Are integral controllers adapted to the new era of ELT adaptive optics?


J.-M. Conan*, H.-F. Raynaud**, C. Kulcsár**, S. Meimon*


* ONERA ** L2TI Univ. Paris 13


With ELTs we are now entering a new era in adaptive optics developments. Meeting unprecedented level of performance with incredibly complex systems implies reconsidering AO concepts at all levels, including controller design. Concentrating mainly on temporal aspects, one may wonder if integral controllers remain an adequate solution. This question is all the more important that, with ever larger degrees of freedom, one may be tempted to discard more sophisticated approaches because they are deemed too complex to implement. The respective performance of integrator versus LQG control should therefore be carefully evaluated in the ELT context. We recall for instance the impressive correction improvement brought by such controllers for the rejection of windshake and vibration components. LQG controller significantly outperforms the integrator because its disturbance rejection transfer function closely matches the energy concentration, respectively at low temporal frequencies for windshake, and around localized resonant peaks for vibrations. The application to turbulent modes should also be investigated, especially for very low spatial frequencies now explored on the huge ELT pupil. The questions addressed here are: 1/ How do integral and LQG controllers compare in terms of performance for a given sampling frequency and noise level?; 2/ Could we relax sampling frequency with LQG control?; 3/ Does a mode to mode adaptation of temporal rejection bring significant performance improvement?; 4/ Which modes particularly benefit from this fine tuning of the rejection transfer function? Based on a simplified ELT AO configuration, and through a simple analytical formulation, performance is evaluated for several control approaches. Various assumptions concerning the perturbation parameters (seeing and outer-scale value, windshake amplitude…) are considered. Bode’s integral theorem allows intuitive understanding of the results. Practical implementation and computation complexity are discussed.

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