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Extremely large optical telescopes are being designed with primary mirrors composed of hundreds of segments. The “out-of-plane” piston, tip, and tilt degrees of freedom of each segment are actively controlled using feedback from relative height measurements between neighboring segments. The “in-plane” segment translations and clocking (rotation) are not actively controlled; however, in-plane motions affect the active control problem in several important ways, and thus need to be considered. We extend earlier analyses by constructing the “full” interaction matrix that relates the height, gap, and shear motion at sensor locations to all six degrees of freedom of segment motion, and use this to consider three effects. First, in-plane segment clocking results in height discontinuities between neighboring segments that can lead to a global control system response. Second, knowledge of the in-plane motion is required both to compensate for this effect and to compensate for sensor installation errors, and thus, we next consider the estimation of in-plane motion and the associated noise propagation characteristics. In-plane motion can be accurately estimated using measurements of the gap between segments, but with one unobservable mode in which every segment clocks by an equal amount. Finally, we examine whether in-plane measurements (gap and/or shear) can be used to estimate out-of-plane segment motion; these measurements can improve the noise multiplier for the “focus-mode” of the segmented-mirror array, which involves pure dihedral angle changes between segments and is not observable with only height measurements.

While it is attractive to integrate a deformable mirror (DM) for adaptive optics (AO) into the telescope itself rather than using relay optics within an instrument, the resulting large DM can be expensive, particularly for extremely large telescopes. A low-cost approach for building a large DM is to use voice-coil actuators connected to the back of the DM through suction cups. Use of such inexpensive voice-coil actuators leads to a poorly damped system with many structural modes within the desired bandwidth. Control of the mirror dynamics using electro-mechanical sensors is thus required for integration within an AO system. We introduce a distributed control approach, and we show that the “inner” back sensor control loop does not need to function at low frequencies, leading to significant cost reduction for the sensors. Incorporating realistic models of low-cost actuators and sensors together with an atmospheric seeing model, we demonstrate that the low-cost mirror strategy is feasible within a closed-loop AO system.

The Thirty Meter Telescope primary mirror is composed of 492 segments that are controlled to high precision in the presence of wind and vibration disturbances, despite the interaction with structural dynamics. The higher bandwidth and larger number of segments compared with the Keck telescopes requires greater attention to modeling to ensure success. We focus here on the development and validation of a suite of quasi-static and dynamic modeling tools required to support the design process, including robustness verification, performance estimation, and requirements flowdown. Models are used to predict the dynamic response due to wind and vibration disturbances, estimate achievable bandwidth in the presence of control-structure-interaction (CSI) and uncertainty in the interaction matrix, and simulate and analyze control algorithms and strategies, e.g. for control of focus-mode, and sensor calibration. Representative results illustrate TMT performance scaling with parameters, but the emphasis is on the modeling framework itself.

We study a concept for a low-cost, large deformable mirror for an Extremely Large Telescope. The use of inexpensive voice-coil actuators leads to a poorly damped faceplate, with many modes within the desired control bandwidth. A control architecture, including rate and position feedback to add damping and stiness, for the faceplate has been presented in our previous papers. An innovative local control scheme which decouples adjacent actuators and suppresses low-order eigenmodes is a key feature in our controller. Here, we present an integrated model of a partially illuminated large deformable mirror in an experimental laboratory setup with a limited amount of actuators. From the model, conclusions are drawn regarding the number of actuators needed to identify the key features, such as local control performance, dynamic range, and controllability and robustness of the deformable mirror.

Large (1m) deformable mirrors are attractive for adaptive optics on ground-based telescopes; the mirrors typically have hundreds or thousands of actuators. The use of force actuators instead of position actuators has the potential to significantly reduce total system cost. However, the use of force actuators results in many lightly-damped structural resonances within the desired bandwidth of the control system. We present a robust control approach for this problem and demonstrate its performance in simulation. First, we demonstrate that high-bandwidth active damping using velocity feedback from mirror sensors that are not quite collocated with the actuators can be robustly implemented, because at sufficiently high frequencies the structural dynamics enter an ``acoustic" limit, where the half power bandwidth of a mode exceeds the modal spacing. This is important, because the system can be made less expensive using sensors placed in between actuators rather than collocated with each actuator. Introduction of active damping leads to a much easier problem for subsequent position control. It is known that a position control system in which each of the actuators is controlled using feedback from a collocated sensor can be made robustly stable. However, the resulting performance at high spatial frequencies is poor because there is no shared information between neighbouring actuators. In contrast, global control gives excellent performance but lacks robustness to model uncertainty. We introduce an innovative local control approach, which significantly improves the high spatial frequency performance without the robustness challenges associated with a global control approach. The overall approach is demonstrated to provide excellent command response suitable for an adaptive optics outer loop.

Unsteady wind loads due to turbulence within the telescope enclosure are one of the largest dynamic disturbances for ground-based optical telescopes. The desire to minimize the response to the wind influences the design of the telescope enclosure, structure, and control systems. There is now significant experience in detailed integrated modeling to predict image jitter due to wind. Based on this experience, a relatively simple model is proposed that is verified (from a more detailed model) to capture the relevant physics. In addition to illustrating the important elements of the telescope design that influence wind response, this model is used to understand the sensitivity of telescope image jitter to a wide range of design parameters.

Uncertainty in the interaction matrix between sensors and actuators can lead to performance degradation or instability in control of segmented mirrors (typically the telescope primary). The interaction matrix is ill conditioned, and thus the position estimate required for control can be highly sensitive to small errors in knowledge of the matrix, due to uncertainty or temporal variations. The robustness to different types of uncertainty is bounded here using the small gain theorem and structured singular values. The control is quite robust to moderate uncertainty in actuator gain, sensor gain, or the ratio of sensor dihedral and height sensitivity. However, the control is extremely sensitive to small errors in geometry, with the maximum error that can be tolerated scaling inversely with the number of segments. The same tools can be applied to adaptive optics; however, the interaction matrix here is better conditioned and so uncertainty is less of an issue, with the tolerable error scaling inversely with the square root of the number of actuators.

One of the factors that can influence the performance of large optical telescopes is the vibration of the telescope structure due to unsteady wind inside the telescope enclosure. Estimating the resulting degradation in image quality has been difficult because of the relatively poor understanding of the flow characteristics. Significant progress has recently been made, informed by measurements in existing observatories, wind-tunnel tests, and computational fluid dynamic analyses. We combine the information from these sources to summarize the relevant wind characteristics and enable a model of the dynamic wind loads on a telescope structure within an enclosure. The amplitude, temporal spectrum, and spatial distribution of wind disturbances are defined as a function of relevant design parameters, providing a significant improvement in our understanding of an important design issue.