Minimum variance prediction and control for adaptive optics

作者：Kulcsar Caroline^*; Raynaud Henri Francois; Petit Cyril; Conan Jean Marc

来源：Automatica, 2012, 48(9): 1939-1954.

DOI：10.1016/j.automatica.2012.03.030

• Adaptive optics
• State-space models
• MIMO control
• LQG optimal control
• Kalman filtering
• Discrete-time stochastic systems
• Sampled data systems

Adaptive Optics (AO) systems enable to compensate the adverse effects of atmospheric turbulence on ground-based telescopes%26apos; images in real time, using a deformable mirror (DM) inserted in the telescope%26apos;s optical path, and measurements provided by a wavefront sensor (WFS). This paper revisits minimum-variance (MV) control design for astronomical AO systems in a state-space framework. It presents a survey of the modeling and control issues arising in this multi-variable disturbance rejection problem. In a linear time-invariant framework, and under some mild assumptions, the optimal solution to MV control for AO systems is shown to be a discrete-time LQG controller. This result holds for a DM with instantaneous response, and for a fairly general class of DM%26apos;s dynamics. The state-space approach is extended to Wide-field Adaptive Optics (WfAO) configurations involving several DMs and/or WFSs. Integral-action control used in existing AO systems is compared with the LQG controller. Experimental WfAO results obtained on a laboratory test bench are presented, showing significant improvement in performance. Finally, open issues and perspectives of applicative and/or theoretical interests are discussed.

• 出版日期2012-9