Adaptive Terminal Sliding Mode Control Strategy for Electromagnetic Levitation System Based on Disturbance Compensation
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摘要:
为提高电磁悬浮系统抗干扰能力，提出一种基于扰动上界补偿的自适应非奇异终端滑模控制（ANTSMC-DUBC）策略. 该策略采用基于扰动上界补偿的非奇异终端滑模控制（NTSMC-DUBC）加快系统状态的收敛速度并避免奇异性， 到达控制律中的扰动补偿项能够抑制集总扰动，从而选择更小的开关增益来减小抖振；设计一种可随滑模函数状态自适应变化的开关增益，在保证系统动态性能的同时提高系统的稳态性能和扰动补偿效率；理论推导证明了所设计的悬浮控制器满足李雅普诺夫稳定性判据. 实验结果表明：所提出的ANTSMC-DUBC控制器在信号跟随、抗干扰和加减载实验中表现出良好的稳态性能和动态性能，并在面对系统内外扰动时具有出色的抗干扰能力；相较于NTSMC，ANTSMC-DUBC面对等效外力干扰时间隙波动小于0.21 mm，系统均方根误差和时间乘积绝对值误差分别降低56.26%和57.57%；进行1.5 kg加减载时最大间隙波动为0.22 mm，没有稳态误差.
Abstract:To improve the anti-disturbance capability of the electromagnetic levitation system, an adaptive nonsingular terminal sliding mode control based on disturbance upper bound compensation (ANTSMC-DUBC) was proposed. The strategy used nonsingular terminal sliding mode control based on disturbance upper bound compensation (NTSMC-DUBC) to speed up the convergence of the system state and avoid singularity. The disturbance compensation term in the reaching control law can suppress the lumped disturbance, so that a smaller switching gain can be selected to reduce chattering. A switching gain that can adaptively change with the state of the sliding mode function was designed to ensure the dynamic performance of the system while improving the steady state performance and the efficiency of disturbance compensation. The theoretical derivation proved that the designed levitation controller satisfied the Lyapunov stability criterion. The experimental results show that the proposed ANTSMC-DUBC controller exhibits good steady state and dynamic performance in signal tracking, anti-disturbance, and load variation tests, and demonstrates excellent anti-disturbance when facing internal and external disturbances in the system. Compared with that of NTSMC, the gap fluctuation of ANTSMC-DUBC is less than 0.21 mm under the equivalent external disturbance, and the system root mean square error and time-weighted absolute error are reduced by 56.26% and 57.57%, respectively. The maximum gap fluctuation is 0.22 mm with no steady state error when the 1.5 kg load variation is performed.
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表 2 悬浮控制器参数
Table 2. Parameters of levitation controllers
参数 NTSMC NTSMC-DUBC ANTSMC-DUBC a0 2420 2420 2420 b0 −6.05 −6.05 −6.05 β 25 25 25 p/q 19/13 19/13 19/13 k 3 1.5 μ 1000 1000 l 3 c 2000 ϕ 0.001 
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表 1 电磁悬浮系统参数
Table 1. Parameters of electromagnetic levitation system
参数 数值 悬浮质量/kg 4.43 电磁铁线圈匝数/匝 525 电磁铁磁极面积/mm2 3144.2 平衡点悬浮间隙/mm 6 平衡点线圈电流/A 2.4 电磁铁线圈电阻/Ω 2 电磁铁线圈电感/mH 91
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表 3 实验性能比较
Table 3. Experimental performance comparison
实验 指标 NTSMC NTSMC-DUBC ANTSMC-
DUBC方波跟随 eRMSE 0.1767 0.1505 0.1141 eITAE 13.1130 6.7114 4.2928 正弦波跟随 eRMSE 0.2212 0.0930 0.0622 eITAE 20.0883 7.7549 5.0415 锯齿波干扰 eRMSE 0.2721 0.0775 0.0717 eITAE 25.0468 6.2254 5.6861 正弦波干扰 eRMSE 0.2302 0.1546 0.1007 eITAE 19.1406 11.7254 8.1219 加减载实验 eRMSE 0.3018 0.1043 0.0609 eITAE 26.3091 5.5048 4.0449
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