Non-Minimum Phase Zeros in the Dynamics of Flexure Mechanisms

柔性机构采用弹性变形而不是滚动或滑动接头来提供沿沿着某些顺应方向的引导运动。它们在包括精密运动平台和扫描仪在内的一些实际应用中是不可或缺的，因为它们的结构简单，无摩擦和间隙，零装配和零维护。在所有这些应用中，期望实现大的运动范围以及高速度以提高产量和生产率。但是，实现大范围和高速度，同时，仍然是一个挑战，由于缺乏足够的理解，在多轴柔性机构的动力学。该研究项目将产生克服这种权衡所需的科学知识，从而在各种实际应用中取得突破。特别是，这些科学知识将被用于实现基于柔性的精密运动平台，具有前所未有的性能，用于下一代晶圆检测工具。这些用于半导体制造业的工具可能有助于提高检测过程的吞吐量。此外，该项目将有助于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，还将为当地科技博物馆创建一个新的互动展览，以激发和激励K-12儿童。在多轴弯曲机构中同时实现大位移和动态性能存在多项挑战。大的位移导致几何非线性随位移而变化。目前尚不清楚哪些非线性是关键的，哪些可以忽略。多轴挠曲机构还通常采用对称或周期性拓扑结构来增强准静态性能，这导致多个紧密间隔的模式。此外，不可避免的制造公差导致参数的不确定性。一起，几何非线性，位移，紧密间隔模式由于拓扑对称性，和参数的不确定性，由于制造公差的变化引起复杂的非最小相位零点在一定条件下的弯曲机构的频率响应。这些复杂的非最小相位零点导致大位移和动态性能之间的严重折衷。这些复杂的非最小相位零点何时以及为何出现？这些零点能被解析预测吗？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不利影响？所有这些问题目前都没有答案，代表了弯曲动力学知识的差距，将通过本研究项目加以解决。

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.