Stability evaluation and improvement of adaptive optics systems by using the Lyapunov stability approach

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• 作者：Liang Wang ; Tao Chen ; Xin-yue Liu ; Xu-dong Lin…
• 关键词：Adaptive optics ; Wavefront control ; Stability ; Lyapunov stability theory ; Influence matrix ; Integral gain
• 刊名：Journal of the Korean Physical Society
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：68
• 期：3
• 页码：486-492
• 全文大小：997 KB
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• 作者单位：Liang Wang (1) (2)
  Tao Chen (1)
  Xin-yue Liu (1)
  Xu-dong Lin (1)
  Xiao-xia Yang (1)
  Hong-zhuang Li (1)
  
  1. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, 130033, China
  2. University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing, 100049, China
  
• 刊物主题：Physics, general; Theoretical, Mathematical and Computational Physics; Particle and Nuclear Physics;
• 出版者：Springer Netherlands
• ISSN：1976-8524

文摘

In this research, investigations on the closed-loop control stability of adaptive optics systems are conducted by using the Lyapunov approach. As an direct metric of the control stability, the error propagator includes the effects of both the integral gain and the influence matrix and is effective for control-stability evaluation. An experimental 97-element AO system is developed for the control-stability investigation, and the Southwell sensor-actuator configuration rather than the Fried geometry is adopted so as to suppress the potential waffle mode. Because filtering out small singular values of the influence matrix can be used to improve the control stability, the effect of the influence matrix and the effect of the integral gain are considered as a whole by using the error propagator. Then, the control stability of the AO system is evaluated for varying the integral gains and the number of filtered-out singular values. Afterwards, an analysis of the evaluations of the error propagator is made, and a conclusion can be drawn that the control stability can be improved by filtering out more singular values of the influence matrix when the integral gain is high. In other words, the error propagator is useful for trading off the bandwidth error and the fitting error of AO systems in a control-stability approach. Finally, a performance measurement of the experimental AO system is conducted when 13 smaller singular values of the influence matrix are filtered out, and the results show that filtering out a small fraction of the singular values has a minor influence on the performance of this AO system.