Dynamic Analysis of the Actively-Controlled Segmented Mirror of the Thirty Meter Telescope

Current and planned large optical telescopes use a segmented primary mirror, with the out-of-plane degrees of freedom of each segment actively controlled. The primary mirror of the Thirty Meter Telescope (TMT) considered here is composed of 492 segments, with 1476 actuators and 2772 sensors. In addition to many more actuators and sensors than at existing telescopes, higher bandwidths are desired to partially compensate for wind-turbulence loads on the segments. Control-structure interaction (CSI) limits the achievable bandwidth of the control system. Robustness can be further limited by uncertainty in the interaction matrix that relates sensor response to segment motion. The control system robustness is analyzed here for the TMT design, but the concepts are applicable to any segmented-mirror design. The key insight is to analyze the structural interaction in a Zernike basis; rapid convergence with additional basis functions is obtained because the dynamic coupling is much stronger at low spatial-frequency than at high. This analysis approach is both computational efficient, and provides guidance for structural optimization to minimize CSI.