Non-Singular Fast Terminal Sliding Mode Rotor Position Control of Active Magnetic Bearings
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摘要:
针对主动磁悬浮轴承转子位置控制中系统响应速度慢、抗干扰能力弱等问题，本文提出将非奇异快速终端滑模函数与改进超螺旋趋近律相结合的位置控制方法，以获得快速、精确的动态响应控制效果. 由于系统内扰和外扰的存在，需要对滑模趋近律增加常值切换增益以保证系统的强鲁棒性，但会使得系统抖振进一步变大，本文通过采用非线性扩张状态观测器对干扰进行实时观测并动态补偿，折衷了抖振与抗干扰性之间的矛盾；通过李雅普诺夫稳定性理论证明了所提方法的稳定性，并对提出的控制方法进行仿真与实验验证. 研究结果表明：与传统的滑模控制器相比，所设计的控制器具有更快的响应速度和更强的抖振抑制能力，转子达到目标位置的时间缩短了56.4%，系统动态性能得到改善；控制电流的平均值减小了68.5%，系统抑制抖振的能力增强，即算法具有较强的鲁棒性.
Abstract:In order to solve problems of slow system response speed and poor anti-interference ability in the position control of the rotor of active magnetic bearings (AMBs), a position control method combining the non-singular fast terminal sliding function with the improved super-twisting reaching law was proposed to obtain fast and accurate control effects of dynamic responses. In addition, due to internal and external interference in the system, constant switching gain was added to the sliding mode reaching law, so as to ensure the robustness of the system, but it could exacerbate the system chattering. Therefore, the interference was observed and compensated by a nonlinear extended state observer, which alleviated the contradiction between chattering and anti-interference. Then, the stability of the proposed method was proven Lyapunov stability theory, and the proposed control method was verified by simulation and experiment. The results show that compared with the traditional sliding mode controller, the designed controller has faster response speed and stronger chattering suppression ability, and the time for the rotor to reach the target position is shortened by 56.4%. The dynamic performance of the system is improved, and the average control current is reduced by 68.5%. The chattering suppression ability of the system is enhanced, indicating that the proposed algorithm has strong robustness.
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图 3 非奇异快速终端滑模函数结构
Figure 3. Structure of non-singular fast terminal sliding mode function
图 10 正弦追踪中转子位移和电流信号
Figure 10. Displacement and current signal of rotor under sinusoidal trace
图 11 方波追踪中转子位移和电流信号
Figure 11. Displacement and current signal of rotor under square wave trace
图 13 集总干扰作用下转子起浮位移和电流信号
Figure 13. Displacement and current signal in case of rotor suspension under lumped interference
图 14 NESO补偿后转子起浮位移和电流信号
Figure 14. Displacement and current signal in case of rotor suspension with NESO compensation
图 15 磁悬浮高速电机转子系统实验平台
Figure 15. Experimental platform of rotor system with magnetic suspension high-speed motor
图 16 转子起浮位移和电流信号
Figure 16. Displacement and current signal in case of rotor suspension
图 17 扰动作用下转子起浮位移和电流信号
Figure 17. Displacement and current signal in case of rotor suspension under interference
图 18 NESO补偿后转子起浮位移和电流信号
Figure 18. Displacement and current signal in case of rotor suspension with NESO compensation
表 1 AMBs参数
Table 1. Parameters of AMBs
参数 值 磁极面积/mm2 720 匝数/Turn 150 气隙长度/mm 0.4 偏置电流/A 2 转子质量/Kg 15 电流刚度系数/N/A 939.5 位移刚度系数/N/mm 4697.5 
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表 2 控制器参数
Table 2. Parameters of controller
控制器 值 SNFTSMC k1=1、k2=0.1、k3=80、k4=50、a=2.5、b=1.5、γ=1.5、λ=1、η=0.5、M=15 SMC k1=30、k2=50、c=10、M=15
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