Data-based modelling of low-order modes for AO control: what do on-sky experiments tell us?

International audience; It is well-known that data-driven models for the tip-tilt modes significantly improve the performance of Adaptive Optics (AO) systems as it allows to compensate for vibration-induced disturbances. Whether identifying from data the temporal dynamics of more modes makes an impact on the performance has been studied on-sky with the CANARY demonstrator at the William Herschel Telescope in July 2019. In this brief paper, we report on these experiments using both Strehl ratios computed from the science camera in H band or by replaying the AO telemetry data in numerical simulations. We show that Linear Quadratic Gaussian (LQG) controllers that embed a data-driven model for the low-orders (that are not limited to the tip-tilt) improve the performance of the AO for two different dynamical behaviours of the atmospheric turbulence.