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Adaptive optics is used in astronomy to obtain high resolution images, close to diffraction limited, of stars and galaxies with ground telescopes, otherwise blurred by atmospheric turbulence. The measurements of one or more wavefront sensor are used to flatten distorted wavefronts with one or more deformable mirror in a feedback loop. In this brief, we shall report our experience on the problem of building an accurate (dynamical) model of the actuation (deformable mirror) and sensing (wavefront sensor) of adaptive optics system. This will be done adapting state-of-the-art system identification and model reduction techniques to the problem at hand. Our results are based on real data collected under various operating conditions from a demonstrator developed at the European Southern Observatory (ESO), which is now operating in the Paranal Observatory (Chile).