Non-Minimum Phase Zeros in the Dynamics of Flexure Mechanisms

点击翻译按钮获取中文摘要

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.