A Decomposition Approach to Distributed Control of Dynamic Deformable Mirrors

Deformable mirrors with spatially invariant dynamic response can be considered as part of the class of decomposable systems. Such systems can be thought of as the interconnection of a number of identical subsystems, and they can be used to model certain classes of large scale systems. We show in this article that the technique allows the design of a distributed ℋ 2 controller for a deformable mirror of any size, with a computational cost that does not increase with the size of the mirror. The method shows a performance close to that of the centralized ℋ 2 optimal controller in a simulation example, which is about two times better (in terms of ℋ 2 norm) than the performance of a decentralized PI controller, with additional notches to suppress the high resonance frequencies of the deformable mirror.