We propose a detailed study of the temporal and noise propagation errors entering the error budget of Single Conjugate Adaptive Optics (SCAO) systems. A transfer-function oriented method is developed for the compu- tation of these errors, in a general linear control context. We apply this formalism to performance comparison between Linear Quadratic Gaussian (LQG) and Integral action controllers. Simulation results are presented, corresponding to a typical SCAO system, in order to validate some approximations on the perturbation power spectral density. We then apply the formalism to evaluate the tip-tilt error budget on GeMS.

Perturbation modelling and vibration compensation are key issues to reach better performance in adaptive optics systems for VLTs and future ELTs. In this context, an LQG controller is to be implemented for the tip-tilt loop of the multi-conjugate adaptive optics instrument GeMS. The performance of several models, associated with their identification techniques are considered for tip-tilt disturbance.

Adaptive Optics (AO) systems aim at detecting and correcting for optical distortions induced by atmospheric turbulences on ground based telescopes astronomical images. They are also extremely sensitive to extraneous sources of perturbations such as vibrations, which degrade their performance. A new well defined vibration at 37Hz has been detected in January 2015 and is still currently affecting the Gemini South telescope secondary mirror. We show how its existence limits the performance of the operational systems at Gemini South: The Gemini Planet Imager (GPI) and the Gemini Multi-Conjugated AO system (GeMS). We further focus on how these vibrations are affecting GeMS performance and propose to implement the Tip-Tilt control strategy first tested on CANARY and routinely used on SPHERE. It combines identification of a sum of auto-regressive models of order 2 with a Linear Quadratic Gaussian (LQG) control. LQG is now routinely used for Tip-Tilt and focus control for GPI and has been successfully tested on all modes on CANARY. We show that the expected gain in performance brought by this LQG Tip-Tilt control strategy on GeMS compared with an Integral Controller is on the order of 15 to 20mas. The analysis was conducted in ”replay mode” using GeMS Tip-Tilt on-sky data. This allows realistic performance assessment before implementation inside the Real-Time Computer (RTC) of GeMS and on-sky tests during the first semester of 2016.