Model Predictive Control of Multi-Mirror Adaptive Optics Systems

In the last decades, large telescopes have been planned and built to explore the universe for fainter objects than ever before. Presently, the largest telescope for optical wavelengths, the Extremely Large Telescope (ELT), is constructed with a primary mirror of 39 m diameter. In order to reduce the total weight of the telescope and due to the enormous size, the optics are mounted on lightweight constructions, which are very sensitive to wind excitations. Therefore, telescope optics and their control have to be considered in the design of the next generation ELT's, where a good vibration compensation is required. To achieve the diffraction limit of the ELT, its optical path is equipped with a deformable mirror and a plane tiptilt mirror for correction. Due to the atmospheric turbulences and structural vibrations, the compensation mirrors can reach their stroke and frequency limitations. Without considering these limitations in the control system the telescope instruments cannot fully reach its optimal performance. Therefore, we propose a solution based on Model Predictive Control (MPC), which can control the mirrors in an optimal way under given constraints. In this paper a model of the Adaptive Optics system, the MPC controller design and an integral control concept for comparison are presented. As a result the residual tip-tilt error can be reduced over a larger frequency range with an MPC controller when considering input constraints.