title: Iterative learning control of a membrane deformable mirror for optimal wavefront correction.
abstract: We present an iterative learning control (ILC) algorithm for controlling the shape of a membrane deformable mirror (DM). We furthermore give a physical interpretation of the design parameters of the ILC algorithm. On the basis of this insight, we derive a simple tuning procedure for the ILC algorithm that, in practice, guarantees stable and fast convergence of the membrane to the desired shape. In order to demonstrate the performance of the algorithm, we have built an experimental setup that consists of a commercial membrane DM, a wavefront sensor, and a real-time controller. The experimental results show that, by using the ILC algorithm, we are able to achieve a relatively small error between the real and desired shape of the DM while at the same time we are able to control the saturation of the actuators. Moreover, we show that the ILC algorithm outperforms other control algorithms available in the literature.
authors.affiliation: Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands. a.haber@tudelft.nl
authors.forename: Aleksandar
authors.initials: A
authors.lastname: Haber
authors.forename: Alessandro
authors.initials: A
authors.lastname: Polo
authors.forename: Carlas S
authors.initials: CS
authors.lastname: Smith
authors.forename: Silvania F
authors.initials: SF
authors.lastname: Pereira
authors.forename: Paul
authors.initials: P
authors.lastname: Urbach
authors.forename: Michel
authors.initials: M
authors.lastname: Verhaegen