Extremely large telescopes are characterized by high degree of freedom control systems used to coordinate multiple segments and mirrors. The dynamics can interact so that single loop requirements do not provide sufficient stability and performance robustness. This paper reviews the relevant multivariable robustness and performance methods, and presents examples from Giant Magellan Telescope (GMT) motion control systems.
Singular value bounds of multivariable frequency responses are well developed computational tools that provide a methodology that can be used for telescope analysis. The singular value bounds are relevant because they give the maximum sensitivity for coupled, multivariable systems. Singular values are recommended for analysis, and can be considered for requirements. With sufficient numbers of sensors, these multivariable bounds are measurable and hence can be validated. There is a practical reason for using multivariable tools, to combine many, perhaps thousands of transfer functions and/or measurements that can be compared against singular value bounds.
The first example is the AZ/EL mount control. Coupling tends to be small, hence single-input analysis tools suffice, nevertheless the mount control system provides a good introduction to multivariable methodology. The maximum singular value of both the sensitivity and complementary sensitivity functions provide a good bound for crossover robustness near the position control bandwidth, typically +6 dB near 1 Hz. The high frequency region of the complementary sensitivity function provides a good bound on robustness with respect to unmodeled structural dynamics, typically–40dB above the maximum frequency of the finite element modes.
Similar multivariable stability robustness bounds can be applied to position control of the M2 assembly, for both the macrocell relative to the top end assembly, and each mirror subassembly relative to the macrocell. The latter includes control of the Fast Steering Mirror, where 21 PZT actuators control the tip and tilt of seven secondary mirrors. The risk is the 21 PZT control loops meet good classical phase and gain margin robustness metrics when measured as individual, single-input-single-output systems, but the multivariable bound exceeds either the +6 dB or – 40 dB bound. This can occur due to interaction in the macrocell, the structure used to support the individual segments. Whether or not this interaction occurs depends on the bandwidth of the control system relative to the structural modes of the macrocell. This tradeoff is important, and the maximum singular value is a good tool to test for this sensitivity.
The Giant Magellan Telescope (GMT) M1 Subsystem includes the seven 8.4 meter M1 (Primary) Segment Mirrors and the steel mirror cell weldments which house the mirror active support and thermal control systems. The segmented nature of the primary mirror and the requirement that each of the six off-axis segment cells be interchangeable impose requirements on the range of motion and control beyond those applicable to the M1 subsystems on 6.5m and 8.4m telescopes using the structured honeycomb mirrors.The subsystem is both technically challenging to design and costly to produce. The M1 Subsystem is allocated a large fraction of the GMT natural seeing image quality budget. Support actuator tolerances, range of motion, accuracy, and precision, as well as the ability of the thermal control system to regulate the primary mirror temperature, all have a significant effect on the image quality. The authors have developed several linear models to estimate the effect of force and moment errors at the M1 Segment Active Supports and the non-uniformity of temperature across M1 segments on the delivered image quality. These results are coupled to the Wavefront Control Subsystem model and are integrated into the GMT system-level simulations to produce a final image quality budget and to quantify the effectiveness of the Wavefront Control Subsystem to compensate for M1 Subsystem error. In this paper, we present the modeling process and preliminary performance results obtained using the models.
The 25.4 m Giant Magellan Telescope (GMT) consists of seven 8.4 m primary mirror (M1) segments with matching segmentation of the Gregorian secondary mirror (M2). The GMT will operate in four basic optical correction modes, Natural Seeing (NS), Ground Layer Adaptive Optics (GLAO), Natural Guide Star Adaptive Optics (NGAO) and Laser Tomography Adaptive Optics (LTAO). Each of these modes must deliver a specified combination of image quality, field of view, and sky coverage over a range of environmental conditions.
With a double segmented mirror configuration, even in the simplest of the correction modes the GMT includes over one thousand controllable degrees of freedom. Exogenous and internal sources of disturbances and noise over these degrees of freedom will limit the image quality. The different ranges of motion and bandwidth of the different degrees of freedom enable a cascade correction of the wavefront error, successively rejecting global to local disturbances. This frequency and spatial separation allows allocating the disturbances in stages, considering the residuals of the low spatial and temporal corrections as the disturbance for the high order corrections.
While a first approach can consider the analysis of systems in isolation in order to allocate coarse budgets, a complex control system such as that of the GMT requires a Dynamic Optics Simulation (DOS) to account for the real interactions between the controlled plant and the controllers. For example, some control loops such as the M1 figure control system will have an update rate of only 0.03 Hz, while the Adaptive Secondary Mirror (ASM) will be updated at 1kHz . The DOS is an end-to-end simulation environment that brings together optics, finite element models (FEM), mechanical motions, surface deformations and control models applied to the GMT main optics. At the center of the DOS there is an optics propagation module with both geometric ray tracing and Fourier propagation capability. The dynamic response of the telescope mount and the large M1 segments has been modeled by applying Craig-Bampton reduction analysis to finite element models. These reductions have been reordered in a second order form, allowing higher computational efficiency than traditional state space models. Each M1 segment is controlled by an array of 330 actuators with realistic precision, noise and discretization errors. The structural dynamics model can be used in time domain simulations that account for all the non-linear effects of actuators and sensors, or in a linear frequency domain model to run more efficiently stochastic analyses.
A high resolution Computational Fluid Dynamics (CFD) model has been developed for simulating unsteady turbulent flow over the optical system. These simulations provide unsteady pressure fluctuations over the main optics and effects of varying index of refraction in the optical path for different operating conditions. These quantities are subsequently used for estimating wind induced image jitter and thermal (dome and mirror) seeing by applying the combined structural, control, and optical models described above.
The DOS allows GMT to understand the sensitivity of image quality to any of the thousands of parameters of our plant and control system., Due to the cascade layers of control loops, DOS allows specifying design parameters without over-constraining the solution space.
The 25.4m Giant Magellan Telescope (GMT) consists of seven 8.4 m primary mirror (M1) segments with matching segmentation of the Gregorian secondary mirror (M2). When operating the GMT in the diffraction-limited Adaptive Optics (AO) modes, using the Adaptive Secondary Mirror (ASM), the M1-M2 pairs of segments must be phased to a small fraction of the observing wavelength. To achieve this level of correction across the scientific field of view (<90” in diameter), the phasing system relies on multiple (up to four) natural guide-star probes deployed across the field of view (from 6’ to 10’ from the center of the field) measuring at slow rates (~0.033 Hz) segment phase piston in the infrared and low-order field-dependent phase aberrations in the visible. This paper describes the overall phasing strategy and requirements when operating in the Natural Guide-star AO (NGAO) and the Laser Tomography AO (LTAO) modes. We will also present a first evaluation of segment piston error induced by wind buffeting on the telescope structure. Wind loads have been computed for different observatory configurations using Computational Fluid Dynamics (CFD) simulations. This analysis showcases the GMT Dynamic Optical Simulation (DOS) environment which integrates the optical and structural dynamic models of the GMT with the Fourier optics models of AO and phasing sensors.