Global Fast Terminal Sliding Mode Control for Maglev Ball System Based on Disturbance Observer
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摘要:
为解决磁悬浮球系统模型不确定性和易受外部干扰影响的问题，提出一种基于终端滑模干扰观测器的全局快速终端滑模控制（GFTSMC）方法. 首先，分析了磁悬浮球系统的数学模型并建立动态方程；然后，设计终端滑模干扰观测器（TSMDO），用以观测和估计系统所受到的扰动，经证明，该观测器对扰动的估计误差能在有限时间内收敛；其次，为克服系统不确定性和外部干扰的影响，设计了基于终端滑模干扰观测器的全局快速终端滑模控制器，可以实现系统的全局快速收敛，所设计的控制律不含切换项，能削弱抖振，以提高系统的抗干扰性和鲁棒性；最后，对所提出的TSMDO-GFTSMC进行了仿真验证，结果表明：与基于扩张状态观测器的连续滑模控制方法相比，采用本文方法，磁悬浮小球的起浮响应时间缩短0.38 s，位移偏差减小90%，跟踪误差由0.420 mm减小为0.032 mm；本文方法提高了对干扰的观测精度，优化了磁悬浮球系统的控制效果，增强了系统的鲁棒性.
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关键词:
- 磁悬浮球系统 /
- 全局快速终端滑模控制 /
- 干扰观测器 /
- 抗干扰性 /
- 鲁棒性
Abstract:In order to solve model uncertainty and susceptibility to external disturbances of the maglev ball system, a global fast terminal sliding mode control (GFTSMC) method based on a terminal sliding mode disturbance observer (TSMDO) was proposed. Firstly, the mathematical model of the maglev ball system was analyzed, and its dynamic equation was established. Then, a TSMDO was designed to observe and estimate system disturbances. It was proven that the estimated disturbance error of the observer converged in finite time. Secondly, in order to overcome the influence of system uncertainty and external disturbance, a global fast terminal sliding-mode controller (GFTSMC) based on a TSMDO was developed to realize the global fast convergence. The designed control law did not include switching terms, which could weaken the chattering and improve the anti-disturbance and robustness of the system. Finally, the effectiveness of the proposed TSMDO-GFTSMC was verified by simulation. The results show that compared with the continuous sliding mode control method based on the extended state observer, the response time of the maglev ball floating is shortened by 0.38 s, and the displacement deviation is reduced by 90%. The tracking error is reduced from 0.420 mm to 0.032 mm. The proposed method improves the observation accuracy against disturbance, optimizes the control effect of the maglev ball system, and enhances the robustness of the system.
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图 3 小球在理想条件下起浮响应轨迹
Figure 3. Response trajectory of ball floating under ideal conditions
图 4 外部负载扰动下磁悬浮小球响应轨迹
Figure 4. Response trajectory of maglev ball under external load disturbance
图 5 内部参数扰动下磁悬浮小球响应轨迹
Figure 5. Response trajectory of maglev ball under internal parameter disturbance
图 6 复合扰动下磁悬浮小球响应轨迹
Figure 6. Response trajectory of maglev ball under complex disturbance
图 7 外部负载扰动下磁悬浮小球正弦响应轨迹
Figure 7. Sinusoidal response trajectory of maglev ball under external load disturbance
图 8 锯齿波扰动下观测器对扰动的估计与观测误差
Figure 8. Estimated and observed disturbance errors of observer under sawtooth waves
表 1 磁悬浮球系统相关参数
Table 1. Relevant parameters of maglev ball system
参数 符号 数值 小球质量 m/g 170 小球半径 r/m 0.03 线圈电感 L/mH 46.7 线圈电阻 R/Ω 13.577 线圈匝数 N/匝 1057 平衡位置 δ0/m 0.0425 平衡位置电流 i0/A 0.633 真空磁导率 μ0/(H·m−1) 4π×10−7 磁导截面积 S/m2 9π×10−4 
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