Vibration identification based on Levenberg-Marquardt optimization for mitigation in adaptive optics systems

An Optimal Integral Controller for Adaptive Optics Systems

Integral controllers are commonly employed in astronomical adaptive optics. This work presents a novel tuning procedure for integral controllers in adaptive optics systems which relies on information about the measured disturbances. This tuning procedure consists of two main steps. First, it models and identifies measured disturbances as continuous-time-damped oscillators using Whittles´s likelihood and the wavefront sensor output signal. Second, it determines the integral controller gain of the adaptive optics system by minimizing the output variance. The effectiveness of this proposed method is evaluated through theoretical examples and numerical simulations conducted using the Object-Oriented Matlab Adaptive Optics toolbox. The simulation results demonstrate that this approach accurately estimates the disturbance model and can reduce the output variance. Our proposal results in improved performance and better astronomical images even in challenging atmospheric conditions. These findings significantly contribute to adaptive optics system operations in astronomical observatories and establish our procedure as a promising tool for fine-tuning integral controllers in astronomical adaptive optics systems.

Adaptive Optics Tip-Tilt Correction Based on Smith Predictor and Filter-Optimized Linear Active Disturbance Rejection Control Method

A tip-tilt mirror (TTM) control method is designed to enhance the control bandwidth and ensure the rejection performance of the adaptive optics (AO) tip-tilt correction system. Optimized with the Smith predictor and filter, linear active disturbance rejection (LADRC) is adopted to achieve the tip-tilt correction. An AO tip-tilt correction experimental platform was built to validate the method. Experimental results show that the proposed method improves the control bandwidth of the system by at least 3.6 times compared with proportional-integral (PI) control. In addition, under the same control bandwidth condition, compared with the Smith predictor and proportional-integral (PI-Smith) control method, the system is more capable of rejecting internal and external disturbances, and its dynamic response performance is improved by more than 29%.

Disturbance Modelling for Minimum Variance Control in Adaptive Optics Systems Using Wavefront Sensor Sampled-Data

Modern large telescopes are built based on the effectiveness of adaptive optics systems in mitigating the detrimental effects of wavefront distortions on astronomical images. In astronomical adaptive optics systems, the main sources of wavefront distortions are atmospheric turbulence and mechanical vibrations that are induced by the wind or the instrumentation systems, such as fans and cooling pumps. The mitigation of wavefront distortions is typically attained via a control law that is based on an adequate and accurate model. In this paper, we develop a modelling technique based on continuous-time damped-oscillators and on the Whittle’s likelihood method to estimate the parameters of disturbance models from wavefront sensor time-domain sampled-data. On the other hand, when the model is not accurate, the performance of the minimum variance controller is affected. We show that our modelling and identification techniques not only allow for more accurate estimates, but also for better minimum variance control performance. We illustrate the benefits of our proposal via numerical simulations.

Coupled dynamic reaction force study of a large-aperture piezoelectric fast steering mirror

The reaction force of a large-aperture piezoelectric fast steering mirror (PFSM) has adverse coupling interference for the stability and pointing accuracy of laser beams, and the dynamic characteristics of the reaction force are coupled with the inner components of the PFSM. In order to compensate for and eliminate the reaction force, it is essential to accurately analyze the dynamic characteristics. In this paper, a simplified piezoelectric-coupling model of PFSM is established. The coupling mathematical equations for investigating the characteristics of the reaction force are deducted based on the piezoelectric constitutive equation and Hamiltonian's principle. Then the coupling characteristics of the reaction force are probed by a finite element (FE) piezoelectric-coupling method. The simulations for three large apertures' (250, 320, and 400 mm) FE models show that the reaction force has a linear positive correlation with the actuating voltage, and coupled with the materials of the central flexure hinge, the relationship between the reaction force and driving frequency is not completely quadratic. Experiments with the 320 mm aperture are completed, and the testing results are consistent with the mathematical model and the FE piezoelectric-coupling simulation. The dynamic characteristics of the reaction force demonstrated in this paper are significance for the accurate estimation of the reaction force, the design of compensation structure, and the optimization of algorithm for beam jitter controlling.

Single preloaded piezoelectric-ceramic-stack-actuator-based fast steering mirror with an ultrahigh natural frequency

To meet the requirements of the adaptive optics systems with high bandwidths and large excursion angles, we propose a fast steering mirror (FSM) with an ultrahigh natural frequency and a large angular range. The proposed FSM is driven by a preloaded piezoelectric ceramic stack actuator (PCSA), which has a higher shear stress limit in the working direction. We describe the structure of the preloading device and analyze the stiffness improvement of the preloaded PCSA. Then we introduce the structure of the proposed FSM and perform theoretical analysis based on the established static model and dynamical model. We also build an experimental setup of the proposed FSM. The experimental results show that the angular range of the proposed FSM is up to 8.4 mrad, and its first natural frequency is 6660 Hz, which surpass the performances of current FSMs.