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Journal of ZheJiang University (Engineering Science)  2026, Vol. 60 Issue (11): 2535-2545    DOI: 10.3785/j.issn.1008-973X.2026.11.022
    
Speed tracking control of high-speed train based on improved fuzzy sliding mode control
Junrui JIA1(),Guangwu CHEN1,*(),Jianqiang SHI1,Zhuang KANG2,Dong WANG1,Limin JIA3
1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
2. School of Information and Cybersecurity, Ningxia University, Zhongwei 755000, China
3. State Key Laboratory of Advanced Rail Autonomous Operation, Beijing Jiaotong University, Beijing 100044, China
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Abstract  

A double-hierarchical interval-type-2 fuzzy sliding mode controller was proposed to address poor tracking accuracy and low robustness of high-speed trains under complex operating environments. In the upper-layer design, an adaptive switching gain based on an interval-type-2 fuzzy logic system was developed, whereby precise estimation of external disturbances was achieved through compensating for the uncertainties of membership functions. For the lower-layer control, a hyperbolic-exponential composite power reaching law was employed, and a continuous smooth function was constructed to replace the traditional sign function. Consequently, the discontinuous switching of the control input was successfully eliminated while the fast convergence characteristics of the power reaching law were effectively retained. A simulation was conducted based on actual data of the CRH380A high-speed train running on the Suzhou North–Shanghai Hongqiao section. The velocity and displacement tracking errors of the proposed controller were 0.000 005 m/s and 0.002 82 m, respectively, achieving high-precision tracking of the target trajectory throughout the operation.



Key words: railway transportation      speed tracking control      sliding mode control      high-speed train      interval-type-2 fuzzy logic system      train running disturbance     
Received: 31 August 2025      Published: 16 October 2026
CLC:  U 284.48+1  
Fund:  国铁集团科技计划项目(N2024G056);甘肃省自然科学基金资助项目(24JRRA252);甘肃省优秀博士生资助项目(23JRRA912).
Corresponding Authors: Guangwu CHEN     E-mail: JJR807C@163.com;cgwyjh1976@163.com
Cite this article:

Junrui JIA,Guangwu CHEN,Jianqiang SHI,Zhuang KANG,Dong WANG,Limin JIA. Speed tracking control of high-speed train based on improved fuzzy sliding mode control. Journal of ZheJiang University (Engineering Science), 2026, 60(11): 2535-2545.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.11.022     OR     https://www.zjujournals.com/eng/Y2026/V60/I11/2535


基于改进模糊滑模控制的高速列车速度跟踪控制

针对高速动车组在复杂运行环境下跟踪精度差与鲁棒性低的问题,提出双层区间二型模糊滑模控制器. 上层基于区间二型模糊逻辑系统设计自适应切换增益,通过处理隶属度函数的不确定性实现对外部干扰的精准估计;下层设计双曲-指数复合幂次趋近律,构造连续光滑函数替代传统符号函数,在保留幂次趋近律快速收敛特性的同时消除控制输入的不连续切换. 以CRH380A型高速动车组在苏州北-上海虹桥路段的实际运行数据为基础进行仿真验证. 仿真结果表明,所提控制器速度与位移的跟踪误差分别为0.000 005 m/s和0.002 82 m,实现了对目标曲线的全时段高精度跟踪.


关键词: 铁路运输,  速度跟踪控制,  滑模控制,  高速列车,  区间二型模糊逻辑系统,  列车运行干扰 
Fig.1 Membership functions of variables in interval-type-2 fuzzy logic system
变量模糊规则
$ \dot{V} $NBNSZOPSPB
?kNBNSZOPSPB
?$ \eta $NBNSZOPSPB
?GNBNSZOPSPB
Tab.1 Fuzzy rules for adaptive switching gain
Fig.2 Comparison of reaching law function characteristics
Fig.3 Structure of double-hierarchical global fast-terminal interval-type-2 fuzzy sliding mode controller
Fig.4 Target speed and line information curves for selected sections of Beijing-Shanghai line
Fig.5 Response curves of disturbance estimation under different empirical coefficients
$ {G}_{1} $MAE/(10?6 m·s?2)${G}_{1} $MAE/(10?6 m·s?2)
16.058 62$ 15 $3.903 01
$ 5 $3.907 16$ 20 $3.903 07
$ 10 $1.313 58——
Tab.2 Mean absolute error of disturbance estimation under different values empirical coefficients
Fig.6 Effect of power parameter on tracking error
Fig.7 Effect of power parameter on control input
Fig.8 Effect of exponential parameter on tracking error
Fig.9 Effect of exponential parameter on control input
参数数值参数数值
$ {a}_{1} $10$ p $5
$ {a}_{2} $5$ q $3
$ {a}_{3} $10$ \delta $0.000 3
$ {a}_{4} $5——
Tab.3 Simulation parameters for speed tracking controller
Fig.10 Disturbance estimation comparison of controllers
Fig.11 Comparison of sliding surface curves for different controllers
控制器$ {\left| s\right| }_{\max } $
SMC[14]0.091 8
GFTFSMC[20]5.105 2
DH_GFTFSMC[21]0.009 0
本研究0.000 2
Tab.4 Peak deviation of sliding surface from equilibrium surface for each controller during large disturbances
Fig.12 Comparison of control inputs of sliding-mode controllers
Fig.13 Comparison of speed tracking performance of sliding-mode controllers
控制器MAE/(m·s?1)MAEs/(m·s?1)
SMC0.001 3640.002 269
GFTFSMC0.007 2540.008 649
DH_GFTFSMC0.000 4010.001 724
本研究0.000 0050.000 009
Tab.5 Statistics of speed tracking errors for sliding-mode controllers
Fig.14 Comparison of displacement tracking performance of sliding-mode controllers
控制器MAE/mMAEs/m
SMC0.023 600.060 52
GFTFSMC4.981 0116.461 00
DH_GFTFSMC0.032 760.060 95
本研究0.002 820.002 80
Tab.6 Statistics of displacement tracking errors for sliding-mode controllers
Fig.15 Comparison of speed tracking performance for different types of controllers
控制器MAE/(m·s?1)MAEs/(m·s?1)
PID[8]0.001 9580.000 126
ADRC[10]0.000 2490.000 028
本研究0.000 0050.000 009
Tab.7 Statistics of speed tracking errors for different types of controllers
Fig.16 Comparison of displacement tracking performance for different types of controllers
控制器MAE/mMAEs/m
PID0.793900.09226
ADRC0.011970.00266
本研究0.002820.00280
Tab.8 Statistics of displacement tracking errors for different types of controllers
Fig.17 Comparison of control inputs for different types of controllers
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