为了克服自适应光学系统中倾斜镜的迟滞响应, 提高响应的线性度, 改善倾斜镜的控制精度, 研究了倾斜镜的迟滞非线性效应。提出了一个基于频率相关的Mutified-Prandtl-Ishlinskii (MPI) 模型的补偿方法来在线自适应逆补偿倾斜镜的迟滞非线性。结合反馈PID控制构成了自适应逆前馈复合控制方案, 其中自适应逆前馈克服了由于频率等因素引起的迟滞曲线变化, 反馈PID则改善了整体的控制性能。建立了倾斜镜二阶系统模型来估计倾斜镜系统的输出, 解决了MPI模型参考信号的问题, 避免了增加额外前馈传感器, 保证了光能量的利用率。实验结果表明, 倾斜镜系统15 Hz非线性迟滞率由原来的24.28%降为1.17%, 线性度提高了约95%, 控制精度较传统PID方法提高了约60%。该方法能够有效补偿倾斜镜的迟滞非线性, 提高了自适应光学系统中倾斜镜的校正精度。

To overcome the hysteresis of a tip/tilt mirror(TTM) in an adaptive optical system and to improve its linearity and control precision, this paper researches the nonlinear effects of the TTM. A compensation method based on the frequency-dependent Mutified-Prandtl-Ishlinskii (MPI) model is proposed for online adaptive inverse compensation of the hysteresis nonlinearity of the TTM. By combining with PID feedback control algorithm, an adaptive inverse feedforward composite control algorithm is proposed. In which, the adaptive inverse feedforward overcomes the hysteresis curve changes due to the frequency factors, and the PID algorithm improves the overall control performance. A second-order model of the TTM is established to estimate the output of the TTM system, which solves the reference signals of the MPI model, avoids adding extra feedforward sensors, and ensures the utilization of light energies. Experiment results indicate that this algorithm effectively solves the problem of hysteresis nonlinearity of the TTM, the 15 Hz hysteresis ratio of the TTM fells from 24.28% to 1.17%,and the linearity is improved by about 95%. As compared with the traditional PID algorithm, the control precision has increased by about 60%. It concludes that this composite control algorithm can compensate the hysteresis nonlinearity of the TTM effectively, and the control precision of the TTM is improved in adaptive optical systems.