Modeling and Control of Nonlinear Micro-distributed Systems

9725149 Wang微机械设备和系统的高级应用要求精确控制其相对于空间和时间的动态行为。 这种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为10-3米至10-6米的量级，因此在建模时必须考虑微小的非线性力和力矩。 所得到的数学模型是在非线性偏微分和/或积分方程的形式。 这项研究的目的是发展适用的理论建模和控制的非线性微分布式系统。 最初的努力将集中在特定的微分布式系统的建模来自应用程序，特别是，系统与自由边界;分叉现象和参数估计的微机械弹性结构，包括可变形镜与非线性静电或静磁致动器，和弹性结构与液体膜耦合。 随后的工作将集中在微分布式系统的设计，稳定和控制。 他们将包括致动器图案的最佳设计;确定可达到的形状在微加工变形镜使用静电驱动;稳定的反馈控制的振动阻尼和精确对准微加工弹性结构使用电磁，压电或热驱动的推导;和层流通过边界面扰动。 重点将放在发展适用的数学理论，有效的计算算法，并为微分布式系统的实际实施。 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。 在数学建模的初步研究已经导致新的非线性偏微分方程，这不仅是有用的控制发展，但他们也是有趣的从数学的观点。 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。 ***

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. ***