Dirac Structures and Implicit Lagrangian Systems in Electric Networks
Dirac Structures and Implicit Lagrangian Systems in Electric Networks
复制标题
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Hiroaki Yoshimura;J. Marsden
中科院分区：
文献类型：
--
作者：
Hiroaki Yoshimura;J. Marsden
本文将狄拉克结构和隐式拉格朗日系统的相关理论应用于电网络。我们展示了如何从组态电荷空间上的KCL（基尔霍夫电流定律）约束分布中类比力学推导出磁链相上的狄拉克结构。在此背景下，提出了隐式端口控制拉格朗日系统的概念。作为一个具体的示例，证明了一维L-C传输线可以在隐式端口控制的拉格朗日系统中表述，其中传输线可以看作是由一系列组成原语模块组成的互连系统，每个原语模块由具有外部端口的L-C电路给出。
In this paper, we apply Dirac structures and the associated theory of implicit Lagrangian systems to electric networks. We show how a Dirac structure on the flux linkage phase can be induced from a KCL (Kirchhoff Current Law) constraint distribution on a configuration charge space in analogy with mechanics. In this context, a notion of implicit port-controlled Lagrangian systems is developed. As a specific illustrative example, it is demonstrated that a one-dimensional L-C transmission line can be formulated in the context of implicit port-controlled Lagrangian systems, where the transmission line may be regarded as an interconnected system of a chain of constituent primitive modules, each of which is given by an L-C circuit with external ports.