液晶自适应光学系统中倾斜镜的建模与控制

Modeling and control of Tip/Tilt Mirror in liquid crystal adaptive optical system

为了提高液晶自适应光学系统的波前探测精度,研究了该系统中倾斜镜的校正方法。分析了液晶自适应光学系统中各环节的物理特性,利用拉格朗日方程给出了倾斜镜系统模型的基本结构;采用子空间辨识方法确定了模型参数,同时利用非线性最小二乘算法对子空间模型的频域特性进行了修正。修正后模型幅频特性均方根误差为0.024 5dB,相频特性均方根误差为1.9008°。引入Smith控制策略来解决倾斜镜校正波前整体倾斜过程中的时滞问题;利用子空间辨识出的模型分别进行Smith和PID的仿真和实验验证,得到的结果与仿真计算相吻合,即在相同稳定裕度的情况下,采用Smith补偿PID算法的误差抑制带宽比传统PID算法提高了23.97%。最后,用提出的方法对一组湍流整体倾斜信号进行了校正。结果显示:采用Smith补偿PID算法的控制精度比传统PID算法提高了21.03%,证实提出的方法优化了倾斜镜的校正精度,保证了开环液晶自适应光学系统的波前探测精度。

To improve the wavefront detection accuracy of a liquid crystal adaptive optical system,a correction method for the Tip/Tilt Mirror（TTM）in the liquid crystal adaptive optical system was researched.The physical characteristics of each ingredient in the adaptive optical system were analyzed,and the basic structure of the TTM model was given based on the Lagrange equation.Then,the model parameters were acquired by using modified subspace identification method,and the frequency domain characteristics of a subspace model were corrected by nonlinear least squares algorithm.After correction,the transfer function precisions are 0.024 5dB for the amplitude and 1.900 8°for the phase in middle and low frequency domains.Furthermore,Smith predictor was introduced to solve the timedelay problem during TTM correction.The model obtained by space identification was used in the simulation and experimental verification by Smith and PID.The experiment result is coincided with simulation result.It is shown that PID with the Smith predictor is superior to traditional PID,and the error residual bandwidth of Smith predictor is enhanced by 23.97%as compared with that of the traditional PID.Finally,a signal of turbulence Tip/Tilt was generated for a correction experiment,and the experimental result shows that the control precision of PID with Smith predictor is improved by21.03%compared with that of traditional PID,which verifies that the proposed method optimizes the correction accuracy of the TTM and ensures the wavefront detection accuracy of the liquid crystal adaptive optical system.