Study of Observability of Nonlinear Distributed Parameter Systems with Applications to Aeroengines and Chemical Reactions

非线性分布参数系统可观性研究及其在航空发动机和化学反应中的应用

• 批准号: 0605181
• 负责人: MingQing Xiao
• 金额: $ 9.1万
• 依托单位: Southern Illinois University at Carbondale
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-15 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0605181&HistoricalAwards=false
• 关键词: Study; Observability; Nonlinear; Distributed; Parameter

This project focuses on the study of observability of nonlinear distributed parameter systems. It consists of three main parts. The first part studies how to translate the observability of infinite-dimensional systems into the finite-dimensional framework from where observer construction is facilitated via topological equivalence approach. The goal is to characterize the asymptotic behaviors of nonlinear distributed parameter systems that have finite-dimensional attractors by a system of ordinary differential equations. The second part pays particular attention to the observer design for aeroengines and chemical reactions, whose systems are governed by nonlinear partial differential equations. The goal is to provide technical methods for the estimation of disturbed flows in aeroengines as well as the estimation of the states of chemical reactions. The last part is devoted to enhancement of the multidisciplinary program at PI's institute.Technical limitations and/or prohibitively high costs associated with current sensor technology create a situation where all process state variables for direct on-line measurements are not able to be measured. Examples include the monitoring of chemical processes and the estimation of disturbed flows in aeroengines, systems which can mathematically be described by nonlinear evolution equations. Existing theories must be developed and expended to meet these challenges. This project focuses on the development of a mathematical methodology that will be adequate for the analytical and computational needs of state estimations. The research outcome of this project will contribute to the improvement of the safety and efficiency of aeroengine operations and the advancement of the control of various chemical reactions.

本课题致力于研究非线性分布参数系统的能观性。它由三个主要部分组成。第一部分研究如何将无穷维系统的能观性转化为有限维框架，在有限维框架下利用拓扑等价方法构造观测器。目标是用常微分方程组刻画具有有限维吸引子的非线性分布参数系统的渐近行为。第二部分重点研究了航空发动机和化学反应的观测器设计，它们的系统由非线性偏微分方程组控制。其目的是为估计航空发动机中的扰动流动以及估计化学反应状态提供技术方法。最后一部分致力于加强PI研究所的多学科计划。与当前传感器技术相关的技术限制和/或令人望而却步的高成本造成无法测量直接在线测量的所有过程状态变量的情况。例如，监测化学过程和估计航空发动机中的扰动流动，这些系统可以用非线性发展方程来数学描述。现有的理论必须得到发展和扩展，以迎接这些挑战。该项目的重点是开发一种足以满足状态估计的分析和计算需要的数学方法。该项目的研究成果将有助于提高航空发动机运行的安全性和效率，推进各种化学反应的控制。