Optimal gain integral control based on a fractional-order delayed observer in adaptive optics

This paper presents a computational method for rapidly determining optimal control gains using fractional-order delay observers (FODO), aimed at enhancing disturbance suppression in adaptive optics (AO) systems. The core of the control strategy is to convert the suppression of time-varying wavefront disturbances into the design of the FODO and the calculation of optimal control parameters. The observer structure primarily includes the dynamic characteristics of wavefront disturbances and the fractional-order time-delay information of the AO system, both of which affect the calculation of control parameters. By leveraging real-time wavefront data, the observer performs optimization and identification, thereby simplifying the complex derivation of formulas and matching computations of wavefront disturbance models. Furthermore, due to the significant computational cost of conventional methods for calculating optimal control gains, we introduce an enhanced parabolic approximation method (EPAM) for fast fitting of control parameters. Numerical simulations show that the proposed FODO achieves excellent wavefront identification accuracy, while the EPAM significantly accelerates the calculation of control parameters. Closed-loop control experiments in astronomical observations further demonstrate that this approach improves the disturbance suppression performance of the AO system.