Deformation Control of Smart Microstructures Governed by Partial Differential Equations

本计划旨在开发用于操纵智能微结构的控制策略，例如由偏微分方程组(PDE)描述的微电子机械系统(MEMS)。本计划的主要目标有两个：1)寻求域内驱动微结构变形控制的解决方案；2)将PDE控制技术应用于现实生活中的微系统，特别是自适应光学(AO)系统中的可变形微镜控制，以实现低复杂性的高性能控制系统。由于具有大量片上传感器的微型器件在设计、制造和操作方面的技术限制，开环控制是大型微镜操作中的主要技术。然而，开环控制方案对环境波动、扰动和模型不确定性具有内在的敏感性。另一方面，虽然从理论上讲，闭环控制的应用可以提高系统的性能，但导致至少需要与执行器一样多的传感器的控制结构的设计方法不适用于目前可用的技术的微系统。这从理论上和实践上都提出了严峻的挑战。为了实现可行的解决方案，我们考虑应用最新开发的偏微分方程控制技术，特别是平坦度和反步设计。针对声光系统中可变形微镜的典型操纵方案，重点研究了域内驱动的二维微镜的控制。通过利用轨迹规划和前馈控制技术，系统可以在较少的闭环系统中运行。这样一来，片上传感器的数量就可以大大减少。所开发的方法将扩展到更现实的设备，包括非线性和执行器动力学。标准的PDES控制技术(例如近似)将被用作基准工具，并将进行广泛的实验来验证和评估所开发的控制系统。

The present program aims at developing control strategies for the manipulation of smart microstructures, e.g. microelectromechanical systems (MEMS), described by partial differential equations (PDEs). The main objective of the present program is twofold: 1) to work towards solutions for deformation control of microstructures with in-domain actuation; 2) to apply PDE control techniques to real-life microsystems, in particular deformable micro-mirror control in adaptive optics (AO) systems, in view of enabling the implementation of high performance control systems with low complexity. Due to technological restrictions in the design, the fabrication, and the operation of micro-devices with large amount of on-chip sensors, open-loop control is the dominant technique used in the operation of large scale micro-mirrors. However, open-loop control schemes are inherently sensitive to environmental fluctuations, disturbances, and model uncertainties. On the other hand, although theoretically the application of closed-loop control may enhance system performance, design methods leading to a control structure that requires at least as many sensors as actuators are not applicable to microsystems with currently available technologies. This raises serious challenges from both theoretical and practical viewpoints. In order to achieve viable solutions, we consider the application of recently developed PDE control techniques, in particular flatness and backstepping designs. The research emphasis will be put on the control of 2D micro-mirrors with in-domain actuation, corresponding to the typical manipulation scheme of deformable micro-mirrors in AO systems. By exploiting the technique of trajectory planning and feedforward control, the system can be operated with few closed control loops. The number of on-chip sensors can then be considerably reduced. The developed methods will be extended to more realistic devices, including nonlinearity and actuator dynamics. Standard PDEs control techniques (e.g. approximation) will be used as benchmarking tool and extensive experimentations will be carried out to validate and evaluate the developed control systems.