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

Abstract

When high performance is expected, vibrations are becoming a burning issue in adaptive optics systems. For mitigation of these vibrations, in this paper, we propose a method to identify the vibration model. The nonlinear least squares algorithm named the Levenberg-Marquardt method is adapted to acquire the model parameters. The experimental validation of the high performance of vibration mitigation associated with our identification method has been accomplished. Benefiting from this method, vibrations have been significantly suppressed using linear quadratic Gaussian control, where the root-mean-square of the residual vibrations has been reduced down to a portion of a microradian. Moreover, the experimental results show that with the model identified, vibrations ranging from wide low-frequency perturbation to high-frequency vibration peaks can be dramatically mitigated, which is superior to classical control strategies.

Application of Artificial Neural Network in miRNA Biomarker Selection and Precise Diagnosis of Colorectal Cancer

“…After the miRNA expression values were normalized between 0 and 1, with mapminmax function and randomized division of the input data into the training dataset (70%), validating dataset (15%), and test dataset (15%), the training process was performed using the Levenberg-Marquardt learning function[21,25] with learning rate of 0.1. Finally, to evaluate the ANN model, the area under receiver operating characteristic (ROC) curve (AUC), confusion matrix, and linear regression were plotted.…”

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

“…Typically, in the AO literature, the modelling and identification of disturbances in AO systems have been addressed using a second-order auto-regressive (AR(2)) discrete-time model with both time-domain data [ 26 , 29 , 32 ] and frequency-domain data [ 6 , 7 , 33 , 34 , 35 ]. In particular, in [ 35 ], an identification approach using a NLS fitting method was presented. This approach was successfully used to design a control strategy to mitigate the vibrations.…”

A review on control methodologies of disturbance rejections in optical telescope

“…9, the 6-order notch filter shown in Eq. (19) is designed at the centered frequencies of 6 Hz, 11 Hz, and 21 Hz respectively. As a result, Q(s) is a band-pass filter.…”

“…This adaptive vibration cancellation algorithm was integrated into a telescope currently operating at the European Southern Observatory in Chile and verified experimentally. Recently, some popular controllers focusing on Linear Quadratic Gaussian (LQG) control laws or using H ∞ /H 2 synthesis methods [19][20][21][22] have been successfully implemented. Existing experiments demonstrate that LQG control can achieve better on-sky performance than a feedback integrator controller in the condition of the optimally identified process model.…”