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Journal of Vibration and Control
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H2 Control of Large Segmented Telescopes

Shengxiang Jiang

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 161 CSL, 1308 West Main Street, Urbana, IL 61801-2307, USA

Petros G. Voulgaris

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 161 CSL, 1308 West Main Street, Urbana, IL 61801-2307, USA, voulgari{at}uiuc.edu

Leland E. Holloway

Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801, USA

Laird A. Thompson

Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801, USA

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 H2 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 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 mirror-to-mirror surface position accuracy of 10-8 m can be achieved.

Key Words: Segmented • distributed • Strehl ratio • spatial-invariance.

This version was published on June 1, 2009

Journal of Vibration and Control, Vol. 15, No. 6, 923-949 (2009)
DOI: 10.1177/1077546308091211
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