EAGER: Revisiting Vibrational Control Theory

EAGER：重新审视振动控制理论

基本信息

批准号：
1709746
负责人：
Haithem Taha
金额：
$ 20万
依托单位：
University of California-Irvine
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-01-01 至 2019-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1709746&HistoricalAwards=false
关键词：
EAGER Revisiting Vibrational Control Theory

项目摘要

This EArly-concept Grant for Exploratory Research (EAGER) project seeks to deepen and extend the analytical tools available for vibrational control. Vibrational control offers unique capabilities for controlling unstable systems without the need for feedback. Consider an upside-down pendulum with a movable base. By measuring the pendulum position, a control system can command side-to-side movement of the base in order to keep it upright. But if position measurements are not available, the pendulum will topple over. Similarly, a person may balance a broomstick on their hand by watching it move. However, if that person were made to wear a blindfold and thick gloves, the task would be impossible. Using vibrational control allows the upside-down pendulum to be kept balanced with no feedback, by moving the base up and down at the right frequency and amplitude. There are no other known methods to accomplish this. Many important applications could benefit from a systematic application of vibrational control, including chemical reactions, material processing, and flexible structures. However the only currently developed tool for vibrational control -- a mathematical technique called first-order averaging -- is very poorly suited to engineering design. Therefore this project will explore three promising alternatives.The research objective of this project is to explore and resolve competing approaches to the analysis and design of vibrational control systems. Vibrational control has the potential to fundamentally transform control applications characterized by underlying instability, limited processing speed, high degrees of freedom, limited actuation, and little or no sensing. First-order averaging is the mathematical technique currently used almost exclusively to analyze and design vibrational controllers. This project considers three promising alternatives to first-order averaging, namely higher-order averaging using power series, higher-order averaging using Volterra series (the "chronological calculus"), and stability maps based on Floquet theory. This project will resolve discrepancies between these approaches, and derive the fundamental benefits and drawbacks of each. The results of this project will change vibrational control from a mathematical curiosity to a powerful and practical engineering tool. The project includes validation on models of flapping-wing micro air vehicles, and ion confinement and filtering.

这个早期概念探索性研究资助 (EAGER) 项目旨在深化和扩展可用于振动控制的分析工具。振动控制提供了无需反馈即可控制不稳定系统的独特功能。考虑一个带有可移动底座的倒置钟摆。通过测量摆锤位置，控制系统可以命令底座从一侧到另一侧移动，以保持其直立。但如果无法进行位置测量，钟摆就会翻倒。类似地，一个人可以通过观察扫帚的移动来平衡其手上的扫帚。但如果让那个人蒙住眼睛，戴上厚厚的手套，那就不可能完成任务了。使用振动控制，通过以正确的频率和幅度上下移动底座，可以使倒置的摆保持平衡，无需反馈。没有其他已知的方法可以实现这一点。许多重要的应用可以受益于振动控制的系统应用，包括化学反应、材料加工和柔性结构。然而，目前开发的唯一振动控制工具——一种称为一阶平均的数学技术——非常不适合工程设计。因此，该项目将探索三种有前途的替代方案。该项目的研究目标是探索和解决振动控制系统分析和设计的竞争方法。振动控制有可能从根本上改变控制应用，这些应用的特点是潜在的不稳定性、有限的处理速度、高自由度、有限的驱动以及很少或没有传感。一阶平均是目前几乎专门用于分析和设计振动控制器的数学技术。该项目考虑了一阶平均的三种有前途的替代方案，即使用幂级数的高阶平均、使用 Volterra 级数（“时间微积分”）的高阶平均以及基于 Floquet 理论的稳定性图。该项目将解决这些方法之间的差异，并得出每种方法的基本优点和缺点。该项目的结果将使振动控制从一种数学好奇心转变为一种强大而实用的工程工具。该项目包括扑翼微型飞行器模型的验证以及离子限制和过滤。