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Observer design for linear switched differential-algebraic equations

线性切换微分代数方程的观测器设计

基本信息

批准号：
259698622
负责人：
Professor Dr. Stephan Trenn
金额：
--
依托单位：
Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2014
资助国家：
德国
起止时间：
2013-12-31 至 2017-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/259698622?language=en
关键词：
Observer design linear switched differential

项目摘要

A dynamical system comprises a mathematical model of an underlying physical phenomenon.It has two basic components: external signals which interconnects the system with its environment and the internal state that evolves according to the model description. The external signals can usually further be split into inputs and outputs.One of the basic problem associated with any dynamical system is that of constructing an observer which uses the available information of the external signals to estimate the internal state. The purpose of this project is to develop observers for dynamical systems modeled as switched differential-algebraic equations (DAEs). The motivation to study this particular system class is twofold: 1) In contrast to ordinary differential equations (ODEs), DAEs include differential as well as algebraic equations. Practically every system's model also contains algebraic equations in the first place so it is natural to use DAEs (instead of the simplified ODEs) as a starting point. 2) Possible structural changes (like switches in electrical circuits or component faults in general physical system) can be modeled within the framework of switched systems. As an application of the proposed project, consider for example (national) electrical grids, which are large electrical circuits modeled as DAEs. An observer would then be used to monitor the energy flows through the transmission lines and could prevent overloading. Sudden structural changes in electrical grids are common and have to be taken into account; examples are: tripping of power lines due to harsh weather conditions, or a sudden drop in the energy production by wind turbines when whole wind parks are switched off in the presence of too strong winds. Hence a possible application of the theoretical results obtained by the proposed project could be improved monitoring tools for electrical grids.

动态系统由一个基本物理现象的数学模型组成，它有两个基本组成部分：将系统与其环境联系起来的外部信号和根据模型描述演变的内部状态。外部信号通常可以进一步分解为输入和输出，任何动力系统的基本问题之一就是构造一个观测器，利用外部信号的信息来估计系统的内部状态。本计画的目的是发展切换微分代数方程式（DAE）动态系统的观测器。研究这一特殊系统类的动机是双重的：1）与常微分方程（ODE）相比，DAE包括微分方程和代数方程。实际上，每个系统的模型首先也包含代数方程，因此使用DAE（而不是简化的ODE）作为起点是很自然的。2)可能的结构变化（如电路中的开关或一般物理系统中的组件故障）可以在切换系统的框架内建模。作为建议项目的一个应用，考虑例如（国家）电网，其是建模为DAE的大型电路。然后，将使用一个观察器来监测通过输电线路的能量流动，并可以防止过载。电网结构的突然变化是常见的，必须考虑在内;例如：由于恶劣的天气条件导致的电力线跳闸，或者当风力发电场在强风中关闭时，风力涡轮机的发电量突然下降。因此，所提出的项目所获得的理论结果的可能的应用可以改进电网的监测工具。