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Adaptive Nonsingular Terminal Sliding Mode Tracking Control for High-speed Trains With Input Constraints and Parametric Uncertainties

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  • Control Theory and Applications
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Abstract

In this paper, a finite-time tracking control strategy for high-speed trains (HSTs) subjected to input constraints and parameter uncertainties is proposed based on adaptive nonsingular terminal sliding mode control (ANTSMC), which achieves the fast and precise displacement-speed trajectory tracking and energy saving results. The dynamic model of HST is established with the basic, additional, and external disturbances firstly. To handle input constraints, a smooth hyperbolic function is designed to approximate saturation function, which guarantees that the control signal does not exceed traction/braking characteristics and ensures safe operation. Then, an adaptive mechanism is used to estimate the upper bounder of the lumped uncertainty and controller’s parameters. Subsequently, the proposed ANTSMC methodology not only assures the finite-time convergence of position and velocity tracking errors, but also effectively compensates parameter uncertainties of the proposed model. Finally, numerical simulations indicate that the proposed method spends the less traction energy in obtaining the better tracking performance of HST.

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References

  1. X. W. Dai, H. Zhao, S. P. Yu, D. L. Cui, Q. Zhang, H. R. Dong, and T. Y. Chai, “Dynamic scheduling, operation control and their integration in high-speed railways: A review of recent research,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 9, pp. 13994–14010, December 2021.

    Article  Google Scholar 

  2. M. Jiang, “Safety risk analysis and development trend of high-speed railway automatic train operation system,” Railway Signaling and Communication Engineering, vol. 16, no. 4, pp. 1–6, April 2019.

    CAS  Google Scholar 

  3. P. Singh and M. P. R. Prasad, “Stability control of high-speed train using robust PID controller,” Proc. of 3rd Conference on Electronics, Communication and Aerospace Technology, pp. 664–668, July 2019.

  4. H. R. Dong, B. Ning, B. G. Cai, and Z. S. Hou, “Automatic train control system development and simulation for high-speed railways,” IEEE Circuits and Systems Magazine, vol. 10, no. 2, pp. 6–18, April 2010.

    Article  Google Scholar 

  5. H. Zhao, X. W. Dai, Q. Zhang, and J. L. Ding, “Robust event-triggered model predictive control for multiple high-speed trains with switching topologies,” IEEE Transactions on Vehicular Technology, vol. 69, no. 5, pp. 4700–4710, May 2020.

    Article  Google Scholar 

  6. L. J. Zhang and X. T. Zhuan, “Optimal operation of heavyhaul trains equipped with electronically controlled pneumatic brake systems using model,” IEEE Transactions on Control Systems Technology, vol. 22, no. 1, pp. 13–22, January 2013.

    Article  CAS  Google Scholar 

  7. Q. Song, Y. D. Song, and W. C. Cai, “Adaptive backstepping control of train systems with traction/braking dynamics and uncertain resistive forces,” Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility, vol. 49, no. 9, pp. 1441–1454, May 2013.

    Article  ADS  Google Scholar 

  8. X. J. Tian, D. Q. Huang, N. Qin, Z. F. Gong, and Q. Y. Wang, “Guaranteed cost optimal control of high-speed train with time-delay in cruise phase,” International Journal of Control, Automation, and Systems, vol. 19, no. 9, pp. 2971–2983, September 2021.

    Article  Google Scholar 

  9. H. R. Dong, X. Lin, S. G. Gao, B. G. Cai, and B. Ning, “Neural networks-based sliding mode fault-tolerant control for high-speed trains with bounded parameters and actuator faults,” IEEE Transactions on Vehicular Technology, vol. 69, no. 2, pp. 1353–1362, May 2020.

    Article  Google Scholar 

  10. Z. H. Mao, X. G. Yan, B. Jiang, and M. Chen, “Adaptive fault-tolerant sliding-mode control for high-speed trains with actuator faults and uncertainties,” IEEE Transactions on Intelligent Transportation Systems, vol. 21, no. 6, pp. 2449–2460, June 2020.

    Article  Google Scholar 

  11. C. F. Xu, X. Y. Chen, X. Zheng, Y. Wang, and W. D. Li, “Slip velocity tracking control of high-speed train using dynamic surface method,” Journal of The China Railway Society, vol. 42, no. 2, pp. 41–49, February 2020.

    Google Scholar 

  12. X. Wang, H. W. Wang, T. Tang, and K. C. Li, “Robust distributed cruise control of multiple high-speed trains based on disturbance observer,” IEEE Transactions on Intelligent Transportation Systems, vol. 22, no. 1, pp. 267–279, January 2020.

    Article  Google Scholar 

  13. X. Lin, H. R. Dong, X. M. Yao, and W. Q. Bai, “Neural adaptive fault-tolerant control for high-speed trains with input saturation and unknown disturbance,” Neurocomputing, vol. 260, pp. 32–42, February 2017.

    Article  Google Scholar 

  14. Z. K. Jin, Z. Y. Yang, X. Wang, and M. W. Zheng, “Adaptive backstepping sliding mode control of tractor-trailer system with input delay based on RBF neural network,” International Journal of Control, Automation and Systems, vol. 19, no. 1, pp. 76–87, October 2020.

    Article  Google Scholar 

  15. H. H. Ji, Z. S. Hou, and R. K. Zhang, “Adaptive iterative learning control for high-speed trains with unknown speed delays and input saturations,” IEEE Transactions on Intelligent Transportation Systems, vol. 13, no. 1, pp. 260–273, January 2016.

    Google Scholar 

  16. L. Zhu, X. F. Li, D. Q. Huang, H. R. Dong, and L. C. Cai, “Distributed cooperative fault-tolerant control of highspeed trains with input saturation and actuator faults,” IEEE Transactions on Intelligent Vehicles, vol. 8, no. 2, pp. 1241–1251, 2023.

    Article  Google Scholar 

  17. G. B. Zhu, J. L. Du, and Y. G. Kao, “Command filtered robust adaptive NN control for a class of uncertain strict-feedback nonlinear systems under input saturation,” Journal of the Franklin institute, vol. 355, no. 15, pp. 7548–7569, October 2018.

    Article  MathSciNet  Google Scholar 

  18. D. Q. Huang, S. Yi, and X. F. Li, “Accurate parking control for urban rail trains via robust adaptive backstepping approach,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 11, pp. 21790–21798, November 2022.

    Article  Google Scholar 

  19. X. W. Bu, Q. Qi, and B. X. Jiang, “A simplified finite-time fuzzy neural controller with prescribed performance applied to waverider aircraft,” IEEE Transactions on Fuzzy Systems, vol. 30, no. 7, pp. 2529–2537, July 2022.

    Article  Google Scholar 

  20. X. W. Bu, B. X. Jiang, and H. M. Lei, “Nonfragile quantitative prescribed performance control of waverider vehicles with actuator saturation,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 4, pp. 3538–3548, August 2022.

    Article  ADS  Google Scholar 

  21. Y. Feng, X. H. Yu, and Z. H. Man, “Non-singular terminal sliding mode control of rigid manipulators,” Automatica, vol. 33, pp. 2159–2167, December 2002.

    Article  MathSciNet  Google Scholar 

  22. S. D. Xu, C. C. Chen, and Z. L. Wu, “Study of nonsingular fast terminal sliding-mode fault-tolerant control,” IEEE Transactions on Industrial Electronics, vol. 62, no. 6, pp. 3906–3913, June 2015.

    Google Scholar 

  23. S. H. Ding and W. X. Zheng, “Nonsingular terminal sliding mode control of nonlinear second-order systems with input saturation,” International Journal of Robust and Nonlinear Control, vol. 26, pp. 1857–1872, July 2015.

    Article  MathSciNet  Google Scholar 

  24. M. Van, M. Mavrovouniotis, and S. S. Ge, “An adaptive backstepping nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 49, no. 7, pp. 1448–1458, July 2019.

    Article  Google Scholar 

  25. Z. G. Han, K. Zhang, T. S. Yang, and M. H. Zhang, “Spacecraft fault-tolerant control using adaptive non-singular fast terminal sliding mode,” IET Control Theory and Applications, vol. 10, no. 16, pp. 1–9, August 2016.

    Article  MathSciNet  CAS  Google Scholar 

  26. J. T. Fei and Z. L. Feng, “Fractional-order finite-time super-twisting sliding mode control of micro gyroscope based on double-loop fuzzy neural network,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 51, no. 12, pp. 7692–7706, December 2021.

    Article  Google Scholar 

  27. X. M. Yao, J. H. Park, H. R. Dong, L. Guo, and X. Lin, “Robust adaptive nonsingular terminal sliding mode control for automatic train operation,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 49, no. 12, pp. 2406–2415, December 2019.

    Article  Google Scholar 

  28. P. Wu, Q. Y. Wang, and X. Y. Feng, “Automatic train operation based on adaptive terminal sliding mode control,” International Journal of Automation and Computing, vol. 12, no. 2, pp. 142–148, April 2015.

    Article  Google Scholar 

  29. Z. Rao, Train Traction Calculation, Beijing, China Railway Publishing House, 2010.

    Google Scholar 

  30. P. M. Tiwari, S. Janardhanan, and M. Un-Nabi, “Rigid spacecraft fault-tolerant control using adaptive fast terminal sliding mode,” Advances and Applications in Sliding Mode Control systems, vol. 576, pp. 381–406, November 2014.

    Article  Google Scholar 

  31. L. Edalati, A. K. Sedigh, M. A. Shooredeli, and A. Moarefianpour, “Adaptive fuzzy dynamic surface control of nonlinear systems with input saturation and time-varying output constraints,” Mechanical Systems and Signal Processing, vol. 100, pp. 311–329, February 2018.

    Article  ADS  Google Scholar 

  32. S. P. Yu, X. H. Yu, B. Shirinzadeh, and D. H. Man, “Continuous finite-time control for robotic manipulators with terminal sliding mode,” Automatica, vol. 41, pp. 1957–1964, November 2005.

    Article  MathSciNet  Google Scholar 

  33. Q. Y. Wang, P. Wu, X. Y. Feng, and Y. D. Zhang, “Precise automatic train stop control algorithm based on adaptive terminal sliding mode control,” Journal of the China Railway Society, vol. 38, no. 2, pp. 56–63, February 2016.

    CAS  Google Scholar 

  34. X. K. Lu, F. Yang, and Q. S. Wang, “Research on traction calculation and simulation system of high-speed railway,” Railway Standard Design, vol. 63, no. 4, pp. 9–16, April 2019.

    Google Scholar 

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Authors and Affiliations

  1. School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Zikang Li, Deqing Huang & Liangcheng Cai

  2. Key Laboratory of Railway Industry of Advanced Energy Traction and Comprehensive Energy Conservation, Southwest Jiaotong University, Chengdu, 610031, China

    Zikang Li, Deqing Huang & Liangcheng Cai

Authors
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Correspondence to Liangcheng Cai.

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This work was supported by the Sichuan Science and Technology Program under Grants 2020YFQ0057 and 2021JDJQ0012, and the National Natural Science Foundation of China under Grants U1934221 and U21A20169.

Zikang Li received his B.S. degree in electrical engineering and automation from East China Jiaotong University, Nanchang, China, in 2017. He is currently pursuing an M.S. degree in control engineering with the School of Electrical Engineering, Southwest Jiaotong University, Chengdu. His current research interests include adaptive sliding mode control and operation control of high-speed trains.

Deqing Huang received his B.S. and Ph.D. degrees in applied mathematics from the Mathematical College, Sichuan University, Chengdu, China, in 2002 and 2007, respectively, and the second Ph.D. degree in control engineering from the Department of Electrical and Computer Engineering (ECE), National University of Singapore (NUS), Singapore, in 2011. From January 2010 to February 2013, he was a Research Fellow at the Department of Electrical and Computer Engineering of NUS. From March 2013 to January 2016, he was a Research Associate at the Department of Aeronautics, Imperial College London, London, UK. In January 2016, he joined as a Professor and the Department Head with the Department of Electronic and Information Engineering, Southwest Jiaotong University, Chengdu, China. His research interests include modern control theory, artificial intelligence, fault diagnosis, and robotics.

Liangcheng Cai received his B.Sc. degree in mathematics from Sichuan Normal University, Chengdu, China, in 2006, and an M.Sc. degree in applied mathematics and a Ph.D. degree in control science and engineering from Central South University, Changsha, China, in 2008 and 2013, respectively. He is currently a Lecturer in the School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China. His research interests include analysis and control of nonlinear system.

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Li, Z., Huang, D. & Cai, L. Adaptive Nonsingular Terminal Sliding Mode Tracking Control for High-speed Trains With Input Constraints and Parametric Uncertainties. Int. J. Control Autom. Syst. 22, 753–764 (2024). https://doi.org/10.1007/s12555-022-0659-6

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  • DOI: https://doi.org/10.1007/s12555-022-0659-6

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