Skip to main content
Log in

Observer-Based Fuzzy Control for Four-Wheel Independently Driven Electric Vehicles with Active Steering Systems

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This paper presents an observer-based control strategy to improve the maneuverability and stability performance of four-wheel independently driven electric vehicles with active front-wheel steering systems. Since the system states are difficult to be measured directly, a novel observer is designed to estimate the vehicle yaw rate and lateral velocity simultaneously. Takagi–Sugeno fuzzy model is used to handle the time-varying parameters of the vehicle model. Based on Lyapunov function theory, stability conditions of the closed-loop system are derived. The fuzzy \(H_{\infty }\) controller is designed to make the resulting T–S fuzzy system asymptotically stable and satisfy \(H_{\infty }\) performance under given constraints. Simulation results are given to demonstrate the validity of the presented control method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Wang, R., Hu, C., Wang, Z., Yan, F., Chen, N.: Integrated optimal dynamics control of 4WD4WS electric ground vehicle with tire-road frictional coefficient estimation. Mech. Syst. Signal Process. 60, 727–741 (2015)

    Article  Google Scholar 

  2. Wu, F.K., Yeh, T.J., Huang, C.F.: Motor control and torque coordination of an electric vehicle actuated by two in-wheel motors. Mechatronics 23(1), 46–60 (2013)

    Article  Google Scholar 

  3. Wang, R., Chen, Y., Feng, D., Huang, X., Wang, J.: Development and performance characterization of an electric ground vehicle with independently actuated in-wheel motors. J. Power Sour. 196(8), 3962–3971 (2011)

    Article  Google Scholar 

  4. Wang, J., Longoria, R.G.: Coordinated and reconfigurable vehicle dynamics control. IEEE Trans. Control Syst. Technol. 17(3), 723–732 (2009)

    Article  Google Scholar 

  5. Zhang, H., Wang, J.: Vehicle lateral dynamics control through AFS/DYC and robust gain-scheduling approach. IEEE Trans. Veh. Technol. 65(1), 489–494 (2016)

    Article  Google Scholar 

  6. Li, X., Zhang, B., Li, P., Zhou, Q., Lu, R.: Finite-horizon \(H_{\infty }\) state estimation for periodic neural networks over fading channels. IEEE Trans. Neural Netw. Learn. Syst. (2019). https://doi.org/10.1109/TNNLS.2019.2920368

    Article  Google Scholar 

  7. Xia, J., Zhang, J., Feng, J., Wang, Z., Zhuang, G.: Command filter-based adaptive fuzzy control for nonlinear systems with unknown control directions. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2911115

    Article  Google Scholar 

  8. Nam, K., Fujimoto, H., Hori, Y.: Lateral stability control of in-wheel-motor-driven electric vehicles based on sideslip angle estimation using lateral tire force sensors. IEEE Trans. Veh. Technol. 61(5), 1972–1985 (2012)

    Article  Google Scholar 

  9. Chu, L., Gao, X., Guo, J., Liu, H., Chao, L., Shang, M.: Coordinated control of electronic stability program and active front steering. Proc. Environ. Sci. 12(1), 1379–1386 (2012)

    Article  Google Scholar 

  10. Nam, K., Fujimoto, H., Hori, Y.: Advanced motion control of electric vehicles based on robust lateral tire force control via active front steering. IEEE/ASME Trans. Mech. 19(1), 289–299 (2014)

    Article  Google Scholar 

  11. Zhang, L., Li, L., Lin, C., Wang, C., Qi, B., Song, J.: Coaxial-coupling traction control for a four-wheel-independent-drive electric vehicle on a complex road. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 228(12), 1398–1414 (2014)

    Article  Google Scholar 

  12. Wang, R., Zhang, H., Wang, J.: Linear parameter-varying controller design for four-wheel independently actuated electric ground vehicles with active steering systems. IEEE Trans. Control Syst. Technol. 22(4), 1281–1296 (2014)

    Article  Google Scholar 

  13. Hu, C., Jing, H., Wang, R., Yan, F., Chadli, M.: Robust \(H_{\infty }\) output-feedback control for path following of autonomous ground vehicles. Mech. Syst. Signal Process. 70, 414–427 (2015)

    Google Scholar 

  14. Wang, R., Jing, H., Hu, C., Chadli, M., Yan, F.: Robust \(H_{\infty }\) output-feedback yaw control for in-wheel motor driven electric vehicles with differential steering. Neurocomputing 173(3), 676–684 (2016)

    Article  Google Scholar 

  15. Guo, H., Chen, H., Cao, D., Jin, W.: Design of a reduced-order non-linear observer for vehicle velocities estimation. IET Control Theory Appl. 7(17), 2056–2068 (2013)

    Article  MathSciNet  Google Scholar 

  16. Latrach, C., Kchaou, M., Guguen, H.: Observer-based decentralised fuzzy control design for nonlinear interconnected systems: an application to vehicle dynamics. Int. J. Syst. Sci. 48(7), 1485–1495 (2017)

    Article  MathSciNet  Google Scholar 

  17. Zhang, B., Du, H., Lam, J., Zhang, N., Li, W.: A novel observer design for simultaneous estimation of vehicle steering angle and sideslip angle. IEEE Trans. Ind. Electron. 63(7), 4357–4366 (2016)

    Article  Google Scholar 

  18. Oudghiri, M., Chadli, M., Hajjaji, A.E.: Observer-based fault tolerant control for vehicle lateral dynamics. Int. J. Veh. Des. 48(3), 173–189 (2008)

    Article  Google Scholar 

  19. Ammar, I.I., Gassara, H., Hajjaji, A.E., Chaabane, M.: New polynomial Lyapunov functional approach to observerbased control for polynomial fuzzy systems with time delay. Int. J. Fuzzy Syst. 20(4), 1057–1068 (2018)

    Article  MathSciNet  Google Scholar 

  20. Benzaouia, A., Hajjaji, A.E.: Conditions of stabilization of positive continuous Takagi–Sugeno fuzzy systems with delay. Int. J. Fuzzy Syst. 20(3), 750–758 (2018)

    Article  MathSciNet  Google Scholar 

  21. Li, H., Yu, J., Hilton, C., Liu, H.: Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T–S fuzzy approach. IEEE Trans. Ind. Electron. 60(8), 3328–3338 (2013)

    Article  Google Scholar 

  22. Xia, J., Zhang, J., Sun, W., Zhang, B., Wang, Z.: Finite-time adaptive fuzzy control for nonlinear systems with full state constraints. IEEE Trans. Syst. Man Cybern. Syst. 49(7), 1541–1548 (2019)

    Article  Google Scholar 

  23. Arceo, J.C., Mrquez, R., Estrada-Manzo, V., Bernal, M.: Stabilization of nonlinear singular systems via Takagi–Sugeno models and robust differentiators. Int. J. Fuzzy Syst. 20(5), 1451–1459 (2018)

    Article  MathSciNet  Google Scholar 

  24. Khooban, M.H., Vafamand, N., Niknam, T., Dragicevic, T., Blaabjerg, F.: Model-predictive control based on Takagi–Sugeno fuzzy model for electrical vehicles delayed model. IET Electr. Power Appl. 11(5), 918–934 (2017)

    Article  Google Scholar 

  25. Yang, F.G., Li, Y.B., Ruan, J.H., Yin, Z.F., Wang, M.H.: T–S model-based study on 4WS vehicle coordinate steering control. J. Syst. Simul. 21(11), 3356–3359 (2009)

    Google Scholar 

  26. Sun, W., Su, S.F., Wu, Y., Xia, J., Nguyen, V.T.: Adaptive fuzzy control with high-order barrier Lyapunov functions for high-order uncertain nonlinear systems with full-state constraints. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2018.2890256

    Article  Google Scholar 

  27. Jing, H., Wang, R., Chadli, M., Hu, C., Yan, F., Li, C.: Fault-tolerant control of four-wheel independently actuated electric vehicles with active steering systems. IFAC-PapersOnLine 48(21), 1165–1172 (2015)

    Article  Google Scholar 

  28. Hu, C., Wang, R., Yan, F.: Integral sliding mode-based composite nonlinear feedback control for path following of fourwheel independently actuated autonomous vehicles. IEEE Trans. Transp. Electr. 2(2), 221–230 (2016)

    Article  Google Scholar 

  29. Li, H., Liu, H., Gao, H., Shi, P.: Reliable fuzzy control for active suspension systems with actuator delay and fault. Int. J. Fuzzy Syst. 20(2), 342–357 (2012)

    Article  Google Scholar 

  30. Sun, W., Su, S.F., Dong, G., Bai, W.: Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2898204

    Article  Google Scholar 

  31. Brahim, I.H., Mehdi, D., Chaabane, M.: Robust fault detection for uncertain T–S fuzzy system with unmeasurable premise variables: descriptor approach. Int. J. Fuzzy Syst. 20(2), 416–425 (2018)

    Article  MathSciNet  Google Scholar 

  32. Li, H., Pan, Y., Yang, X., Yu, Z., Zhao, X.: Fuzzy output-feedback control for non-linear systems with input time-varying delay. IET Control Theory Appl. 8(9), 738–745 (2014)

    Article  MathSciNet  Google Scholar 

  33. Du, H., Zhang, N., Naghdy, F.: Velocity-dependent robust control for improving vehicle lateral dynamics. Transp. Res. Part C 19(3), 454–468 (2011)

    Article  Google Scholar 

  34. Zhang, Y., Cheng, G., Liu, C.: Finite-time unbiased \(H_{\infty }\) filtering for discrete jump time-delay systems. Appl. Math. Model. 38(13), 3339–3349 (2014)

    Article  MathSciNet  Google Scholar 

  35. Zhang, L., Liang, H., Sun, Y., Ahn, C.K.: Adaptive event-triggered fault detection scheme for semi-Markovian jump systems with output quantization. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2912846

    Article  Google Scholar 

  36. Du, P., Liang, H., Zhao, S., Ahn, C.K.: Neural-based decentralized adaptive finite-time control for nonlinear largescale systems with time-varying output constraints. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2918351

    Article  Google Scholar 

  37. Zhang, L., Lam, H.K.,  Sun, Y.,  Liang, H.: Fault detection for fuzzy semi-Markov jump systems based on interval type-2 fuzzy approach. IEEE Trans. Fuzzy Syst.(2019). https://doi.org/10.1109/TFUZZ.2019.2936333

  38. Liang, H., Zhang, L., Sun, Y., Huang, T.: Containment control of semi-Markovian multi-agent systems with switching topologies. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2946248

  39. Lu, R., Xu, Y., Xue, A., Zheng, J.: Networked control with state reset and quantized measurements: observer-based case, IEEE Trans. Ind. Electron. 60(11), 5206–5213 (2012)

    Article  Google Scholar 

  40. Wang, Z., Liu, D.: Data-based controllability and observability analysis of linear discrete-time systems. IEEE Trans. Neural Netw. 22(12), 2388–2392 (2011)

    Article  Google Scholar 

  41. Wang, Z., Xu, Y., Lu, R., Peng, H.: Finite-time state estimation for coupled Markovian neural networks with sensor nonlinearities. IEEE Trans. Neural Netw. Learn. Syst. 28(3), 630–638 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was partially supported by the National Natural Science Foundation of China (61703111, 61973091), the Guangdong Natural Science Funds for Distinguished Young Scholar (2019B151502026, 2017A030306014), the Innovative Research Team Program of Guangdong Province Science Foundation (2018B030312006) and the Science and Technology Program of Guangzhou (201904020006).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qi Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, L., Li, P., Lin, W. et al. Observer-Based Fuzzy Control for Four-Wheel Independently Driven Electric Vehicles with Active Steering Systems. Int. J. Fuzzy Syst. 22, 89–100 (2020). https://doi.org/10.1007/s40815-019-00770-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-019-00770-3

Keywords

Navigation