Optimal [H-2] and [H-infinity] control of extremely large segmented telescopes



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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 the use of 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. The E-ELT will address key scientific challenges and will aim for a number of notable firsts, including discovering Earth-like planets around other stars in the ``habitable zones'' where life could exist, attempting to uncover the relationship between black holes and galaxies, measuring the properties of the first stars and galaxies, and probing the nature of dark matter and dark energy. In 2009, a feasibility study, conducted by National Instruments, proved the feasibility of the real-time (RT) control system architecture for the E-ELT's 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 research report prescribes the optimal controller algorithms for large segmented telescopes. In this respect, optimal controller designs for the primary mirror of the E-ELT, where optimality is formulated in the [H-2] and [H-infinity] frameworks are derived. Moreover, the designed controllers are simulated to show that the desired performance metrics are met.