Modeling and modal control for adaptive optics of ground-based telescopes

This work of thesis addresses modelling and control problem of a deformable mirror for Adaptive Optics applications on ground telescopes. Mirror mechanical model is defined as high-dimensional and densely coupled, based on spatial and structural configuration of the system. Modelling is then approached through modal analysis, which is exploited to perform model order reduction based on frequency characteristics of the system and on possible reference shapes for the mirror; possible modeling strategies are explored for the electro-mechanical description of the system and for the wave-front phase distortion due to atmospheric turbulence. Low-level control problem is addressed through combination of centralized modal feed-forward control and decentralized spatial feedback control, and then extended to explore advantages of a fully centralized approach. The whole design is validated through numerical simulations. Modal control advantages and criticisms are addressed, together with a possible real time simulation strategy for deformable mirrors dynamics.