Global Controllability and Stabilization of Bilinear SystemsWith Applications To Large Power Networks

双线性系统的全局可控性和稳定性及其在大型电力网络中的应用

• 批准号: 9530917
• 负责人: Ronald Mohler
• 金额: $ 17.15万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-15 至 1999-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9530917&HistoricalAwards=false
• 关键词: Global; Controllability; Stabilization; Bilinear; SystemsWith

9530917 Mohler The aim of this research is to develop a new global controllability and stabilization methodology for multidimensional nonhomogeneous time-invariant bilinear systems (BLS) with applications to large power transmission networks, particularly Flexible AC Transmission Systems (FACTS). A through understanding of the qualitative behavior of a dynamic system is the foundation of all the methods for controllability and stabilization studies. To this end, the basis for this proposal is formed by a new method recently introduced by the proposers to study the global qualitative behavior of BLS. Its core is a nonlinear decomposition technique converting the study into the analysis of the qualitative behavior of a finite number of the corresponding "basic" uncontrolled systems. The work assumes the unboundedness of (otherwise finite) control. One of the goals of this proposal is to refine this technique and to distinguish the conditions under which the goal controllability can be achieved (in infinite time) by bounded finite controls (which is the main practical requirement). The intent here is to focus on the 3-D case and to give its complete solution in terms of eigenvectors and eigenfunctions of the matrices involved. In turns out that the aforementioned qualitative method fits quite nicely to the analysis of some multidimensional nonlinear dynamic systems controlled via multipliers (coefficients), 9530917 including large power transmission networks. The latter systems are of great practical importance and were the subject of intensive studies for numerous researchers and practical engineers from the turn of the century. On the other hand, in relation to the topic of this proposal, mostly additive damping and local controllability were considered. The emphasis of this proposed research is given to the global aspects of reachability and controllability, and stabilization (these are closely related) via multipliers/coefficients. This type of control structure is motivated by numerous adaptive system applications such as FACTS, which play an important role in enhancing dynamic performance of modern power systems and can increase transient stability margins. To our knowledge, very little is known about the questions which this proposal addresses. The research proposed here can be split into two parts. We start, on the other hand, with the analysis making use of unbounded controls as traditionally assumed unavoidable in general global studies. On the other hand, taking into account that practical controls are normally finite and may be even of a certain sign, we also introduce these assumptions for the aforementioned unbounded controls. The idea of this approach is that if a global controllability/reachability/stabilization result holds for unbounded (but finite, say nonnegative) controls, then one can expect/show it to be true in the local aspect (not necessarily small) for the real device of restricted capability. Yet it is of particular interest, however, to distinguish, based on the proposed methodology, the cases when the global result can be achieved by bounded controls. ***

本研究的目的是为多维非齐次时不变双线性系统（BLS）开发一种新的全局可控性和稳定化方法，并将其应用于大型输电网络，特别是柔性交流输电系统（FACTS）。对动态系统定性行为的透彻理解是可控性和稳定性研究的所有方法的基础。为此，这一建议的基础是由最近提出的一种新的方法来研究劳工统计局的全局定性行为。它的核心是一种非线性分解技术，将研究转化为对有限个相应的“基本”非受控系统的定性行为的分析。工作假定控制是无界的（否则是有限的）。本提案的目标之一是改进这种技术，并区分在何种条件下，目标可控性可以通过有界有限控制（这是主要的实际要求）来实现（在无限时间内）。这里的目的是集中在三维情况下，并给出它的完全解在特征向量和特征函数的矩阵中。结果表明，上述定性方法很好地适用于一些由乘法器（系数）控制的多维非线性动态系统的分析，包括大型输电网络。后一种系统具有重要的实际意义，自世纪之交以来一直是众多研究人员和实际工程师深入研究的课题。另一方面，针对本提案的主题，主要考虑了加性阻尼和局部可控性。本研究的重点是可达性和可控性，以及通过乘数/系数的稳定性（这些是密切相关的）的全局方面。这种类型的控制结构是由许多自适应系统应用驱动的，如FACTS，它在提高现代电力系统的动态性能和增加暂态稳定裕度方面起着重要作用。据我们所知，对这项建议所涉及的问题所知甚少。这里提出的研究可以分为两个部分。另一方面，我们开始分析利用无界控制，传统上认为在一般的全球研究中是不可避免的。另一方面，考虑到实际控制通常是有限的，甚至可能具有一定的符号，我们也为上述无界控制引入了这些假设。这种方法的思想是，如果全局可控性/可达性/稳定化结果适用于无界（但有限，即非负）控制，那么人们可以期望/证明它在局部方面（不一定小）适用于有限能力的实际设备。然而，根据所提出的方法，区分可以通过有界控制实现全局结果的情况是特别有趣的。＊＊＊