Optimal H2 and H∞ Control of Extremely Large Segmented Telescopes

Extremely large telescopes (ELTs) are the next generation of ground-based reflecting telescopes of optical wavelengths. ELTs possess an aperture of more than 20 meters and share a number of common features, particularly the use of a segmented primary mirror and adaptive optics systems. In 2005, the European Southern Observatory introduced a new giant telescope concept, named the European Extremely Large Telescope (E-ELT), which is scheduled for operation in 2018. In 2009, a feasibility study proved the feasibility of the real-time (RT) control system architecture for the E-ELT’s primary mirror, which consists of nearly 1,000 mirror segments with 3,000 actuators and 6,000 sensors. The goal of the RT control system was to maintain a perfectly aligned field of mirrors at all times with a loop-time of 1 ms. The study assumed a prescribed controller algorithm. This paper prescribes two such controllers. In this respect, optimal controller designs for the primary mirror, where optimality is formulated in the H2 and H∞ frameworks are derived. Moreover, the designed controllers are simulated to show that the desired performance, which is defined in terms of imaging requirements, is met.