Non-Minimum Phase Zeros in the Dynamics of Flexure Mechanisms

弯曲机构动力学中的非最小相位零点

• 批准号: 1634824
• 负责人: Shorya Awtar
• 金额: $ 30万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1634824&HistoricalAwards=false
• 关键词: Non; Minimum; Phase; Zeros; Dynamics

Flexure mechanisms employ elastic deformation instead of rolling or sliding joints to provide guided motion along certain compliant directions. They are indispensable in several practical applications including precision motion stages and scanners because of their joint-less simple construction, lack of friction and backlash, and zero assembly and maintenance. In all these applications, there is a desire to achieve large motion range as well as high speed to improve throughput and productivity. But achieving large range and high speed, simultaneously, remains a challenge due to a lack of adequate understanding in dynamics of multi-axis flexure mechanisms. This research project will generate the scientific knowledge needed to overcome this tradeoff, leading to breakthroughs in various practical applications. In particular, this scientific knowledge will be leveraged in realizing flexure-based precision motion stages, with unprecedented performance, for the next-generation wafer inspection tools. These tools, used in the semiconductor manufacturing industry, can potentially help improve inspection process throughput by an order of magnitude. Additionally, this project will help disseminate theoretical knowledge and practical skills in dynamics, controls, and mechatronics, among university students as well as industry engineers. Furthermore, a new interactive exhibit will be created for a local science and technology museum to excite and inspire K-12 children.There are several challenges in simultaneously achieving large displacement and dynamic performance in multi-axis flexure mechanisms. Large displacements result in geometric nonlinearities that vary with the displacement. It is not clear which nonlinearities are critical and which ones may be ignored. Multi-axis flexure mechanisms also commonly employ symmetric or periodic topologies to enhance quasi-static performance, which results in multiple closely spaced modes. Furthermore, unavoidable manufacturing tolerances lead to parametric uncertainty. Together, geometric nonlinearities that vary with displacement, closely spaced modes due to topological symmetry, and parametric uncertainty due to manufacturing tolerances give rise to complex non-minimum phase zeros in the frequency response of flexure mechanisms under certain conditions. These complex non-minimum phase zeros result in severe tradeoffs between large displacement and dynamic performance. When and why do these complex non-minimum phase zeros appear? Can these zeros be analytically predicted? Do they have a physical meaning? Is there a way to suppress them or overcome their detrimental effects via physical/control system design? All these questions are currently unanswered and represent a gap in the knowledge on flexure dynamics that will be addressed via this research project.

挠性机构使用弹性变形而不是滚动或滑动关节来提供沿某些柔顺方向的引导运动。它们在包括精密运动平台和扫描仪在内的几个实际应用中是不可或缺的，因为它们的连接较少，结构简单，没有摩擦和间隙，并且零组装和维护。在所有这些应用中，都希望实现大运动范围以及高速度，以提高吞吐量和生产率。但是，由于对多轴柔性机构的动力学缺乏足够的了解，同时实现大范围和高速度仍然是一个挑战。这一研究项目将产生克服这一权衡所需的科学知识，导致在各种实际应用中取得突破。特别是，这一科学知识将被用于实现基于挠性的精密运动平台，具有前所未有的性能，用于下一代晶片检测工具。这些用于半导体制造行业的工具可能有助于将检查过程的吞吐量提高一个数量级。此外，该项目还将帮助在大学生和工业工程师中传播动力学、控制和机电一体化方面的理论知识和实践技能。此外，还将为当地一家科技馆创建一个新的互动展览，以激励和启发K-12儿童。在多轴挠性机构中同时实现大位移和动态性能存在几个挑战。较大的位移会导致几何非线性，该非线性会随位移而变化。目前还不清楚哪些非线性是关键的，哪些可以忽略。多轴柔性机构通常还采用对称或周期性的拓扑结构来提高准静态性能，从而产生多个紧密间隔的振型。此外，不可避免的制造公差会导致参数不确定性。在一定条件下，随位移变化的几何非线性、拓扑对称性引起的密集振型以及制造公差引起的参数不确定性共同导致了挠性机构频率响应中复杂的非最小相位零点。这些复杂的非最小相位零点导致了大位移和动态性能之间的严重权衡。这些复杂的非最小相位零点出现的时间和原因是什么？这些零可以通过分析来预测吗？它们有物理意义吗？有没有办法通过物理/控制系统设计来抑制它们或克服它们的有害影响？所有这些问题目前都没有得到回答，代表着关于弯曲动力学的知识空白，将通过这项研究项目加以解决。

项目成果

Experimental validation of complex non-minimum phase zeros in a flexure mechanism

弯曲机构中复杂非最小相位零点的实验验证

• DOI: 10.1016/j.precisioneng.2019.08.002
• 发表时间: 2019
• 期刊: Precision Engineering
• 作者: Cui, Leqing;Awtar, Shorya
• 通讯作者: Awtar, Shorya

On the Zeros of an Undamped Three Degrees-of-Freedom Flexible System

无阻尼三自由度柔性系统的零点研究

• DOI: 10.1115/1.4050339
• 发表时间: 2021
• 期刊: ASME Letters in Dynamic Systems and Control
• 作者: Rath, Siddharth;Cui, Leqing;Awtar, Shorya
• 通讯作者: Awtar, Shorya

On the Zeros of An Undamped Three-DoF Flexible System

无阻尼三自由度柔性系统的零点

• 发表时间: 2020
• 期刊: Proceedings of the ASME Dynamic Systems and Control Conference
• 作者: Rath, Siddharth;Cui, Leqing;Awtar, Shorya
• 通讯作者: Awtar, Shorya