Experimental Modeling and Low-Order Control of a Multi-Actuator Adaptive Optics System

Abstract

This paper develops a fixed-order <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> suboptimal controller for an experimental adaptive optics (AO) system used for real-time wavefront correction. The system contains a 40-actuator deformable mirror (DM40) used to emulate atmospheric-turbulence-induced wavefront disturbances, a 140-actuator deformable mirror (DM140) used as the correcting element, and two Shack–Hartmann wavefront sensors (SH-WFSs): one for observing the generated turbulence-like wavefront and the other for measuring the corrected residual wavefront. Both static and dynamic models are derived from experimental input-output data collected from the real AO bench; the static influence matrix is obtained using Hadamard-based excitation patterns, whereas the dynamic state-space models are identified using the PBSIDopt implementation of predictor-based subspace identification. The identified models have orders 21 and 7 for the DM140 and DM40 subsystems, respectively, giving a 28th-order AO model before controller synthesis. Since conventional full-order <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> synthesis may produce controllers with an order comparable to that of the identified AO plant, direct implementation can be challenging for real-time multi-actuator AO systems. Therefore, a low-order <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> controller is synthesized in this study. The experimental results show that the third-order controller improves the residual wavefront response compared with the open-loop case under dominant Zernike disturbances, including defocus, astigmatism, coma, and trefoil components, while also revealing implementation challenges related to actuator saturation, asymmetric constraints, calibration errors, and unmodeled nonlinear dynamics.