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Event-Triggered Sliding Mode Control Using the Interval Type-2 Fuzzy Logic for Steer-by-Wire Systems with Actuator Fault

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Abstract

This paper proposes a fuzzy modeling and event-triggered adaptive sliding mode control for steer-by-wire (SbW) systems subject to uncertain nonlinearity, time-varying perturbation, actuator fault, and limited communication resources. First, an interval type-2 fuzzy logic system (IT2 FLS) based on Lyapunov's adaptive scheme is built to model the uncertain nonlinearity. Then, an event-triggered adaptive sliding mode control method is designed to overcome the limited communication resources, time-varying perturbation, and actuator fault. This method eliminates the chattering phenomenon by utilizing nested adaptive technology and has practical finite-time stability. Theoretical analysis shows that the Zeno phenomenon is excluded. Finally, the validity of the methods is evaluated using simulations and vehicle experiments.

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References

  1. Kirli, A., Chen, Y., Okwudire, C., Ulsoy, G.: Torque-vectoring-based backup steering strategy for steer-by-wire autonomous vehicles with vehicle stability control. IEEE Trans. Veh. Technol 68(8), 7319–7328 (2019)

    Google Scholar 

  2. Vaio, M.D., Falcone, P., Hult, R., Petrillo, A., Santini, S.: Design and experimental validation of a distributed interaction protocol for connected autonomous vehicles at a road intersection. IEEE Trans. Veh. Technol 68(10), 9451–9465 (2019)

    Google Scholar 

  3. Peng, H., Wang, W., An, Q., Xiang, C., Li, L.: Path tracking and direct yaw moment coordinated control based on robust mpc with the finite time horizon for autonomous independent-drive vehicles. IEEE Trans. Veh. Technol 69(6), 6053–6066 (2020)

    Google Scholar 

  4. Zhang, L., Wang, Z., Ding, X., Li, S., Wang, Z.: Fault-tolerant control for intelligent electrified vehicles against front wheel steering angle sensor faults during trajectory tracking. IEEE Access 9, 65174–65186 (2021). https://doi.org/10.1109/ACCESS.2021.3075325

    Article  Google Scholar 

  5. Marino, R., Scalzi, S., Netto, M.: Nested pid steering control for lane keeping in autonomous vehicles. Control Eng. Pract. 19(12), 1459–1467 (2011)

    Google Scholar 

  6. Yih, P., Gerdes, J.: Modification of vehicle handling characteristics via steer-by-wire. IEEE Trans. Control Syst. Technol. 13(6), 965–976 (2005)

    Google Scholar 

  7. Falcone, P., Borrelli, F., Asgari, J., Tseng, H.E., Hrovat, D.: Predictive active steering control for autonomous vehicle systems. IEEE Trans. Control Syst. Technol. 15(3), 566–580 (2007)

    Google Scholar 

  8. Yamaguchi, Y., Murakami, T.: Adaptive control for virtual steering characteristics on electric vehicle using steer-by-wire system. IEEE Trans. Ind. Electron. 56(5), 1585–1594 (2009)

    Google Scholar 

  9. Wang, H., Kong, H., Man, Z., Tuan, D.M., Cao, Z., Shen, W.: Sliding mode control for steer-by-wire systems with ac motors in road vehicles. IEEE Trans. Ind. Electron. 61(3), 1596–1611 (2014)

    Google Scholar 

  10. Wu, X.D., Zhang, M.M., Xu, M.: Active tracking control for steer-by-wire system with disturbance observer. IEEE Trans. Veh. Technol. 68(6), 5483–5493 (2019)

    Google Scholar 

  11. Do, M.T., Man, Z., Zhang, C., Wang, H., Tay, F.S.: Robust sliding mode-based learning control for steer-by-wire systems in modern vehicles. IEEE Trans. Veh. Technol. 63(2), 580–590 (2014)

    Google Scholar 

  12. Sun, Z., Zheng, J., Man, Z., Wang, H.: Robust control of a vehicle steer-by-wire system using adaptive sliding mode. IEEE Trans. Ind. Electron. 63(4), 2251–2262 (2016)

    Google Scholar 

  13. Wang, H., Man, Z., Kong, H., Zhao, Y., Yu, M., Cao, Z., Zheng, J., Do, M.: Design and implementation of adaptive terminal sliding mode control on a steer-by-wire equipped road vehicle. IEEE Trans. Ind. Electron. 63(9), 5774–5785 (2016)

    Google Scholar 

  14. Sun, Z., Zheng, J.C., Man, Z.H., Fu, M.Y., Lu, R.Q.: Nested adaptive super-twisting sliding mode control design for a vehicle steer-by-wire system. Mech. Syst. Signal Process. 122, 658–672 (2019)

    Google Scholar 

  15. Huang, C., Naghdy, F., Du, H.: Delta operator-based fault estimation and fault-tolerant model predictive control for steer-by-wire systems. IEEE Trans. Control Syst. Technol. 26(5), 1810–1817 (2018)

    Google Scholar 

  16. Huang, C., Naghdy, F., Du, H.: Fault tolerant sliding mode predictive control for uncertain steer-by-wire system. IEEE Trans. Cybern 49(1), 1810–1817 (2019)

    Google Scholar 

  17. Utkin, V.I.: Sliding Modes in Control and Optimization. Springer-Verlag, Berlin (1992)

    MATH  Google Scholar 

  18. Edwards, C., Spurgeon, S.K.: Sliding mode control: theory and applications. Taylor & Francis, UK (1998)

    MATH  Google Scholar 

  19. Hamayun, M.T., Edwards, C., Alwi, H.: Augmentation scheme for fault-tolerant control using integral sliding modes. IEEE Trans. Control Syst. Technol. 22(1), 307–313 (2014)

    MATH  Google Scholar 

  20. Utkin, V.I., Poznyak, A.S.: Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method. Automatica 49(1), 39–47 (2013)

    MathSciNet  MATH  Google Scholar 

  21. Wu, H.M., Karkoub, M.: Hierarchical fuzzy sliding-mode adaptive control for the trajectory tracking of differential-driven mobile robots. Int. J. fuzzy syst. 21(1), 33–49 (2019)

    MathSciNet  Google Scholar 

  22. Ding, X., Wang, Z., Zhang, L.: Hybrid control-based acceleration slip regulation for four-wheel-independent-actuated electric vehicles. IEEE Trans. Transp. Electrification PP (2020). https://doi.org/10.1109/TTE.2020.3048405

  23. Zhang, L., Wang, Y., Wang, Z.: Robust lateral motion control for in-wheel-motor-drive electric vehicles with network induced delays. IEEE Trans. Veh. Technol. 68(11), 10585–10593 (2019)

    Google Scholar 

  24. Hess, R.A., Wells, S.R.: Sliding mode control applied to reconfigurable flight control design. J. Guid., Control Dynam 26, 452–462 (2003)

  25. Ma, X., Wong, P.K., Zhao, J., Xie, Z.: Cornering stability control for vehicles with active front steering system using t-s fuzzy based sliding mode control strategy. Mech. Syst. Signal Process. 125, 347–364 (2019)

    Google Scholar 

  26. Burton, J.A., Zinober, A.S.I.: Continuous approximation of variable structure control. Int. J. Syst. Sci. 17, 875–885 (1986)

    MATH  Google Scholar 

  27. Huang, Y.J., Kuo, T.C., Chang, S.H.: Adaptive sliding-mode control for nonlinear systems with uncertain parameters. IEEE Trans. Syst. Man Cybern. B 38(2), 534–539 (2008)

    Google Scholar 

  28. Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. Control 58(6), 1247–1263 (1993)

    MathSciNet  MATH  Google Scholar 

  29. Laghrouche, S., Plestan, F., Glumineau, A.: Higher order sliding mode control based on integral sliding mode. Automatica 43(3), 531–537 (2007)

    MathSciNet  MATH  Google Scholar 

  30. Edwards, C., Shtessel, Y.: Adaptive continuous higher order sliding mode control. Automatica 65(1), 183–190 (2016)

    MathSciNet  MATH  Google Scholar 

  31. Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Automa. Control 52(9), 1680–1685 (2007)

    MathSciNet  MATH  Google Scholar 

  32. Henningsson, T., Johannesson, E., Cervin, A.: Sporadic event-based control of first-order linear stochastic systems. Automatica 44(11), 2890–2895 (2008)

    MathSciNet  MATH  Google Scholar 

  33. Xu, C., Wu, B., Cao, X., Zhang, Y.: Distributed adaptive event-triggered control for attitude synchronization of multiple spacecraft. Nonlinear Dyn. 95(4), 2625–2638 (2019)

    MATH  Google Scholar 

  34. Li, H., Chen, G., Xiao, L.: Event-triggered sampling scheme for pinning control in multi-agent networks with general nonlinear dynamics. Neural Comput. Appl. 27(8), 2587–2599 (2016)

    Google Scholar 

  35. Zhang, J., Zhang, H., Lu, Y., Sun, S.: Cooperative output regulation of heterogeneous linear multi-agent systems with edge-event triggered adaptive control under time-varying topologies. Neural Comput. Appl. 32, 15573–15584 (2020)

    Google Scholar 

  36. Luan, Z., Zhang, J., Zhao, W., Wang, C.: Trajectory tracking control of autonomous vehicle with random network delay. IEEE Trans. Veh. Technol 69(8), 8140–8150 (2020)

    Google Scholar 

  37. Tuohy, S., Glavin, M., Hughes, C., Jones, E., Trivedi, M., Kilmartin, L.: Intra-vehicle networks: A review. IEEE Trans. Intell. Transp. Syst. 16(2), 534–545 (2015)

    Google Scholar 

  38. Behera, A.K., Bandyopadhyay, B.: New methodologies for adaptive sliding mode control. Int. J. Control 88(9), 1916–1931 (2016)

    MathSciNet  MATH  Google Scholar 

  39. Liu, Y., Jiang, B., Lu, J., Cao, J., Lu, G.: Event-triggered sliding mode control for attitude stabilization of a rigid spacecraft. IEEE Trans. Syst., Man, Cybern., Syst. (2020, https://doi.org/10.1109/TSMC.2018.2867061)

  40. Kumari, B., Behera, A.K., Bandyopadhyay, B.: Event-triggered sliding mode-based tracking control for uncertain euler-lagrange systems. IET Control Theory Appl. 12(9), 1228–1235 (2018)

    MathSciNet  Google Scholar 

  41. Xu, X., Su, P., Wang, F., Chen, L., Atindana, V.A.: Coordinated control of dual-motor using the interval type-2 fuzzy logic in autonomous steering system of agv. Int. J. fuzzy syst. (1) (2020)

  42. Nair, R.R., Behera, L., Kumar, S.: Multirobot systems with disturbances. IEEE Trans. Control Syst. Technol. 27(1), 39–47 (2019)

    Google Scholar 

  43. Haggag, S., Alstrom, D., Cetinkunt, S., Egelja, A.: Modeling, control, and validation of an electro-hydraulic steer-by-wire system for articulated vehicle applications. IEEE/ASME Trans. Mechatronics 10(6), 688–692 (2005)

    Google Scholar 

  44. Zhu, W., Jiang, Z.: Event-based leader-following consensus of multi-agent systems with input time delay. IEEE Trans. Autom. Control 60(5), 1362–1367 (2015)

    MathSciNet  MATH  Google Scholar 

  45. Sun, Z., Zheng, J., Man, Z., Wang, H.: Adaptive fast non-singular terminal sliding mode control for a vehicle steer-by-wire system. IET Control Theory Appl. 11(8), 1245–1254 (2017)

    MathSciNet  Google Scholar 

  46. Lin, F., Hung, Y., Ruan, K.: An intelligent second-order sliding-mode control for an electric power steering system using a wavelet fuzzy neural network. IEEE Trans. Fuzzy Syst. 22(6), 1598–1611 (2014)

    Google Scholar 

  47. Tao, G., Joshi, S.M., Ma, X.L.: Adaptive state feedback and tracking control of systems with actuator failures. IEEE Trans. Autom. Control 46(1), 78–95 (2000)

    MathSciNet  MATH  Google Scholar 

  48. Wang, W., Wen, C.: Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica 46(12), 2082–2091 (2010)

    MathSciNet  MATH  Google Scholar 

  49. Mao, Z., Yan, X.G., Jiang, B., Chen, M.: Adaptive fault-tolerant sliding-mode control for high-speed trains with actuator faults and uncertainties. IEEE Trans. Intell. Transp. Syst 21(6), 2449–2460 (2020)

    Google Scholar 

  50. H. Ma, H., Li, H.Y., Liang, H.J., Dong, G.W.: Adaptive fuzzy event-triggered control for stochastic nonlinear systems with full state constraints and actuator faults. IEEE Trans. Fuzzy Syst. 27(11), 2242–2254 (2019)

  51. Lai, G., Liu, Z., Chen, C.L.P., Zhang, Y., Chen, X.: Adaptive compensation for infinite number of time-varying actuator failures in fuzzy tracking control of uncertain nonlinear systems. IEEE Trans. Fuzzy Syst. 26(2), 474–486 (2018)

    Google Scholar 

  52. Wang, B., Zhang, Y.: An adaptive fault-tolerant sliding mode control allocation scheme for multirotor helicopter subject to simultaneous actuator faults. IEEE Trans. Ind. Electron. 65(5), 4227–4236 (2018)

    Google Scholar 

  53. Jing, Y., Yang, G.: Fuzzy adaptive fault-tolerant control for uncertain nonlinear systems with unknown dead-zone and unmodeled dynamics. IEEE Trans. Fuzzy Syst. 27(12), 2265–2278 (2019)

    Google Scholar 

  54. Mendel, J.M.: General type-2 fuzzy logic systems made simple: A tutorial. IEEE Trans. Fuzzy Syst. 22(5), 1162–1182 (2014)

    Google Scholar 

  55. Wang, L.: A new look at type-2 fuzzy sets and type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 25(3), 963–706 (2017)

    Google Scholar 

  56. Mendel, J.M., Hagras, H., Tan, W.W., Melek, W.W., Ying, H.: Introduction to Type-2 Fuzzy Logic Control: Theory and Applications. Wiley (2014)

  57. Mendel, J.M.: On km algorithms for solving type-2 fuzzy set problems. IEEE Trans. Fuzzy Syst. 21(3), 426–446 (2013)

    Google Scholar 

  58. Manceur, M., Essounbouli, N., Hamzaoui, A.: Second-order sliding fuzzy interval type-2 control for an uncertain system with real application. IEEE Trans. Fuzzy Syst. 20(2), 262–275 (2012)

    Google Scholar 

  59. Wu, D.: On the fundamental differences between interval type-2 and type-1 fuzzy logic controllers. IEEE Trans. Fuzzy Syst. 20(5), 832–848 (2012)

    Google Scholar 

  60. Mendel, J.M., John, R.I.B.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2), 117–127 (2002)

    Google Scholar 

  61. Lin, C.M., La, V.H., Le, T.L.: Dc-dc converters design using a type-2 wavelet fuzzy cerebellar model articulation controller. Neural Comput. Appl. 32, 2217–2229 (2020)

    Google Scholar 

  62. Eshghi, A., Mousavi, S.M., Mohagheghi, V.: A new interval type-2 fuzzy approach for analyzing and monitoring the performance of megaprojects based on earned value analysis (with a case study). Neural Comput. Appl. 31, 5109–5133 (2019)

    Google Scholar 

  63. Luo, C., Tan, C., Wang, X., Zheng, Y.: An evolving recurrent interval type-2 intuitionistic fuzzy neural network for online learning and time series prediction. Appl. Soft Comput. 78 (2019)

  64. Cao, L., Li, H., Wang, N., Zhou, Q.: Observer-based event-triggered adaptive decentralized fuzzy control for nonlinear large-scale systems. IEEE Trans. Fuzzy Syst. 27(6), 1201–1214 (2019)

    Google Scholar 

  65. Zhu, Z., Xia, Y., Fu, M.: Attitude stabilization of rigid spacecraft with finite-time convergence. Int. J. Robust Nonlin. Control 21(6), 686–702 (2011)

    MathSciNet  MATH  Google Scholar 

  66. Ying, H.: Interval type-2 takagi-sugeno fuzzy systems with linear rule consequent are universal approximators. In: NAFIPS 2009 - 2009 Annual Meeting of the North American Fuzzy Information Processing Society (2009)

  67. Na, J., Chen, Q., Ren, X.M., Guo, Y.: Adaptive prescribed performance motion control of servo mechanisms with friction compensation. IEEE Trans. Ind. Electron. 61(1), 486–494 (2014)

    Google Scholar 

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (Grant No. 51775103 and 61773068), the State Key Laboratory Foundation of Synthetical Automation for Process Industries, Northeastern University, and Ningxia Natural Science Foundation of China (Grant No. 2022AAC03348).

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Correspondence to Yongfu Wang.

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Li, H., Tie, M. & Wang, Y. Event-Triggered Sliding Mode Control Using the Interval Type-2 Fuzzy Logic for Steer-by-Wire Systems with Actuator Fault. Int. J. Fuzzy Syst. 24, 3104–3117 (2022). https://doi.org/10.1007/s40815-022-01323-x

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  • DOI: https://doi.org/10.1007/s40815-022-01323-x

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