The dynamic control process in an adaptive optics (AO) system is the third important factor to affect the performances of the AO system. A numerical simulation of the dynamic control process in an AO system is carried out for the first time to complete a comprehensive numerical simulation of an AO system. By means of the numerical simulation the long-exposure Strehl ratio and other useful metrics for evaluating the performances of an AO system can be obtained. In comparison to the theoretical analyses of automatic control theory, a numerical simulation of the dynamic control process in an AO system is advantageous. The frequency response characteristics are closely related to the dynamic control performance of an AO system. The bandwidth, phase margin and gain margin which are very important parameters for experimenters can be obtained conveniently from a numerical simulation of the frequency response characteristics. A numerical simulation of the frequency response characteristics in an AO system is presented in this paper for the first time. The numerical simulation results agree with the experimental data excellently. The simulation computational results of frequency response by using composite input of multiple frequencies compare to the single-frequency simulation results very well and can be used to determine the practical parameters of bandwidth and margins. The performances of an AO system can be effectively investigated by means of a combination of a numerical simulation of frequency response characteristics with that of the dynamic control process.

Phase compensation effectiveness and long time period working stability are two most important performances of an adaptive optics (AO) system. Effects of reconstruction matrix and controller coefficients on these performances are investigated by means of a pure numerical simulation in this paper. A new modified reconstruction matrix is proposed and compared with other existing matrixes in practical application. It is shown that the recently proposed reconstruction matrix can produce better phase compensation results and much better long time period working stability in an AO system. Different reconstruction matrix can greatly affect the long time period working stability under certain conditions. Under some conditions, an AO system with a reconstruction matrix can work stably in a quite long time period, but a working instability can occur in a super-long time period. It is found that the controller coefficients have even greater effect on the long time period working stability in an AO system. The controller coefficient a1=l .00 is a marginally stable (sub-stable) condition for an AO system. When a1<1, the long time period working stability of an AO system is much improved.