极端环境下光学红外望远镜伺服系统模型预测

在极端环境下光学红外望远镜伺服系统建模的实际工作过程中，实测的望远镜状态数据经常包含有各种噪声。为了减小噪声对模型辨识精度的影响，提出了一种基于带有控制的非线性动力学稀疏辨识（Spark Identification of Nonlinear Dynamics with Control, SINDYc）算法的稀疏辨识方法。针对望远镜伺服系统，对SINDYc算法进行了理论分析和数值模拟，对比了在不同的噪声水平下，望远镜伺服系统预测模型的状态变量曲线，并拟合了不同噪声水平下辨识模型的决定系数曲线。基于南极望远镜实验平台，设计了正弦和方波信号作为激励信号进行模型辨识实验，对SINDYc算法的建模准确性进行了实验验证。数值模拟模型的预测输出结果显示:SINDYc算法在20%噪声水平以下时，模型辨识精度在0.99以上；在10%噪声水平以下时，状态变化跟随最大偏差值在信号幅值的5%以内。辨识实验数据表明，在两种不同信号激励下望远镜伺服系统模型预测的辨识精度分别为0.9857与0.9952，证实了基于SINDYc算法的稀疏辨识方法的有效性和准确性。该方法辨识出的系统模型可以为未来的南极大口径光学红外望远镜控制系统的分析及控制器设计提供很好的分析模型。

Model prediction of optical infrared telescope servo system in extreme environment

In practical terms of model identification for optical infrared telescope servo system, the measured states often contain noise. In order to improve accuracy of modeling, a sparse identification method based on Spark Identification of Nonlinear Dynamics with Control (SINDYc) algorithm was proposed. For the telescope servo system, theoretical analysis and numerical simulation of the SINDYc algorithm were carried out. The state variable curves of the telescope servo system model under different noise levels were compared, and the determination coefficient curve of the identification model under different noise levels was fitted. Based on the antarctic telescope experimental platform, sine and square wave signals were designed as excitation signals for model identification experiments, and the modeling accuracy of the SINDYc algorithm was experimentally verified. The prediction results of the numerical simulation model show that the identification accuracy of SINDYc algorithm is above 0.99 when the noise level is below 20%. When the noise level is below 10%, the maximum deviation is within 5% of the signal amplitude. The identification experimental data show that the accuracy of model prediction is 0.9857 and 0.9952 under the excitation of two different signals. The effectiveness and accuracy of the sparse identification method based on the SINDYc algorithm are confirmed by numerical simulation and experimental validation. The obtained model by this identification method can provide a good analytical model for the analysis and controller design of future large-aperture optical infrared telescope control systems.