Mixed sensitivity H-infinity control of an adaptive optics system

Dingan Song,Zhenming Peng,Xinyang Li

doi:10.1117/1.oe.55.9.094106

Abstract

Design of the controller of an adaptive optical system is very complex because its model is usually with uncertainty. To deal with uncertainty and to improve robust stability, the mixed sensitivity H∞ control has been introduced to design the controller. In order to testify the validity, wavefront aberration correction capability as well as the robust stability has been compared between the mixed sensitivity H∞ controller and the classic integral controller. The computer simulation results demonstrate that the system with the mixed sensitivity H∞ controller, though it cannot guarantee a better correction performance, has greater robust stability than the one with the classic integral controller. That is to say, greater robust stability is achieved at the expense of the correction capability in the system with H∞ controller. Moreover, the greater the uncertainty is, the more proceeds the mixed sensitivity H∞ controller will produce. It proves the efficiency of the mixed sensitivity H∞ controller in dealing with uncertainty in adaptive optics system.

Highlights

IntroductionMany uncertain factors exist in its model, such as time delay and gain of system
An adaptive optics (AO) system is a complex system
5 Simulation Results From Ref. 9, the characteristic parameters of Fred constant r0 and Greenwood frequency Fg can be calculated by the power spectral density (PSD) of atmospheric turbulence

Summary

Introduction

Many uncertain factors exist in its model, such as time delay and gain of system. These uncertainties will reduce the performance, or even jeopardize its stability. It is our hope to study a method that can ensure the stability of an AO system while maintaining its correction performance. To deal with the uncertainty of time delay and gain, the multiplicative perturbation model was used modeling the system and designing the controller with H∞ theory. The system’s stability and efficiency are analyzed by computer simulation.

Principium and Model of AO System

Controller Design

Integrator

Conclusion