Super-Twisting Sliding Mode Control of Linear Magnetic Drive System Based on Fuzzy Variable Gain
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摘要:
针对直线磁力驱动系统的位置跟踪精度易受外部扰动等不确定因素影响以及滑模控制中的抖振问题,提出一种基于模糊变增益的超螺旋滑模控制策略. 首先,介绍直线磁力驱动系统的工作原理,建立含扰动的直线磁力驱动系统数学模型;其次,使用超螺旋滑模算法设计速度控制器,实现系统精确、快速的收敛,并通过Lyapunov函数证明系统稳定性,进一步地,使用模糊算法对超螺旋滑模增益进行自适应调节;最后,对所提复合控制方法进行实验验证. 结果表明:基于模糊变增益的超螺旋滑模控制位置跟踪精度高,响应速度快;相对于超螺旋滑模控制,阶跃位置跟踪响应时间缩短28%,稳态误差从3 μm减小到1 μm,并且没有抖振现象;正弦位置跟踪相位差减小13%,位置跟踪精度提升14%;方波位置跟踪有更好的动态性能;施加扰动后,系统到达稳态时间减小13%,受到负载之后的延迟时间减小80%,抗扰性能大幅提升.
Abstract:To enhance the position tracking accuracy of the linear magnetic drive system susceptible to uncertainties such as external perturbations and address the jitter in sliding mode control, a super-twisting sliding mode control strategy was proposed based on the fuzzy variable gain. First, the working principle of the linear magnetic drive system was introduced, and its mathematical model was established with perturbations considered. Next, a speed controller based on the super-twisting sliding mode algorithm was designed to ensure fast and accurate system convergence. The stability of the system was verified by using the Lyapunov function, and the gain of the algorithm was adaptively adjusted via a fuzzy algorithm. Finally, the proposed composite control method was validated through experiments. Results demonstrate that super-twisting sliding mode control based on the fuzzy variable gain achieves high position tracking accuracy and fast response. Compared to that of the original super-twisting sliding mode control, the step position tracking response time is reduced by 28%, and the steady state error decreases from 3 µm to 1 µm. There is no jitter. The phase difference in sinusoidal position tracking is reduced by 13%, and the tracking accuracy increases by 14%. Additionally, square wave position tracking exhibits enhanced dynamic performance. The time of the system to reach a steady state declines by 13% after perturbations are applied, and the delay time is reduced by 80% after the load is applied, significantly enhancing perturbation resistance.
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表 1 模糊规则
Table 1. Fuzzy rules
s $\dot s$ NB NM ZE PM PB NB PB PM ZE NM NB NM PM PM ZE NM NM ZE ZE ZE ZE ZE ZE PM NM NM ZE PM PM PB NB NM ZE PM PB 表 2 直线磁力驱动系统参数表
Table 2. Parameters of linear magnetic drive system
参数 M/kg Pn τ/mm ψf/Wb R/Ω Lq/mH Ld/mH 取值 2.99 5 12 5.5 3.8 0.85 0.85 表 3 控制器参数表
Table 3. Controller parameters
控制方法 参数 FST-SMA 位置环 Kp=11;速度环 k1=2, k2=10,
Ep=1.2,Ed=0.8,Ei=0.5ST-SMA 位置环 Kp=11;速度环 k1=2, k2=10 PI 位置环 Kp=11;速度环 kp=5, ki=2 表 4 正弦轨迹跟踪控制器参数表
Table 4. Parameters of sinusoidal trajectory tracking controller
控制方法 参数 FST-SMA 位置环 Kp=80;速度环 k1=4, k2=20,
Ep=1.2,Ed=0.8,Ei=0.5ST-SMA 位置环 Kp=80;速度环 k1=4, k2=20 PI 位置环 Kp=80;速度环 kp=10, ki=6 -
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