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状态空间模型

LTI 模型的状态空间表示

状态空间中模型的表示不是唯一的。坐标变换会生成包含的矩阵不同但动态特性相同的状态空间模型。要获得状态空间模型的最小实现,或转换分析和控制设计的标准形式,可以使用状态坐标变换。

坐标变换对于缩放病态模型也很有用。状态空间模型的正确缩放对于精确计算至关重要。例如,如果一个动态系统的状态向量中有两个状态,其单位分别为光年和毫米,则模型的缩放效果就会很差。这种相差极大的单位可能会将非常大和非常小的条目引入 A 矩阵中。在计算过程中,矩阵中大小条目混合使用可能会破坏模型的重要特性,并导致不正确的结果。

函数

balrealBalanced state-space realization
prescaleOptimal scaling of state-space models
modalrealCompute modal state-space realization (自 R2023b 起)
comprealCompute companion state-space realization (自 R2023b 起)
ss2ssState coordinate transformation for state-space model
ssequivEquivalence transformation for state-space models (自 R2023b 起)
xperm Reorder states in state-space models
xsortSort states based on state partition (自 R2020b 起)
xelimEliminate states from state-space models (自 R2023b 起)
augstateAppend state vector to output vector
ctrbControllability of state-space model
obsvObservability of state-space model
gramControllability and observability Gramians

主题

  • State-Space Realizations

    A state-space model can be expressed in an infinite number of realizations. Common forms, sometimes called canonical forms, include modal, companion, observable, and controllable forms.

  • Scaling State-Space Models

    When working with state-space models, proper scaling is important for accurate computations.

  • Scaling State-Space Models to Maximize Accuracy

    This example shows that proper scaling of state-space models can be critical for accuracy and provides an overview of automatic and manual rescaling tools.