Deformation Control of Smart Microstructures Governed by Partial Differential Equations

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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.