信号：

Wolfram Language code: r1 = NDSolveValue[{we, Derivative[1][$][t] == 0, $[0] == 0, Subscript[x, 1][0] == 0, Subscript[x, 2][0] == 0, 𝒯[0] == 0}, out, {t, 0, 5}, DiscreteVariables -> {Subscript[x, 1][t], Subscript[x, 2][t], 𝒯[t]}]

用保持器模型获得的解：

Wolfram Language code: r2 = InputOutputResponse[HolderModel[<|"SamplingPeriod" -> sp, "Order" -> 1|>], u, {t, 0, 5}]

它们是一样的：

Wolfram Language code: Plot[{r1, r2}, {t, 0, 5}, PlotRange -> All]

保持器模型逆转了采样器模型的操作：

Wolfram Language code: f = 3; u = Sech[f t]; sp = 1 / ( 50f);

将采样器模型与保持器模型串联在一起：

Wolfram Language code: sys = SystemsConnectionsModel[{SamplerModel[<|"SamplingPeriod" -> sp|>], HolderModel[<|"SamplingPeriod" -> sp|>]}, {{1, 1} -> {2, 1}}, {{1, 1}}, {{2, 1}}]

输出信号与输入信号相同：

Wolfram Language code: InputOutputResponse[sys, u, {t, 0, π}]; Plot[{u, %[[1]]}, {t, 0, π}, PlotRange -> All]
Wolfram Research (2024)，HolderModel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/HolderModel.html.

文本

Wolfram Research (2024)，HolderModel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/HolderModel.html.

CMS

Wolfram 语言. 2024. "HolderModel." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/HolderModel.html.

APA

Wolfram 语言. (2024). HolderModel. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/HolderModel.html 年

BibTeX

@misc{reference.wolfram_2026_holdermodel, author="Wolfram Research", title="{HolderModel}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/HolderModel.html}", note=[Accessed: 15-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_holdermodel, organization={Wolfram Research}, title={HolderModel}, year={2024}, url={https://reference.wolfram.com/language/ref/HolderModel.html}, note=[Accessed: 15-November-2026]}