Levitation Control Strategy Based on Adaptive Non-singular Terminal Sliding Mode
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摘要:
针对采用传统线性滑模控制的电磁悬浮系统存在响应速度慢以及抗干扰能力差的问题，提出了一种基于自适应非奇异终端滑模的悬浮控制方法，该方法将自适应控制引入到终端滑模控制，结合滑模控制对扰动不敏感的优点，利用自适应控制对滑模趋近律系数进行在线自适应调节，改善悬浮系统的动态性能. 首先，建立了电磁悬浮系统数学模型；然后，利用李雅普诺夫稳定理论证明了所设计控制器的稳定性；最后，进行了仿真和实验验证. 实验结果表明：自适应非奇异终端滑模对信号跟踪具有更快的响应速度和更小的稳态误差，对峰峰值为2 N的正弦或锯齿干扰力气隙波动可限定在0.2 mm以内，进行0.1 kg加减载实验时气隙波动为0.6 mm，各项性能均优于终端滑模和线性滑模.
Abstract:Aiming at the problems of slow response speed and poor anti-interference ability of the traditional linear sliding mode control (LSMC) for electromagnetic levitation systems, a levitation control method based on adaptive non-singular terminal sliding mode control (ANTSMC) is proposed. The proposed method introduces an adaptive controller into the terminal sliding mode control (TSMC) to take its advantage of insensitivity to disturbance in sliding mode control. The convergence law coefficients in the sliding mode control are adjusted on line by adaptive control to improve the dynamic performance of the levitation system. First, a mathematical model of the electromagnetic levitation system is established. Then the stability of the designed controller is proved by Lyapunov stability theory. Finally, simulation and experimental verification are carried out. Experimental results show that the system with ANTSMC has a faster response speed and a smaller steady-state error in signal tracking. For sinusoidal or sawtooth interference with peak to peak value of 2 N, air gap fluctuations can be limited to 0.2 mm. The air gap fluctuates 0.6 mm during the 0.1 kg loading and unloading experiments. Generally the proposed levitation controller based on ANTSMC has better performance than those based on TSMC and LSMC.
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Key words:
- maglev /
- terminal sliding mode /
- adaptive control /
- Lyapunov function
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图 3 正弦干扰和锯齿干扰响应曲线
Figure 3. Response curves of sinusoidal disturbance and sawtooth disturbance
图 9 负载质量为0.1 kg时悬浮气隙响应曲线
Figure 9. Suspension air gap response curves withload mass of 0.1 kg
表 1 电磁悬浮球系统参数
Table 1. Parameters of the electromagnetic levitation ball system
参 数 数 值 参 数 数 值 m/kg 0.318 x0/m 0.008 N/匝 530 i0/A 2.7 A/m2 π × 10−4 
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表 2 悬浮控制器仿真参数
Table 2. Simulation parameters of levitation controllers
控制器 β ξ φ γ ε η LSMC 50 40 NTSMC 20 40 ANTSMC 10 1000 0.5 0.03 1
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表 3 悬浮控制器实验参数
Table 3. Parameters of levitation controllers
控制器 β ξ φ γ ε η LSMC 40 1 NTSMC 20 1 ANTSMC 20 100 0.5 0.03 1
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