Deformation Control of Smart Microstructures Governed by Partial Differential Equations

本计划的目的是开发控制策略的智能微结构，如微机电系统（MEMS），描述的偏微分方程（PDE）的操作。本计划的主要目标有两个方面：1）致力于解决具有域内驱动的微结构变形控制问题; 2）将PDE控制技术应用于实际微系统，特别是自适应光学（AO）系统中的可变形微镜控制，以实现低复杂度的高性能控制系统。由于设计、制造和操作具有大量片上传感器的微器件的技术限制，开环控制是用于操作大规模微镜的主导技术。然而，开环控制方案固有地对环境波动、干扰和模型不确定性敏感。另一方面，虽然理论上闭环控制的应用可以提高系统性能，设计方法导致的控制结构，需要至少一样多的传感器作为执行器是不适用于微系统与目前可用的技术。这从理论和实践的角度提出了严峻的挑战。为了实现可行的解决方案，我们考虑应用最近开发的PDE控制技术，特别是平坦度和反推设计。本论文的研究重点是二维微镜的域内驱动控制，对应于自适应光学系统中典型的变形微镜操作方案。通过采用轨迹规划和前馈控制技术，系统可以在较少的闭环控制回路下运行。片上传感器的数量可以大大减少。所开发的方法将被扩展到更现实的设备，包括非线性和致动器动态。标准偏微分方程控制技术（如近似）将被用作基准工具，并将进行广泛的实验，以验证和评估开发的控制系统。

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.