Modeling and Control of Nonlinear Micro-distributed Systems

非线性微分布式系统的建模与控制

• 批准号: 9725149
• 负责人: Paul Wang
• 金额: $ 20万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9725149&HistoricalAwards=false
• 关键词: Modeling; Control; Nonlinear; Micro; distributed

9725149WangAdvanced applications of micromachined devices and systems call for precise control of their dynamic behavior with respect to both space and time. The design and control of such systems require consideration of distributed-parameter models. Since the physical size of such systems is of the order of 10-3 meter to 10-6 meter, it is necessary to take into account the minute nonlinear forces and moments in modeling. The resulting mathematical models are in the form of nonlinear partial differential and/or integral equations. The objective of this proposed study is to develop applicable theories for the modeling and control of such systems referred hereafter as nonlinear micro-distributed systems. The initial effort will be focused on the modeling of specific micro-distributed systems derived from applications, in particular, systems with free boundaries; bifurcation phenomena and parameter estimation in micromachined elastic structures including deformable mirrors with nonlinear electrostatic or magnetostatic actuators, and elastic structures coupled with liquid films. The subsequent efforts will be focused on the design, stabilization and control of micro-distributed systems. They will include the optimal design of actuator patterns; the determination of attainable shapes in micromachined deformable mirrors using electrostatic actuation; the derivation of stabilizing feedback controls for vibration damping and precise alignment in micromachined elastic structures using electromagnetic, piezoelectric, or thermal actuation; and for laminar flow via boundary surface perturbations. Emphasis will be placed on the development of applicable mathematical theory, efficient computational algorithms, and practical implementation for micro-distributed systems. The proposed study represents a new research direction for distributed-parameter control system theory. Preliminary studies in mathematical modeling already led to new nonlinear partial differential equations which are not only useful for control development, but they are also interesting from the mathematical standpoint. The results have potential applications in micro-sensors, micro-imaging systems, and adaptive optical systems. ***

微机械设备和系统的先进应用要求精确控制它们在空间和时间上的动态行为。这类系统的设计和控制需要考虑分布参数模型。由于此类系统的物理尺寸在10-3米到10-6米的量级，因此在建模时必须考虑微小的非线性力矩。得到的数学模型是以非线性偏微分方程组和/或积分方程组的形式出现的。这项研究的目的是为这类系统的建模和控制发展适用的理论，以下称为非线性微分布式系统。最初的工作将集中在应用中的特定微分布系统的建模，特别是具有自由边界的系统；微机械弹性结构中的分叉现象和参数估计，包括带有非线性静电或静磁致动器的可变形反射镜，以及与液膜耦合的弹性结构。随后的工作将集中在微型分布式系统的设计、稳定和控制上。它们将包括执行器图案的优化设计；使用静电驱动的微加工可变形反射镜中可获得的形状的确定；使用电磁、压电或热驱动的微机械弹性结构中的减振和精确对准的稳定反馈控制的推导；以及通过边界表面扰动的层流流动。重点将放在发展适用的数学理论、有效的计算算法和微型分布式系统的实际实施上。该研究为分布参数控制系统理论提供了一个新的研究方向。在数学建模方面的初步研究已经导致了新的非线性偏微分方程组，它们不仅对控制的发展有用，而且从数学的角度来看也很有趣。研究结果在微传感器、微成像系统和自适应光学系统中具有潜在的应用价值。***