Perturbation Methods for Nonlinear Control of Lagrangian Systems

拉格朗日系统非线性控制的摄动方法

• 批准号: 0100162
• 负责人: Francesco Bullo
• 金额: $ 16.3万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-15 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100162&HistoricalAwards=false
• 关键词: Perturbation; Methods; Nonlinear; Control; Lagrangian

The principal goal of this proposed work is to develop proper orthogonal decomposition (POD) as a viable complementary alternative to conventional experimental modal analysis for vibration systems.Proper orthogonal decomposition has been used for obtaining "energy modes," as opposed to normal modes, from sensed system outputs. Proper orthogonal decomposition can indeed yield normal modes in lightly damped systems if the mass distribution is known. This research aims to overcome the requirement of a known mass distribution, estimate modal frequencies and damping factors and associate them with the correct mode, expand the applicability to arbitrary excitations, and compare the performance of POD with classical experimental modal analysis. Auxiliary objectives are the extension from 1-D distributed-parameter systems to 2-D systems, and the application of POD to multi-modal nonlinear responses. The research approach will involve theoretical analyses, numerical simulations, and experiments. Simulations and experiments will be used to test theoretical developments on simple systems with analytical solutions, and also on systems with complicated geometries. If POD were sufficiently developed, it would significantly enhance our ability to extract vibration parameters as a complement to traditional modal analysis. Experimental vibration facilities are globally prevalent, geared for industrial problems of noise, performance, and safety. Even if POD were used in a fraction of such laboratories, the total POD activity would be quite large. It will be particularly advantageous to systems for which sensed inputs are not available. The project is geared for a doctoral student's research program. The project will also involve an undergraduate researcher for applying POD and conventional modal analysis on experimental systems

这项工作的主要目标是开发适当的正交分解（POD），作为振动系统传统实验模态分析的可行补充替代方案。适当的正交分解已用于从感测系统输出中获取“能量模式”，而不是正常模式。 如果质量分布已知，适当的正交分解确实可以在轻阻尼系统中产生正常模式。本研究旨在克服已知质量分布的要求，估计模态频率和阻尼因子并将其与正确的模态相关联，扩展对任意激励的适用性，并将 POD 的性能与经典实验模态分析进行比较。 辅助目标是从一维分布参数系统到二维系统的扩展，以及 POD 在多模态非线性响应中的应用。研究方法将涉及理论分析、数值模拟和实验。 模拟和实验将用于测试具有解析解的简单系统以及具有复杂几何形状的系统的理论发展。 如果 POD 得到充分发展，它将显着增强我们提取振动参数的能力，作为传统模态分析的补充。 实验振动设施在全球范围内普遍存在，旨在解决噪声、性能和安全等工业问题。 即使 POD 在此类实验室的一小部分中使用，总 POD 活性也将相当大。 这对于无法获得感测输入的系统尤其有利。 该项目适合博士生的研究计划。 该项目还将邀请一名本科生研究人员在实验系统上应用 POD 和传统模态分析