Improving the performance of a Laser Guide Star Adaptive Optics system using identification methods

The light coming from a star travels undisturbed for billions of kilometers until it reaches the boundaries of the Earth atmosphere: the small differences in the refraction index distort the spherical wavefront, creating phase errors in the image-forming ray paths. Even at the best sites, ground-based telescopes observing at visible wavelengths cannot, because of atmospheric turbulence alone, achieve an angular resolution better than telescopes of 10to 20-cm diameter. Adaptive optics (AO) is a technique to remove the effects of these distortions in real-time by operating a deformable mirror that rapidly adapts its shape to the atmospheric disturbance canceling it. ESO (European Southern Observatory) now operates several AO systems in the Paranal observatory on the Chilean Andes, where the 4 telescopes of the VLT (very large telescope) are installed. Several of them are the result of a common project called MACAO, for multi application curvature adaptive optics. In this paper we will focus on one particular installation, SINFONI, that combines MACAO with an integral field spectrometer. MACAO for SINFONI features a quite complex control loop because the guide star used here is artificial, generated with a laser. One subsystem of MACAO, the LGS tip/tilt control, does not perform as expected. We analyse the behaviour of this subsystem by first identifying its model and then we try to improve it by designing an optimal controller