Global Radius of Curvature Estimation and Control for the Hobby-Eberly Telescope

A system, which estimates the global radius of curvature (GroC) and corrects for changes in GroC on a segmented primary mirror has been developed for and verified on McDonald Observatory's Hobby Eberly Telescope (HET). The GroC estimation and control system utilizes HET's primary mirror control (PMC) system and the Segment Alignment Maintenance System (SAMS), an inductive edge sensor system. A special set of boundary conditions is applied to the derivation of the optimal edge match control. The special boundary conditions allow the further derivation of an observer, which enables estimation and control of the Groc mode to within HET's specification. The magnitude of the GroC mode can then be controlled despite the inability of the SAMS edge sensor system, by itself, to observe or control the GroC mode. The observer can be extended to any segmented mirror telescope. It will be shown that the observer improves with accuracy as the number of segments increases. This paper presents the mathematical theory of the observer. Simulation results will demonstrate the inherent accuracy and robustness of the system. Performance verification data from the HET will be presented.