Distributed H∞ control of dynamically coupled segmented telescope mirrors: Design and simulation

Next generation telescopes are to employ segmented mirrors to realize extremely large primary mirror surfaces. For example, one of the current next generation large telescope projects, the Thirty Meter Telescope (TMT), will employ a 30 m primary mirror with 492 segments. With the high degree of segmentation, control of these segments against external disturbances to maintain the parabolic mirror shape becomes a challenging task. In this paper, a preliminary study of H∞ control of the segmented primary mirror is presented. Both spatially-invariant distributed and centralized H∞ controllers are designed for a proof-of-concept 37-segment system model. In our proposed mirror design, the segments are dynamically coupled through a uniform support structure, which is modeled using the finite element method. In addition, the segments have the coupled control objective of maintaining the overall mirror shape to allow the highest possible image resolution. A spatially-invariant distributed model is obtained by using a finite element model of the 7-segment system. The resulting model is then used to synthesize a spatially-invariant distributed controller, and is expanded to obtain the 37-segment system by interconnecting the distributed model in a honeycomb-like pattern. The simulation results of the distributed controller is presented and compared with the results from the centralized H∞ controller applied to the 37-segment model. It is shown that both centralized and spatially-invariant distributed controllers satisfy the imaging performance requirements.