| The adaptive optics(AO)system can compensate the random wavefront aberration caused by medium change or internal disturbance of the optical systemduring the transmission of the wavefront,improving the imaging resolution or the quality of the laser beam.Wavefront control technology is one of the key technologies of AO system,directly determining the correction performance of the system.Wavefront control mainly consists of two control loops,the tip-tilt mirror and the deformable mirror,which are used to correct the overall tilt and higher order aberrations of the wavefront,respectively.The two are independent and can be studied separately.In the current AO system,the most common control method is classical integral control owing to its simple structure and easy realization.However,it is hardfor this method to ensure the stability of the system and the optimal correction performance,and it is very difficult to be adjusted in complex systems with multi loops.To improve the performance of the system,several modern control methods are introduced to study the AO system,such as adaptive predictive control and optimal control,but these control methods rely heavily on system model and turbulence model,and it is difficult to guarantee the stability of the system as well as the correction capabilityunder the influence of uncertainty.To solve these problems,the research of robust control technology in AO system is proposed in this paper.It is expected to improve the robust stability and correction performance of the system at the same time.For partial failure of AO system,the 0-1fault model is also proposed to describe fault status of the system.This dissertation focuses on the stability of the system,and has carried out the following researches:Firstly,the uncertainty that may exist in the system is discussed,and theuncertainty model of the system is established.In this dissertation,static and delay characteristics of AO system are discussed from three aspects,namely the wavefront restoration algorithm,the SVD decoupling algorithm and the time delay of signal transmission.Uncertainty that may exist in AO system is reduced to gain uncertainty and delay uncertainty of control loop.A mathematical model of AO system is established as the basis of robust H_?controller design.Secondly,a H_?controller is designed forSingle-Input-Single-Output(SISO)control loopof the AO system,and the effectiveness of the algorithm is verified byfrequency domain and time domain simulation.Due to large scale of input and output of AO system,direct design of controller is complex,andthe computation time of wavefront reconstruction as well as the difficuty to design hardware will be greatly increased.What's more,real-time requirements of the system will also be reduced.Therefore,decoupling algorithm is employed in this dissertation,which decomposes AO system into multiple parallel SISO control loops,and designs controller independently for each loop.According to different working conditions,AO system contains two situations where gain uncertainty exists only and gain and delay uncertainties exist simultaneously.H_?controller is designed for these two cases in this dissertation.Simulations of frequency domain analysis and turbulence correction prove that the algorithm can improve the robustness and stability margin of the system without losing correction capability.Compared with integral control,under the condition where gain uncertainty exists only,the robust stability index of the system decreases from 0.6336 to 0.4398,and the phase margin increases by 8.659°to the maximum.In situation where gain and delay uncertainties exist simultaneously,the robust stability index of the system is reduced from 0.4375 to 0.3821,and the phase margin is raised by10.4975°.Correction capability of the system even increases to a certain extentwhen gain and delay get larger.Thirdly,the correction capability and stability of H_?control are verified in Multiple-Input-Multiple-Output(MIMO)control loop.AO system is typical MIMO control system;therefore,it is necessary to verify the effectiveness of the algorithm in this kind ofcontrol loop.In this dissertation,simulated data of atmospheric random phase screengenerated by Matlab toolbox are used as inputs.And AO system with61-unit-drive deformable mirror and80-subaperture Hartmann isused as the simulation object to carry out simulation of turbulence correction.Results show that H_?control can improve the stability of the AO system without losing the correction capability in cases where gain uncertainty exists only and gain and delay uncertainties exist simultaneously.When the system is under design state,the residual wavefront RMS value of integral control is slightly smaller,but the value of PV is slightly larger,the correction results of the two control methods are very close.When uncertainty range of the system increases to a certain extent,integral control can not guarantee the stability of the system,while using H_?control can ensuresteady work of the system even though the correction capability decreases.The simulation results agree with the expectation,indicating the effectiveness of the algorithm.Fourthly,to effectively describe failure states of AO system,the 0-1 fault model is used to model partial failure of the system.Under normal working condition,traditional model of AO system can efficiently describe the working state of the system and ensure stability of the system,but when parts of the AO system fail,it cannot reflect the working state of the system correctly,making it difficult for the system to work steadily.In this dissertation,therefore,the 0-1 fault model is proposed to model the partial failure of AO system.States of actuators and deformable mirrors of the Hartmann sensor's sub aperture is described by two diagonal switch arrays,which can effectively describe partial failure of the system.Simulation and experimental results show that when parts of the AO system fail,under the traditional model the system cannot work steadily because control voltage diverges,but when adopting the 0-1 fault model,it works steadily and achieves the desired effect even though the correction capability decreases slightly.In this dissertation,research of robust control technology in AO system shows that this method can improve stability of the system without losing correction capability to distorted wavefront,showing practical and theoretical significance.The 0-1 fault model,which can effectively describe failure states of actuators and deformable mirrors of Hartmann sensor's subapertures,is of obvious engineering significance.The model can also be applied to the research of fault-tolerant AO system and intelligent AO system,which indicates certain theoretical significance. |
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