Subspace identifcation of Roesser models for large-scale adaptive optics

Abstract

Current control algorithms for large-scale adaptive optics are computationally demanding and an accurate wavefront correction is hardly achieved within the time requirements. An idea is to exploit the local interactions between the wavefront sensor and the actuators and to develop compact models that describe thespatial dynamics of the mirror for future use in control. The goal of this research is to study the subspace identification of 2D Roesser models to model the spatial dynamics of a deformable mirror. Two subspace identification algorithms for 2D Roesser models are presented. Both rely on the decomposition of the Roesser model into two 1D state-space models. The difference is how the models are connected. In the first case the 1D models are connected in a feed-back loop. In the second case the 1D models are connected in series. The subspace identification using the feed-back decomposition provides good estimates of the system matrices, but can only be applied to a subclass of Roesser models. Is is also shown that using the estimates from the subspace method as an initial guess for a parametric identification allows to identify more general Roesser models. A subspace identification algorithm for the decomposition in series has been studied and handles a subset of Roesser models as well.