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Nonlinear extended state observer-based output feedback stabilization control for uncertain nonlinear half-car active suspension systems

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Abstract

This paper proposes a nonlinear extended state observer-based output feedback stabilization controller for a half-car active suspension system, to overcome factors leading to performance deterioration, such as nonlinearities, parameter uncertainties, unmodeled dynamics, and uncertain external disturbances. Nonlinear extended state observers are first developed to estimate the unmeasurable states and unknown dynamics of heave and pitch motions. Then, finite-time stabilization control laws are synthesized to improve the vehicle body attitude and ride comfort. The proposed control scheme is an improvement over the existing linear extended state observer-based techniques, given its high observation quality and finite-time convergence. From the perspective of practical implementation, the controller is independent of an accurate mathematical model and only requires the measurable output signals. By constructing weighted error and auxiliary state systems, and employing geometric homogeneity theory, the finite-time stability of estimation errors and suspension states is systematically proven within the Lyapunov framework. Furthermore, the zero dynamics stability is analyzed to guarantee the suspension space constraint and road holding. Finally, numerical simulations are conducted on some representative road excitations and the results are compared to the existing solution and passive suspension. The analysis has confirmed the effectiveness and robustness of the proposed control method.

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References

  1. Zirkohi, M.M., Lin, T.-C.: Interval type-2 fuzzy-neural network indirect adaptive sliding mode control for an active suspension system. Nonlinear Dyn. 79(1), 513–526 (2015)

    Google Scholar 

  2. Gohrle, C., Schindler, A., Wagner, A., Sawodny, O.: Road profile estimation and preview control for low-bandwidth active suspension systems. IEEE/ASME Trans. Mechatron. 20(5), 2299–2310 (2015)

    Google Scholar 

  3. Pan, H., Jing, X., Sun, W.: Robust finite-time tracking control for nonlinear suspension systems via disturbance compensation. Mech. Syst. Signal Process. 88, 49–61 (2017)

    Google Scholar 

  4. Wang, G., Chadli, M., Chen, H., Zhou, Z.: Event-triggered control for active vehicle suspension systems with network-induced delays. J. Frankl. Inst. 356(1), 147–172 (2019)

    MathSciNet  MATH  Google Scholar 

  5. Zhang, Y., Liu, Y., Liu, L.: Minimal learning parameters-based adaptive neural control for vehicle active suspensions with input saturation. Neurocomputing (2019)

  6. Pusadkar, U.S., Chaudhari, S.D., Shendge, P., Phadke, S.: Linear disturbance observer based sliding mode control for active suspension systems with non-ideal actuator. J. Sound Vib. 442, 428–444 (2019)

    Google Scholar 

  7. Mustafa, G.I., Wang, H., Tian, Y.: Vibration control of an active vehicle suspension systems using optimized model-free fuzzy logic controller based on time delay estimation. Adv. Eng. Softw. 127, 141–149 (2019)

    Google Scholar 

  8. Du, M., Zhao, D., Yang, B., Wang, L.: Terminal sliding mode control for full vehicle active suspension systems. J. Mech. Sci. Technol. 32, 2851–2866 (2018)

    Google Scholar 

  9. Gao, H., Lam, J., Wang, C.: Multi-objective control of vehicle active suspension systems via load-dependent controllers. J. Sound Vib. 290(3–5), 654–675 (2006)

    Google Scholar 

  10. Li, H., Jing, X., Karimi, H.R.: Output-feedback-based \({H_\infty }\) control for vehicle suspension systems with control delay. IEEE Trans. Ind. Electron. 61(1), 436–446 (2014)

    Google Scholar 

  11. Li, P., Lam, J., Cheung, K.C.: Multi-objective control for active vehicle suspension with wheelbase preview. J. Sound Vib. 333(21), 5269–5282 (2014)

    Google Scholar 

  12. Sun, W., Gao, H., Kaynak, O.: Finite frequency \({H_\infty }\) control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 19(2), 416–422 (2011)

    Google Scholar 

  13. Wang, G., Chen, C., Yu, S.: Optimization and static output-feedback control for half-car active suspensions with constrained information. J. Sound Vib. 378, 1–13 (2016)

    Google Scholar 

  14. Chen, H., Guo, K.-H.: Constrained \({H_\infty }\) control of active suspensions: an LMI approach. IEEE Trans. Control Syst. Technol. 13(3), 412–421 (2005)

    Google Scholar 

  15. Yazici, H., Sever, M.: L2 gain state derivative feedback control of uncertain vehicle suspension systems. J. Vib. Control. 24(16), 3779–3794 (2017)

    Google Scholar 

  16. Du, H., Lam, J., Sze, K.Y.: Non-fragile output feedback \({H_\infty }\) vehicle suspension control using genetic algorithm. Eng. Appl. Artif. Intell. 16(7–8), 667–680 (2003)

    Google Scholar 

  17. Sun, W., Gao, H., Kaynak, O.: Adaptive backstepping control for active suspension systems with hard constraints. IEEE/ASME Trans. Mechatron. 18(3), 1072–1079 (2013)

    Google Scholar 

  18. Sun, W., Pan, H., Zhang, Y., Gao, H.: Multi-objective control for uncertain nonlinear active suspension systems. Mechatronics 24(4), 318–327 (2014)

    Google Scholar 

  19. Deshpande, V.S., Shendge, P.D., Phadke, S.B.: Nonlinear control for dual objective active suspension systems. IEEE Trans. Intell. Transp. Syst. 18(3), 656–665 (2017)

    Google Scholar 

  20. Pang, H., Zhang, X., Xu, Z.: Adaptive backstepping-based tracking control design for nonlinear active suspension system with parameter uncertainties and safety constraints. ISA Trans. 88, 23–36 (2019)

    Google Scholar 

  21. Wen, S., Chen, M.Z., Zeng, Z., Yu, X., Huang, T.: Fuzzy control for uncertain vehicle active suspension systems via dynamic sliding-mode approach. IEEE Trans. Syst. Man Cybern.-Syst. 47(1), 24–32 (2017)

    Google Scholar 

  22. Sun, W., Zhao, Z., Gao, H.: Saturated adaptive robust control for active suspension systems. IEEE Trans. Ind. Electron. 60(9), 3889–3896 (2013)

    Google Scholar 

  23. Sun, W., Gao, H., Kaynak, O.: Vibration isolation for active suspensions with performance constraints and actuator saturation. IEEE/ASME Trans. Mechatron. 20(2), 675–683 (2015)

    Google Scholar 

  24. Pan, H., Sun, W., Jing, X., Gao, H., Yao, J.: Adaptive tracking control for active suspension systems with non-ideal actuators. J. Sound Vib. 399, 2–20 (2017)

    Google Scholar 

  25. Cao, J.T., Li, P., Liu, H.H.: An interval fuzzy controller for vehicle active suspension systems. IEEE Trans. Intell. Transp. Syst. 11(4), 885–895 (2010)

    Google Scholar 

  26. Deshpande, V.S., Bhaskara, M., Phadke, S.: Sliding mode control of active suspension systems using a disturbance observer. In: 2012 12th International Workshop on Variable Structure Systems. January 12–14; Mumbai, India, pp. 70-75 (2012)

  27. Yagiz, N., Hacioglu, Y., Taskin, Y.: Fuzzy sliding-mode control of active suspensions. IEEE Trans. Ind. Electron. 55(11), 3883–3890 (2008)

    Google Scholar 

  28. 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)

    Google Scholar 

  29. Huang, Y., Na, J., Wu, X., Liu, X., Guo, Y.: Adaptive control of nonlinear uncertain active suspension systems with prescribed performance. ISA Trans. 54, 145–155 (2015)

    Google Scholar 

  30. Liu, S.B., Zhou, H.Y., Luo, X.X., Xiao, J.: Adaptive sliding fault tolerant control for nonlinear uncertain active suspension systems. J. Frankl. Inst. 353(1), 180–199 (2016)

    MathSciNet  MATH  Google Scholar 

  31. Chen, S.-A., Wang, J.-C., Yao, M., Kim, Y.-B.: Improved optimal sliding mode control for a non-linear vehicle active suspension system. J. Sound Vib. 395, 1–25 (2017)

    Google Scholar 

  32. Rath, J.J., Defoort, M., Karimi, H.R., Veluvolu, K.C.: Output feedback active suspension control with higher order terminal sliding mode. IEEE Trans. Ind. Electron. 64(2), 1392–1403 (2017)

    Google Scholar 

  33. Pan, H., Sun, W., Gao, H., Hayat, T., Alsaadi, F.: Nonlinear tracking control based on extended state observer for vehicle active suspensions with performance constraints. Mechatronics 30, 363–370 (2015)

    Google Scholar 

  34. Rath, J., Veluvolu, K., Defoort, M.: Output feedback based sliding mode control of active suspension using backstepping. In: 2015 3rd International Conference on Control, Engineering and Information Technology (CEIT). May 25–27; Tlemcen, Algeria, pp. 1–6 (2015)

  35. Wang, J., Jin, F., Zhou, L., Li, P.: Implementation of model-free motion control for active suspension systems. Mech. Syst. Signal Process. 119, 589–602 (2019)

    Google Scholar 

  36. Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009)

    Google Scholar 

  37. Zhao, Z.-L., Guo, B.-Z.: A novel extended state observer for output tracking of MIMO systems with mismatched uncertainty. IEEE Trans. Autom. Control 63(1), 211–218 (2018)

    MathSciNet  MATH  Google Scholar 

  38. Zhao, Z.-L., Guo, B.-Z.: On convergence of nonlinear extended stated observers with switching functions. In: 2016 35th Chinese Control Conference (CCC). July 27–29; Chengdu, China, pp. 664–669 (2016)

  39. Zhao, Z.-L., Jiang, Z.-P.: Semi-global finite-time output-feedback stabilization with an application to robotics. IEEE Trans. Ind. Electron. 66(4), 3148–3156 (2019)

    Google Scholar 

  40. Luan, F., Na, J., Huang, Y., Gao, G.: Adaptive neural network control for robotic manipulators with guaranteed finite-time convergence. Neurocomputing 337, 153–164 (2019)

    Google Scholar 

  41. Wang, H., Mustafa, G.I., Tian, Y.: Model-free fractional-order sliding mode control for an active vehicle suspension system. Adv. Eng. Softw. 115, 452–461 (2018)

    Google Scholar 

  42. Pan, H., Sun, W.: Nonlinear output feedback finite-time control for vehicle active suspension systems. IEEE Trans. Ind. Inform. 15(4), 2073–2082 (2018)

    Google Scholar 

  43. Perruquetti, W., Floquet, T., Moulay, E.: Finite-time observers: application to secure communication. IEEE Trans. Autom. Control 53(1), 356–360 (2008)

    MathSciNet  MATH  Google Scholar 

  44. Guo, B.-Z., Zhao, Z.-L.: On the convergence of an extended state observer for nonlinear systems with uncertainty. Syst. Control Lett. 60(6), 420–430 (2011)

    MathSciNet  MATH  Google Scholar 

  45. Bhat, S.P., Bernstein, D.S.: Geometric homogeneity with applications to finite-time stability. Math. Control Signals Syst. 17(2), 101–127 (2005)

    MathSciNet  MATH  Google Scholar 

  46. Rosier, L.: Homogeneous Lyapunov function for homogeneous continuous vector field. Syst. Control Lett. 19(6), 467–473 (1992)

    MathSciNet  MATH  Google Scholar 

  47. Zhao, Z.-L., Guo, B.-Z., Jiang, Z.-P.: A new extended state observer for output tracking of nonlinear MIMO systems. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC). December 12–15; Melbourne, Australia, pp. 6732–6737 (2017)

  48. Khalil, H.K.: Nonlinear Systems. Prentice Hall, Englewood Cliffs (1996)

    Google Scholar 

  49. Slotine, J.-J.E., Li, W.: Applied Nonlinear Control, 199(1). Prentice Hall, Englewood Cliffs (1991)

    Google Scholar 

  50. Ginebra, Mechanical vibration-road surface profiles-reporting of measured data, ISO-8608 (1995)

Download references

Acknowledgements

This work is supported by the National Key R&D Program of China (Grant No.2016YFC0802900), China.

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, China

    Miaomiao Du & Dingxuan Zhao

  2. College of Mechanical Engineering, Yanshan University, Qinhuangdao, 066004, China

    Dingxuan Zhao, Mengke Yang & Hao Chen

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  1. Miaomiao Du
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  2. Dingxuan Zhao
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  4. Hao Chen
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Correspondence to Dingxuan Zhao.

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Du, M., Zhao, D., Yang, M. et al. Nonlinear extended state observer-based output feedback stabilization control for uncertain nonlinear half-car active suspension systems. Nonlinear Dyn 100, 2483–2503 (2020). https://doi.org/10.1007/s11071-020-05638-y

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