Distributed control of large segmented telescopes

In this paper we conduct a preliminary study of controlling the primary mirror of a large segmented telescope. This work is motivated by the need of astronomers to study the development of structure in the Universe. First, we present some background about large segmented telescopes and our collaborative research program on large telescopes. Second, we formulate a model of the primary mirror system in state space. Third, we design a centralized controller using H₂ methods for a seven-segment system which establishes the best possible performance characteristics for a laboratory-type of unit that we plan to build. Simulation results are displayed. Finally, we apply spatially-invariant distributed control techniques to an infinite segmented system that approximates a large mirror. Through the H₂ norm, we calculate upper bounds for the relative displacements between adjacent segments with either a spatially-invariant infinite controller or a truncated local controller. Simulation results are also presented with a truncated local controller applied to a 19-segment system. In all cases, the results indicate that the required accuracy of 10^-8 m can be achieved