LMI-based distributed H∞ control of dynamically coupled large segmented telescope mirrors

Segmented mirrors are to be used in the next generation of ground-based optical telescopes to increase the size of the primary mirror. A larger primary mirror enables the collection of more light, which results in higher image resolutions. The main reason behind the choice of segmented mirrors over monolithic mirrors is to reduce manufacturing, transportation, and maintenance costs of the overall system. Although segmented mirrors are cost-effective, they bring new challenges to the telescope control problem. The objective of keeping the mirror segments, which are dynamically coupled through a common support structure, aligned requires cooperation among individual segment controllers to maintain a smooth overall mirror surface. The vast number of inputs and outputs makes the computations for the centralized control schemes intractable. This paper investigates the linear matrix inequality (LMI)-based distributed H_∞ control of dynamically coupled segmented telescope mirrors. First, a distributed model of a candidate dynamically coupled system is obtained via finite element analysis (FEA). Then, a distributed controller is designed by using the LMI approach. Closed-loop simulations of a 492-segment system (in line with the Thirty Meter Telescope model) with the synthesized controller are run, and it is shown that the LMI-based distributed H_∞ controller can satisfy the stringent imaging performance requirements.