基于改进LESO的磁浮系统非奇异终端滑模控制策略

高涛; 王龙; 杨杰; 周发助

doi:10.3969/j.issn.0258-2724.20260179

基于改进LESO的磁浮系统非奇异终端滑模控制策略

doi: 10.3969/j.issn.0258-2724.20260179

高涛^{1, 2,},
王龙^{1, 2},
杨杰^{2, 3, ,},
周发助^{1, 2}

1.
江西理工大学磁浮轨道交通装备江西省重点实验室，江西赣州 341000
2.
江西理工大学电气工程与自动化学院，江西赣州 341000
3.
上海电机学院电气学院，上海 201306

基金项目: 国家重点研发计划（2023YFB4302100），江西省自然科学基金（20252BAC200358）

详细信息

作者简介:
高涛（1991—），男，讲师，博士，研究方向为磁悬浮控制方法，E-mail：gaot.jl@foxmail.com

通讯作者:
杨杰（1979—），男，教授，博导，研究方向为轨道交通与磁悬浮控制，E-mail：yangjie@jxust.edu.cn

中图分类号: TP273
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出版历程
- 收稿日期: 2026-04-12
- 网络出版日期: 2026-11-04

Nonsingular Terminal Sliding Mode Control Strategy For Maglev Systems Based On Improved LESO

GAO Tao^{1, 2
,},
WANG Long^{1, 2},
YANG Jie^{2, 3
, ,},
ZHOU Fazhu^{1, 2}

1.
Jiangxi Key Laboratory of Maglev Rail Transit Equipment, Jiangxi University of Science and Technology, Ganzhou 341000, China
2.
School of Electrical Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou 341000, China
3.
School of Electrical Engineering, Shanghai Dianji University, Shanghai 201306, China

摘要

摘要:
针对单点电磁悬浮系统固有的强非线性力学属性，以及外部扰动与内部参数不确定性所导致的悬浮动态控制性能退化问题，提出一种基于改进线性扩张状态观测器（LESO）的非奇异快速终端滑模控制（NFTSMC）策略. 首先，建立了单电磁铁悬浮系统非线性模型；其次，针对传统滑模控制（SMC）远离滑模面时的收敛速率受限与抖振问题，基于非奇异快速终端滑模面设计控制器，通过引入改进函数提出一种新型幂次趋近律；再次，将系统不确定项、外部扰动及建模误差集总为总扰动，构建改进型LESO实现扰动实时估计与动态补偿，有效抑制抖振并提升复杂工况下抗干扰鲁棒性；同时，基于Lyapunov稳定性理论严格证明跟踪误差有限时间收敛特性；最后，通过与PID控制器、传统滑模控制器（SMC）及非奇异终端滑模控制器NFTSMC的对比仿真与实验，验证了所提控制算法在系统稳定性、动态响应、抗干扰能力方面的优越性. 实验结果表明；提出的LESO-NFTSMC控制器在外部冲击负载实验中表现出良好动态性能，在调节时间、抖振幅值及外部冲击超调量相较于SMC分别提升了52.2%、85.3%与63.6%，证明了其在动态响应、抑振和抗冲击方面的显著优势.
- 电磁悬浮系统 /
- 动力学模型 /
- 改进型线性扩张观测器 /
- 非奇异快速终端滑模 /
- 动态性能
Abstract:
To address the degradation in dynamic levitation control performance caused by the strong mechanical nonlinearities inherent in single-point electromagnetic suspension (EMS) systems, along with external disturbances and internal parameter uncertainties, a nonsingular fast terminal sliding mode control (NFTSMC) strategy based on an improved linear extended state observer (LESO) is proposed. First, a nonlinear model of the single-electromagnet suspension system was established. Second, to tackle the issues of a slow convergence rate and chattering in conventional sliding mode control (SMC) when the system state is far from the sliding surface, a controller was designed based on a nonsingular fast terminal sliding mode surface, and a novel power reaching law was proposed by introducing an improved function. Third, system uncertainties, external disturbances, and modeling errors were collectively treated as a total disturbance, and an improved LESO was developed to estimate this disturbance in real time and provide dynamic compensation, effectively suppressing chattering and improving robustness against disturbances under complex operating conditions. Meanwhile, the finite-time convergence property of the tracking error was rigorously proved based on Lyapunov stability theory. Finally, comparative simulations and experiments with a PID controller, conventional SMC, and NFTSMC were conducted to verify the superiority of the proposed control algorithm in terms of system stability, dynamic response, and anti-disturbance capability. Experimental results demonstrate that the proposed LESO-NFTSMC controller exhibits favorable dynamic performance under external impact loading. Compared with SMC, the proposed controller reduces the settling time, chattering amplitude, and overshoot under external impact loading by 52.2%, 85.3%, and 63.6%, respectively, demonstrating its significant advantages in dynamic response, vibration suppression, and impact resistance.
- electromagnetic levitation system /
- dynamic model /
- improved linear extended state observer /
- nonsingular fast terminal sliding mode /
- dynamic performance

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图 1 单点悬浮系统结构示意

Figure 1. Single-point suspension system configuration

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图 2 LESO-NFTSMC控制框图

Figure 2. LESO-NFTSMC control block

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图 3 加入脉冲激励信号的位置响应曲线

Figure 3. Position response under pulse excitation

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图 4 b取不同值时4种控制器的位置响应曲线

Figure 4. Position responses of four controllers for different values of b

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图 5 加入线性调频信号和阶跃扰动信号的位置响应曲线

Figure 5. Position response under linear chirp excitation and step disturbance

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图 6 单电磁铁悬浮实验平台

Figure 6. Single-electromagnet suspension test platform

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图 7 轨道不平顺动态跟踪实验响应曲线

Figure 7. Dynamic tracking test responses under track irregularities

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图 8 位置扰动实验响应曲线

Figure 8. Position disturbance test responses

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图 9 外部负载冲击扰动实验响应曲线

Figure 9. External load impact disturbance test responses

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表 1 悬浮系统物理参数

Table 1. Physical parameters of suspension system

参数取值参数取值

m/kg 3.22 x/mm 4

A_h/m² 0.0004 i/A 2.4

μ₀/（H·m⁻¹） 4π × 10⁻⁷ R/Ω 2.7

N 820

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表 2 两种控制器的参数

Table 2. Parameters of two controllers

参数 NFTSMC LESO-NFTSMC

k₁ 0.001 0.001

k₂ 0.009 0.009

k₄ 60 60

k₅ 60 60

k₆ 275 275

k₇ 500 500

α 1.13 1.13

β 1.07 1.07

c 0.3 0.3

d 1.3 1.3

ω₀ 110 -

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