Control oriented strategy to consider constraints of the deformable mirror M4 for the Mid-infrared ELT Imager and Spectrograph

The Mid-infrared ELT Imager and Spectrograph (METIS) will be equipped with a single conjugate adaptive optics (SCAO) system comprising the deformable mirror M4, the tip-tilt mirror M5, a wavefront sensor, and a modal controller implemented on real-time computers. To prevent any damage to M4 during operation and windup phenomena due to internal checks of M4, its absolute shape, time-discrete change of shape, and inter-actuator strokes are limited. Hence, we present a strategy to consider M4's Cartesian constraints in the modal METIS-SCAO controller within this conceptual study. This strategy modifies the modal control error before it is fed into the SCAO controller considering the spatio-temporal and segmented characteristics of M4. Additionally, we present three different algorithms realizing this strategy. Furthermore, the presented strategy features the following characteristics, among others: add-on to a previously designed METIS-SCAO controller, no permanent trade-off between performance and constraint compliance, and application of numerically cheap approximating models. Moreover, we verify the functionality of the presented algorithms via standalone and closed loop simulations of the METIS-SCAO system. The simulations show that all presented algorithms work as intended and successfully enforce M4's constraints. Therefore, the presented strategy and the three corresponding algorithms are applicable to the METIS-SCAO system. (C) The Authors. Published by SPIE under a Creative Commons Attribution 4.0 International License.