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On the Existence of Lagrangians for Clarke and Park Transformed Switched-Mode Electrical Networks ?

机译：关于Clarke和Park转换开关模式电网的拉格朗日式的存在 ？

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摘要

It is well-known that the classical passivity-based control (PBC) design is founded on the existence of the Euler-Lagrange (EL) equations. For a large class of systems, including mechanical, electrical, and electro-mechanical systems, its application is usually rather straightforward and requires a standard Lagrangian formulation. For three-phase electrical networks, with or without switches, it is often desirable to reformulate the resulting equations of motion into an orthogonal reference frame using the Clarke or Park transformation, or a combination of both. However, such transformations are always performed after the EL equations have been set up and a formal procedure to obtain the transformed equations directly from a Lagrangian thus far lacks in the literature. The contribution of this paper is to show that, by invoking the Helmholtz conditions and the concept of the traditor, such Lagrangians do exist, but require the inclusion of certain non-energetic cross terms.
机译：众所周知，经典的基于无源性的控制（PBC）设计基于Euler-Lagrange（EL）方程的存在。对于包括机械，电气和机电系统在内的大量系统，其应用通常非常简单，并且需要标准的拉格朗日公式。对于带有或不带有开关的三相电网，通常希望使用Clarke或Park变换或两者的组合将所得的运动方程式重新形成为正交参考系。然而，这样的变换总是在已经建立了EL方程并且在形式上是直接从拉格朗日方程直接获得变换方程的正式程序之后进行的，这在文献中是缺乏的。本文的贡献在于表明，通过调用亥姆霍兹条件和传统器的概念，确实存在这样的拉格朗日算子，但需要包括某些非能量交叉项。

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