High fidelity adaptive mirror simulations with reduced order models

TL;DR

The paper tackles the challenge of simulating large adaptive mirrors with full-system coupling by developing a preprocessing framework that builds reduced order, high-fidelity structural models. It compares modal truncation, balanced truncation, and data-driven interpolation (Rational Krylov and Loewner) to produce ROMs that preserve input-output behavior, quantified via $\mathcal{H}_\infty$ and related metrics. Validation on the GMT P72 prototype shows that balanced truncation with modal approximation and Krylov-based methods achieve similar accuracy to the high-order model at a reduced state dimension (e.g., $330\times330$) with substantial speedups, while data-driven Loewner requires more data and can underperform at smaller reductions. The framework enables efficient, scalable simulations of full adaptive mirror systems, facilitating design optimization for next-generation telescopes. The approach is implemented in a MATLAB-C hybrid, integrates with a parallel C++ mirror simulator, and is applicable to larger ELT-scale systems.

Abstract

In the design process of large adaptive mirrors numerical simulations represent the first step to evaluate the system design compliance in terms of performance, stability and robustness. For the next generation of Extremely Large Telescopes increased system dimensions and bandwidths lead to the need of modeling not only the deformable mirror alone, but also all the system supporting structure or even the full telescope. The capability to perform the simulations with an acceptable amount of time and computational resources is highly dependent on finding appropriate methods to reduce the size of the resulting dynamic models. In this paper we present a framework developed together with the company Microgate to create a reduced order structural model of a large adaptive mirror as a preprocessing step to the control system simulations. The reduced dynamic model is then combined with the remaining system components allowing to simulate the full adaptive mirror in a computationally efficient way. We analyze the feasibility of our reduced models for Microgate's prototype of the adaptive mirror of the Giant Magellan Telescope.

Figures (7)

• Figure 1: Deformable mirror and supporting structure.
• Figure 2: Graphical illustration of performing high fidelity adaptive mirror simulations with reduced order models.
• Figure 3: Picture (left) and FE model (right) of the GMT P72 Gallieni2020.
• Figure 4: Logarithmic plot of the relative $\mathcal{H}_\infty$ error in dB between the HO and the reduced order transfer functions with reduced state matrices of dimension $144\times 144$ (left) and $330 \times 330$ (right) for BT (blue), ITIA (orange), ISTIA (yellow) and LF (green).
• Figure 5: Root locus plot of the HO model in black and the reduced order model with size $330\times 330$ with BT in blue, ITIA in orange and LF in green. The gain scaling is varied between $1$ and $2$. We show only the important section around the real $0$ axis (dashed red line). Moreover, we show only the poles with positive imaginary part and not their conjugate complex counterpart. Circles indicate stable systems, whereas crosses indicate unstable systems.