Control of Many Coupled Oscillators and Application to Segmented-Mirror Telescopes

The largest optical telescopes today use a segmented primary mirror, with the out-of-plane position of each segment actively controlled. The segments are supported by a flexible structure that introduces dynamic coupling. This coupling leads to control-structure-interaction (CSI), which limits the achievable bandwidth of the primary mirror control system. As telescopes increase in size, the number of mirror segments increase, and the potential for CSI increases. The dynamics can be approximated by n identical oscillators coupled through the support structure. These dynamics are explored herein. First, in the special case where the support-structure modes provide an orthonormal basis for the oscillator dynamics, the problem can be transformed into n separate coupled oscillator problems. The application to more realistic support structures is then investigated using the dynamic model of the Thirty Meter Telescope. The achievable bandwidth is estimated by projecting the dynamics onto Zernike basis functions, with higher bandwidth possible for higher spatial frequency