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摘要:
快速反射镜的工作环境一般比较恶劣，容易受到振动冲击、温度变化等影响，导致故障。本文针对最为普遍的恒偏差故障，提出了一种基于线性矩阵不等式（Linear matrix inequality, LMI）的故障观测器设计方法，旨在提高故障检测的可靠性，增强快速反射镜的稳定性以及抗干扰能力。首先，采用基于汉克尔（Hankel）矩阵的模型辨识方法得到了考虑耦合效应的两轴快速反射镜模型。然后，建立了快速反射镜系统的故障模型，采用基于LMI的方法对快速反射镜的故障观测器进行设计。最后，通过仿真与实验对该方法进行验证。结果表明，当快速反射镜的两轴发生执行器和传感器恒偏差故障时，基于黎卡提（Riccati）方程的故障观测器只能检测出其中一个轴的故障，基于LMI的故障观测器对
X 轴能在故障发生后0.1 s内检测出故障，对Y 轴能在故障发生后0.06 s内检测出故障。上述结果表明本文设计的LMI故障观测器能够更加准确地实现对快速反射镜的故障检测。Abstract:Fast steering mirror (FSM) typically operates in harsh environments, susceptible to vibrations, temperature fluctuations, and other factors, which can lead to malfunctions. Focusing on the most prevalent constant bias fault, this paper proposes an LMI-based fault observer design method, aiming to enhance the reliability of fault detection and strengthen the stability and anti-interference capabilities of the FSM. Firstly, the model identification method based on Hankel matrix is employed to identify the two-axis fast steering mirror model including the coupling effect. Then, the fault model of the fast steering mirror system is established, and the fault observer of the fast steering mirror is designed by using the LMI-based method. Finally, the proposed method is verified through simulations and experiments. The results indicate that when both axes of the fast steering mirror have constant bias faults in the actuators and sensors, the Riccati-based fault observer can only detect the fault in one axis, while the LMI-based fault observer can detect faults within 0.1 seconds after the fault of the X-axis occurs, and detect faults within 0.06 seconds after the fault of the Y-axis occurs. Therefore, the fault observer designed by the LMI method proposed in this paper can improve the fault detection performance of the fast steering mirror.
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图 2 考虑耦合效应的两轴FSM系统框图
Figure 2. The system diagram of two-axis FSM considering coupling effects
图 4 辨识模型与实际系统频域响应特性曲线对比
Figure 4. The comparison between of frequency responses of identified model and real systems
图 7 传感器故障时基于Riccati的偏转角残差
Figure 7. The residuals of angle calculated by the Riccati when the sensor malfunctions
图 8 传感器故障时基于Riccati的评价函数与阈值
Figure 8. The evaluation function and threshold calculated by the Riccati when the sensor malfunctions
图 9 传感器故障时基于LMI的偏转角残差
Figure 9. The residuals of angle calculated by the LMI when the sensor malfunctions
图 10 传感器故障时基于LMI的评价函数与阈值
Figure 10. The evaluation function and threshold by the LMI when the sensor malfunctions
图 11 传感器和执行器同时故障基于Riccati的偏转角残差
Figure 11. The residuals of angle calculated by the Riccati when both the sensor and the actuator malfunction
图 12 基于Riccati的评价函数与阈值
Figure 12. The evaluation function and threshold by the Riccati
图 14 传感器和执行器同时故障基于LMI的评价函数与阈值
Figure 14. The evaluation function and threshold by the LMI when both the sensor and the actuator malfunction
图 17 基于Riccati的评价函数与阈值
Figure 17. The evaluation function and threshold by the Riccati
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