| 引用本文: | 夏天威,孙凯.关于非线性动态系统状态变量的参与因子的唯一性[J].控制理论与应用,2025,42(11):2147~2155.[点击复制] |
| XIA Tian-wei,SUN Kai.On the uniqueness of participation factors in nonlinear dynamical systems[J].Control Theory & Applications,2025,42(11):2147~2155.[点击复制] |
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| 关于非线性动态系统状态变量的参与因子的唯一性 |
| On the uniqueness of participation factors in nonlinear dynamical systems |
| 摘要点击 1815 全文点击 141 投稿时间：2024-12-10 修订日期：2025-05-01 |
| 查看全文 查看/发表评论 下载PDF阅读器 HTML |
| DOI编号 10.7641/CTA.2025.40618 |
| 2025,42(11):2147-2155 |
| 中文关键词 参与因子 模态形状 模态组成 非线性系统 振荡 |
| 英文关键词 participation factor mode shape mode composition nonlinear system oscillations |
| 基金项目 |
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| 中文摘要 |
| 在非线性动态系统的模态分析与控制中,状态变量在某个关键或选定模态中的参与因子是简化稳定性研究的
重要工具,它使得研究能集中于参与度高的少数状态变量.对于一个线性系统,其状态变量在某一模态的线性参与因子
由左、右特征向量分别定义的模态组成和模态形状共同唯一确定.然而,其他类型参与因子的唯一性需要更为深入的研
究. 针对非线性参与因子及其他5种参与因子的变体,本文证明了其唯一性的充分条件.该条件考虑了模态组成和模态
形状中不确定缩放因子的影响.这些缩放因子源于在分析和控制实际动态系统时选择状态变量的物理单位或数值范围
的变化.因此,获得和理解参与因子唯一性的充分条件对于在实际场景中正确地将参与因子的概念用于稳定性分析和控
制至关重要.此外,本文还探讨了状态变量扰动幅度与合理选择缩放因子之间的关系. |
| 英文摘要 |
| In the modal analysis and control of nonlinear dynamical systems, participation factors (PFs) of state variables
with respect to a critical or selected mode serve as a pivotal tool for simplifying stability studies by focusing on a subset of
highly influential state variables. For linear systems, PFs are uniquely determined by the mode’s composition and shape,
which are defined by the system’s left and right eigenvectors, respectively. However, the uniqueness of other types of
PFs has not been thoroughly addressed in literatures. This paper establishes sufficient conditions for the uniqueness of
nonlinear PFs and five other PF variants, taking into account uncertain scaling factors in a mode’s shape and composition.
These scaling factors arise from variations in the choice of physical units, which depend on the value ranges of real-world
state variables. Understanding these sufficient conditions is essential for the correct application of PFs in practical stability
analysis and control design. |