On-sky validation of an optimal LQG control with vibration mitigation: from the CANARY Multi-Object Adaptive Optics demonstrator to the Gemini Multi-Conjugated Adaptive Optics facility

International audience; Adaptive optics provides real time correction of wavefront perturbations on ground-based telescopes and allow to reach the diffraction limit performances. Optimizing control and performance is a key issue for ever more demanding instruments on ever larger telescopes affected not only by atmospheric turbulence, but also by vibrations, windshake and tracking errors. Linear Quadratic Gaussian control achieves optimal correction when provided with a temporal model of the disturbance. We present in this paper the first on-sky results of a Kalman filter based LQG control with vibration mitigation on the CANARY instrument at the Nasmyth platform of the 4.2-m William Herschel Telescope (La Palma, Spain). The results demonstrate a clear improvement of performance for full LQG compared with standard integrator control, and assess the additional improvement brought by vibration filtering with a tip-tilt model identified from on-sky data (by 10 points of Strehl ratio), thus validating the strategy retained on the instrument SPHERE (eXtreme-AO system for extra-solar planets detection and characterization) at the VLT. The MOAO on-sky pathfinder CANARY features two AO configurations that have both been tested: single- conjugated AO and multi-object AO with NGS and NGS Rayleigh LGS, together with vibration mitigation on tip and tilt modes. We finally present the ongoing development done to commission such a control law on a regular Sodium laser Multi-Conjuagated Adaptive Optics (MCAO) system GeMS at the 8-m Gemini South Telescope. This implementation does not require new hardware and is already available in the real-time computer.