The Extremely Large Telescope (ELT), with a primary mirror diameter of 39 m, will be built in the Atacama desert in Chile. One of the three first light instruments is the Multi-Adaptive Optics Imaging Camera for Deep Observations (MICADO). In order to achieve diffraction-limited images in MICADO, disturbances in the optical path need to be mitigated. Two disturbance sources have been identified, to be compensated by advanced control schemes: the field of view rotation tracking deviation due to mechanical imperfections for the counter-rotation of the earth’s rotation and the induced structural vibrations in the optical path. The field of view rotation shall be corrected by counter-rotating the MICADO instrument by a four-point contact ball bearing. Due to the slow rotation speeds of the bearing stick-slip friction effects cause a violation of the rotation accuracy requirement. A model-based friction compensation is developed, to handle these stick-slip effects. In the past, Adaptive Optics (AO) systems were designed, to compensate mainly for the atmospheric turbulence. However, structural vibrations become more dominant in telescope structures such as the ELT. A larger primary mirror allows for a higher diffraction-limited resolution, the wavefront error budget for the structural vibrations at each telescope mirror however is consequently tightened. Thus, the disturbances need to be compensated by a deformable mirror and an additional tip-tilt mirror. An over-actuated system with non-negligible compensation mirror dynamics and input constraints needs to be controlled based on the wavefront sensor of the AO system for the image motion. A model predictive control approach is developed to fulfill these requirements.weiterlesen