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Longitudinal Vehicle Stability Control Based on Modified Sliding Mode Control

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Abstract

In order to improve speed tracking accuracy and ensure longitudinal stability control in vehicles under conditions of parameter uncertainty and external interference, this study introduces a modified sliding mode control (SMC) method. The proposed method replaces the reaching rate function in conventional SMC with a saturation function, which effectively reduces the chattering phenomenon in the control process. The longitudinal modified SMC method consists of two stages for both driving and braking control, designed according to the longitudinal vehicle dynamics model. Within the first stage, the control law determines the engine torque or brake torque; while the second stage oversees the modulation of throttle opening or brake pressure. To ensure a smooth transition between driving and braking modes, switching rules are defined predicated on predefined thresholds governing the driving or braking torque and speed errors. The stability of this control system is verified through Lyapunov stability analysis. To validate the effectiveness and practicality of the algorithm, simulations are performed using CarSim/Simulink, and experiments are conducted on a hybrid Lincoln MKZ. Results from both simulations and experiments demonstrate that the modified SMC method improves speed tracking accuracy and longitudinal control stability, even when dealing with rapidly changing speeds. Moreover, the algorithm exhibits a remarkable ability to resist external interference, making it a reliable solution for real-world applications.

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Abbreviations

LQR:

Linear quadratic regulator

MPC:

Model predictive control

PID:

Proportional integral derivative

SMC:

Sliding mode control

References

  1. Li, Y., Ruan, J., Li, C., Fu, M.: Longitudinal motion control of intelligent vehicle. Chin. J. Mech. Eng. 42(11), 94–102 (2006)

    Article  Google Scholar 

  2. Shakouri, P., Ordys, A., Laila, D.S., Askari, M.: Adaptive cruise control system: comparing gain-scheduling PI and LQ controllers. IFAC Proc. Vol. 44(1), 12964–12969 (2011). https://doi.org/10.3182/20110828-6-IT-1002.02250

    Article  Google Scholar 

  3. Karafyllis, I., Theodosis, D., Papageorgiou, M.: Lyapunssov-based two-dimensional cruise control of autonomous vehicles on lane-free roads. Automatica 145, 110517 (2022). https://doi.org/10.1016/j.automatica.2022.110517

    Article  Google Scholar 

  4. Jo, A., Lee, H., Seo, D., Yi, K.: Model-reference adaptive sliding mode control of longitudinal speed tracking for autonomous vehicles. Proc. Inst. Mech. Eng. Part D-J. Automob. Eng. 237(2–3), 493–515 (2023). https://doi.org/10.1177/09544070221077743

  5. Nie, L., Guan, J., Lu, C., Yin, Z., Zheng, H.: Longitudinal speed control of autonomous vehicle based on a self-adaptive PID of radial basis function neural network. IET Intell. Transp. Syst. 12(6), 485–494 (2018). https://doi.org/10.1049/iet-its.2016.0293

    Article  Google Scholar 

  6. Guo, N., Zhang, X., Zou, Y.: Real-time predictive control of path following to stabilize autonomous electric vehicles under extreme drive conditions. Automot. Innov. 5(4), 453–470 (2022). https://doi.org/10.1007/s42154-022-00202-3

    Article  Google Scholar 

  7. Visioli, A.: Practical PID control. Springer Science & Business Media (2006)

  8. Åström, K.J., Hägglund, T.: Advanced PID Control. Research Triangle Park, ISA-The Instrumentation, Systems, and Automation Society (2006)

  9. Kebbati, Y., Ait-Oufroukh, N., Vigneron, V., Ichalal, D., Gruyer, D.: Optimized self-adaptive PID speed control for autonomous vehicles. Paper presented at the 2021 IEEE International Conference on Automation and Computing, Portsmouth, United Kingdom, 2–4 September 2021

  10. Xu, L., Lu, J., Zhang, J.: Speed control of pure electric vehicle based on adaptive fuzzy PID controller. Paper presented at the International Symposium for Intelligent Transportation and Smart City 2017 Proceedings, Springer, Singapore (2017)

  11. Toulotte, P.-F., Delprat, S., Guerra, T.-M., Boonaert, J.: Vehicle spacing control using robust fuzzy control with pole placement in LMI region. Eng. Appl. Artif. Intell. 21(5), 756–768 (2008). https://doi.org/10.1016/j.engappai.2007.07.009

    Article  Google Scholar 

  12. Enache, N.M., Mammar, S., Glaser, S., Lusetti, B., Nouvelière, L.: Composite lyapunov based vehicle longitudinal control assistance. Paper presented at the 2009 IEEE European Control Conference, Budapest, Hungary, 23–26 August 2009

  13. Kim, H., Kim, D., Shu, I., Yi, K.: Time-varying parameter adaptive vehicle speed control. IEEE Trans. Veh. Technol. 65(2), 581–588 (2015). https://doi.org/10.1109/TVT.2015.2402756

    Article  Google Scholar 

  14. Kebbati, Y., Ait-Oufroukh, N., Vigneron, V., Ichalal, D.: Coordinated PSO-PID based longitudinal control with LPV-MPC based lateral control for autonomous vehicles. Paper presented at the 2022 IEEE European Control Conference, London, United Kingdom, 12–15 July 2022

  15. Chen, L., Qin, Z., Hu, M., Bian, Y., Peng, X.: Path Tracking Controller Design of Automated Parking Systems via NMPC with an Instructible Solution. PREPRINT (Version 1) available at Research Square (2022). https://doi.org/10.21203/rs.3.rs-1388380/v1

  16. Cheng, S., Li, L., Guo, H.Q., Chen, Z., Peng, S.: Longitudinal collision avoidance and lateral stability adaptive control system based on MPC of autonomous vehicles. IET Intell. Transp. Syst. 21(6), 2376–2385 (2019). https://doi.org/10.1109/TITS.2019.2918176

    Article  Google Scholar 

  17. Zhu, M., Chen, H., Xiong, G.: A model predictive speed tracking control approach for autonomous ground vehicles. Mech. Syst. Signal Proc. 87, 138–152 (2017). https://doi.org/10.1016/j.ymssp.2016.03.003

    Article  Google Scholar 

  18. Chen, S., Chen, H., Negrut, D.: Implementation of MPC-based path tracking for autonomous vehicles considering three vehicle dynamics models with different fidelities. Automot. Innov. 3(4), 386–399 (2020). https://doi.org/10.1007/s42154-020-00118-w

    Article  Google Scholar 

  19. He, X., Lou, B., Yang, H., Lv, C.: Robust decision making for autonomous vehicles at highway on-ramps: a constrained adversarial reinforcement learning approach. IET Intell. Transp. Syst. 24(4), 4103–4113 (2022). https://doi.org/10.1109/TITS.2022.3229518

    Article  Google Scholar 

  20. Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding Mode Control and Observation. Springer, New York (2014)

    Book  Google Scholar 

  21. Liang, H., Chong, K.T., No, T.S., Yi, S.-Y.: Vehicle longitudinal brake control using variable parameter sliding control. Control. Eng. Pract. 11(4), 403–411 (2003). https://doi.org/10.1016/S0967-0661(02)00176-4

    Article  Google Scholar 

  22. Nouveliere, L.: Experimental vehicle longitudinal control using a second order sliding mode technique. Control. Eng. Pract. 15(8), 943–954 (2007). https://doi.org/10.1016/j.conengprac.2006.11.011

    Article  Google Scholar 

  23. Plestan, F., Shtessel, Y., Bregeault, V., Plestan, F.: New methodologies for adaptive sliding mode control. Int. J. Control. 83(9), 1907–1919 (2010). https://doi.org/10.1080/00207179.2010.501385

  24. Yau, H.T., Kuo, C.L., Yan, J.J.: Fuzzy sliding mode control for a class of chaos synchronization with uncertainties. Int. J. Nonlinear Sci. Numer. Simul. 7(3), 333–338 (2006). https://doi.org/10.1515/IJNSNS.2006.7.3.333

    Article  Google Scholar 

  25. Xu, S., Peng, H., Song, Z., Chen, K., Tang, Y.: Accurate and smooth speed control for an autonomous vehicle. Paper presented at the 2018 IEEE Intelligent Vehicles Symposium, Changshu, China, 26–30 June 2018

  26. Xu, S., Peng, H., Song, Z., Chen, K., Tang, Y.: Design and test of speed tracking control for the self-driving lincoln MKZ platform. IEEE Trans. Intell. Veh. 5(2), 324–334 (2019). https://doi.org/10.1109/TIV.2019.2955908

    Article  Google Scholar 

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Acknowledgements

This work was supported by Hunan Provincial Natural Science Foundation of China (2021JJ40086, 2022JJ40059), National Natural Science Foundation of China (52172384, 52202466), and Young Elite Scientists Sponsorship Program by CAST (2022QNRC001).

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Correspondence to Manjiang Hu.

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Qin, Z., Jing, H., Chen, L. et al. Longitudinal Vehicle Stability Control Based on Modified Sliding Mode Control. Automot. Innov. (2024). https://doi.org/10.1007/s42154-023-00263-y

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