Mathematical Sciences: Minimal Order Dynamic Pole Assignment Problems

数学科学：最小阶动态极点分配问题

• 批准号: 9224541
• 负责人: Xiaochang Wang
• 金额: $ 3.19万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9224541&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Minimal; Order; Dynamic

9224541 Wang This project addresses the problem of pole assignment by output feedback with dynamic compensation. Its goals are to find the minimal order among real dynamic compensators needed for arbitrary pole assignability and to derive a formula for the degree of the Rosenthal compactification of dynamic compensator space. Techniques involving the Schubert calculus developed by the principal investigator in solving the static output feedback pole assignment problem are expected to be important in the study of the minimal order dynamic compensator problem. The poles of a linear system determine its frequencies and amplitudes of vibration, and their locations determine whether or not the system is stable. Therefore, in control design for a physical system such as an airplane or robot arm, a major objective is to move the poles of the plant into its stability region, i.e., a region where the principle modes of vibration die out at a prescribed rate, using output feedback. Output feedback usually involves a dynamic compensator and the higher the order of that compensator, the more complicated the controller needed to shift the poles becomes.Therefore, it is important to be able to design minimal order dynamic compensators. This project will brings the method of algebraic geometry to bear on this problem. ***

小行星9224541 本计画系针对输出回授动态补偿之极点配置问题。其目标是找到任意极点可配置所需的真实的动态补偿器之间的最小阶数，并推导出动态补偿器空间的Rosenthal紧化度公式。技术涉及舒伯特演算开发的主要研究者在解决静态输出反馈极点配置问题预计将是重要的最小阶动态补偿器问题的研究。 线性系统的极点决定了它的频率和振幅，而极点的位置决定了系统是否稳定。因此，在物理系统（如飞机或机器人手臂）的控制设计中，主要目标是将对象的极点移动到其稳定区域，即，利用输出反馈，主振动模式以规定的速率消失的区域。输出反馈通常包含一个动态补偿器，补偿器的阶数越高，需要移动极点的控制器就越复杂，因此，能够设计最小阶动态补偿器是很重要的。这个项目将使代数几何的方法来解决这个问题。 ***