Analysis of Nonlinear Oscillations via Lyapunov Approach
通过李亚普诺夫方法分析非线性振荡
基本信息
- 批准号:0925269
- 负责人:
- 金额:$ 28.68万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2009
- 资助国家:美国
- 起止时间:2009-09-01 至 2013-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Objective The objective of this program is to develop a systematic and numerically tractable Lyapunov approach for evaluation of the magnitude of nonlinear oscillations.Intellectual merit The intellectual merit is that the Lyapunov approach provides a quantitative and reliable characterization of the magnitude of nonlinear oscillation. Although nonlinear oscillations have been extensively studied, most efforts were devoted to qualitative description of the complex behavior. There also exist some approximate, but not reliable, methods, such as the describing function method, to estimate the magnitude of oscillations. The main tools of the Lyapunov approach include the description of a piecewise linear element with saturation functions and a compatible piecewise quadratic function. These tools convert the analysis problem into numerically tractable linear-matrix-inequality based optimization problem. The methods can be adapted for designing parameters for minimization of unwanted oscillations. The methods will be applied to optimal design of some power electronic systems for suppression of unwanted oscillations.Broader impacts This program will have significant impact on many branches of science and engineering since nonlinear oscillations exist in systems of various types. The research results will be submitted to interdisciplinary journals and conferences for publication, so as to promote the application of Lyapunov theory, and other methods for control systems. Appropriate research results will be incorporated into the graduate course ``Nonlinear Systems," which the PI has been teaching and renovating. The proposed work will seek broad participation from graduate and undergraduate students. In particular, female and minority students will be encouraged to participate in the program.In this program, a fundamental tool in control systems, the Lyapunov function, will be extended to address a highly interdisciplinary subject - nonlinear oscillation - which is studied in almost all branches of science and engineering. It is expected that this program will promote cross fertilization between control theory and other research fields, and yield revolutionary discovery in nonlinear dynamics.
该奖项根据 2009 年美国复苏和再投资法案(公法 111-5)提供资金。 目标 该计划的目标是开发一种系统的、数值上可处理的李雅普诺夫方法,用于评估非线性振荡的幅度。 智力优点 智力优点是,李雅普诺夫方法提供了非线性振荡幅度的定量和可靠的表征。尽管非线性振荡已被广泛研究,但大多数努力都致力于复杂行为的定性描述。还存在一些近似但不可靠的方法来估计振荡的幅度,例如描述函数方法。李亚普诺夫方法的主要工具包括具有饱和函数的分段线性元和兼容的分段二次函数的描述。 这些工具将分析问题转换为基于数值可处理的线性矩阵不等式的优化问题。该方法可适用于设计参数以最小化不需要的振荡。这些方法将应用于一些电力电子系统的优化设计,以抑制不需要的振荡。更广泛的影响 由于非线性振荡存在于各种类型的系统中,因此该程序将对科学和工程的许多分支产生重大影响。研究成果将提交给跨学科期刊和会议发表,以促进Lyapunov理论以及其他控制系统方法的应用。适当的研究成果将被纳入 PI 一直在教授和更新的研究生课程“非线性系统”中。拟议的工作将寻求研究生和本科生的广泛参与。特别是,将鼓励女性和少数族裔学生参与该项目。在该项目中,控制系统的基本工具李亚普诺夫函数将扩展到解决高度跨学科的主题 - 非线性振荡 - 这是 研究过几乎所有科学和工程领域。预计该项目将促进控制理论与其他研究领域的交叉融合,并在非线性动力学领域产生革命性的发现。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
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Tingshu Hu其他文献
Algebraic method for parameter identification of circuit models for batteries under non-zero initial condition
- DOI:
10.1016/j.jpowsour.2014.06.069 - 发表时间:
2014-12-05 - 期刊:
- 影响因子:
- 作者:
Lalitha Devarakonda;Tingshu Hu - 通讯作者:
Tingshu Hu
Tingshu Hu的其他文献
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{{ truncateString('Tingshu Hu', 18)}}的其他基金
Control design of power electronic interfaces for optimal performance of renewable energy systems
电力电子接口的控制设计可实现可再生能源系统的最佳性能
- 批准号:
1200152 - 财政年份:2012
- 资助金额:
$ 28.68万 - 项目类别:
Continuing Grant
Nonlinear/Switching Control Design for Constrained Control Systems with Application to Magnetic Suspension
约束控制系统的非线性/开关控制设计及其在磁悬浮中的应用
- 批准号:
0621651 - 财政年份:2006
- 资助金额:
$ 28.68万 - 项目类别:
Standard Grant
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