H 2 Control of Large Segmented Telescopes

In this paper we conduct a preliminary study of control of the primary mirror of a large segmented telescope, i.e. aligning the segments to form a paraboloid. This work is motivated by the need of astronomers to study faint objects and to reach the highest possible angular resolution. First, we present background information 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 H 2 methods for a seven-segment system which establishes the best possible performance characteristics for the 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 H 2 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 mirror-to-mirror surface position accuracy of 10 -8 m can be achieved.