Dynamics modeling and active disturbance rejection control method of translation in a magnetically suspended universally stabilized platform
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摘要:
针对空间激光通信等复杂航天任务对卫星平台高精高稳指向控制技术的迫切需求，开展球面磁悬浮万向稳定平台(MSUSP)构型设计与控制方法研究。分析MSUSP万向稳定悬浮特性，设计直角-正三棱锥构型的空间结构，建立球面磁轴承3自由度动力学模型，通过坐标变换实现磁轴承动子平动测量解耦。在此基础上，为实现外部扰动条件下的磁轴承动子稳定控制，设计基于坐标变换的3通道自抗扰控制器，将各通道之间的未建模动态及外部扰动当作合并外扰，进行跟踪、补偿，从而提高扰动条件下控制器的快速性和稳定性。分析仿真结果表明：相较于传统方法，所提方法平动阶跃响应时间缩短42.86%，不同频率正弦扰动下的磁轴承动子抗干扰性均得到大幅提升，证明了所提方法的有效性和优越性。
Abstract:In response to the urgent demand for high-precision and high-stability pointing control technology of satellite platforms for complex space missions such as space laser communication, research has been conducted on the configuration design and control method of a spherical magnetically suspended universally stabilized platform (MSUSP). Firstly, the omnidirectional stable suspension characteristics of the MSUSP were analyzed, and a space structure with a right-angled equilateral triangular pyramid configuration was designed. Coordinate transformation was used to decouple the magnetic bearing rotor translation, and a three-degree-of-freedom dynamic model of the spherical magnetic bearing was created. Based on this, in order to achieve stable control of the magnetic bearing rotor under external disturbance conditions, a three-channel self-disturbance rejection controller based on coordinate transformation was designed, which treated the unmodeled dynamics and external disturbances between each channel as merged disturbances for tracking and compensation, thereby improving the speed and stability of the controller under disturbance conditions. The effectiveness and superiority of the suggested method were demonstrated by the analysis of simulation results, which revealed that this method significantly improved the anti-interference performance of the magnetic bearing rotor under various frequency sinusoidal disturbances and reduced the step response time for translational motion by 42.86% when compared to traditional methods.
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图 3 磁轴承与径向平面夹角示意图
Figure 3. Schematic diagram of the angle between the magnetic bearing and the radial plane
图 4 磁阻力磁轴承单通道工作示意图
Figure 4. Schematic diagram of single-channel operation of magnetic resistance magnetic bearing
图 5 磁轴承坐标系与位移坐标系相对位置示意图
Figure 5. Schematic diagram of the relative positions of the magnetic bearing coordinate system and the displacement coordinate system
图 6 位移传感器相对位置示意图
Figure 6. Schematic diagram of the relative position of the displacement sensor
图 7 位移坐标系转换示意图
Figure 7. Schematic diagram of displacement coordinate system conversion
图 10 方波信号及其一阶导数的ESO观测效果
Figure 10. Effect of ESO observation of square wave signals and their first-order derivatives
图 11 正弦信号及其一阶导数的ESO观测效果
Figure 11. Effects of ESO observations of sinusoidal signals and their first-order derivatives
图 13 不同频率下抗干扰性能验证
Figure 13. Verification of anti-interference performance at different frequencies
表 1 MSUSP参数
Table 1. MSUSP parameters
$ {K}_{{\mathrm{i}}} $/(N·A−1) $ {K}_{{\mathrm{s}}} $/(N·μm−1) m/kg Lm/mH Rm/$ \Omega $ 225 0.315 14.7 4 13.5 
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表 2 ADRC参数
Table 2. ADRC parameters
r $ {h}_{0} $ $ {\delta }_{g} $ $ ({c}_{1},{c}_{2},{c}_{3}) $ $ ({\beta }_{1},{\beta }_{2}) $ $ ({\alpha }_{n1},{\alpha }_{n2}) $ $ {\delta }_{n} $ 160 0.001 0.01 (63,77,12) (100,20) (0.75,1.5) 0.08
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表 3 PID控制器参数
Table 3. PID controller parameters
$ {K}_{\text{P}} $ $ {K}_{\text{I}} $ $ {K}_{\text{D}} $ 3 0.5 10
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