Skip to main content
SpringerLink
Log in

Fixed-time integral sliding mode control of a high-order nonlinear system

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper investigates the problem of fixed-time tracking control for a class of high-order nonlinear systems with matched disturbances. A novel continuous fixed-time sliding mode disturbance observer is first proposed to accurately estimate the external disturbances. Then, a new integral high-order sliding mode (IHOSM) surface is proposed in the sense of fixed-time stability by the bi-limit homogeneous method. Subsequently, utilizing the disturbance estimation information, an IHOSM-based fixed-time control scheme is proposed which can enforce the closed-loop control system reach the real sliding mode surface. Meanwhile, it is applied to an error dynamic system of a wheeled mobile robot to achieve fast accurate trajectory tracking. Finally, the comparative experiment results demonstrate the effectiveness and superiority of the proposed control approach.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

Data availability

The datasets of this work are available from the corresponding author on reasonable request.

References

  1. Lin, W., Qian, C.: Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems. Syst. Control Lett. 39(5), 339–351 (2000)

    Article  MathSciNet  Google Scholar 

  2. Shen, Y., Zhai, J.: Global dynamic output feedback for high-order nonlinear systems with uncertain output function. Nonlinear Dyn. 104(3), 2389–2409 (2021)

    Article  Google Scholar 

  3. Man, Z., Yu, X.: Terminal sliding mode control of MIMO linear systems. IEEE Trans. Circuits Syst. I, Fundam. Theory and Appl. 44(11), 1065–1070 (1997)

    Article  MathSciNet  Google Scholar 

  4. Venkataraman, S.T., Gulati, S.: Control of nonlinear systems using terminal sliding modes. J. Dyn. Sys., Meas., Control 115(3), 554–560 (1993)

    Article  Google Scholar 

  5. Wang, N., Karimi, H.R., Li, H., Su, S.: Accurate trajectory tracking of disturbed surface vehicles: A finite-time control approach. IEEE/ASME Trans. Mechatron. 24(3), 1064–1074 (2019)

    Article  Google Scholar 

  6. Feng, Y., Yu, X., Man, Z.: Non-singular terminal sliding mode control of rigid manipulators. Automatica 38(12), 2159–2167 (2002)

    Article  MathSciNet  Google Scholar 

  7. Zuo, Z.: Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl. 9(4), 545–552 (2015)

    Article  MathSciNet  Google Scholar 

  8. Qi, W., Gao, X., Ahn, C.K., Cao, J., Cheng, J.: Fuzzy integral sliding mode control for nonlinear semimarkovian switching systems with application. IEEE Trans. Syst. Man, Cybern. Syst. (2020). https://doi.org/10.1109/TSMC.2020.3034484

  9. Utkin, V., Shi, J.: Integral sliding mode in systems operating under uncertainty conditions. In: 35th IEEE Conf. Decision Control, vol. 4, pp. 4591–4596. Kobe, Japan (1996)

  10. Wang, Y., Pu, H., Shi, P., Ahn, C.K., Luo, J.: Sliding mode control for singularly perturbed Markov jump descriptor systems with nonlinear perturbation. Automatica 127, 109515 (2021)

    Article  MathSciNet  Google Scholar 

  11. Ding, Y., Wang, X., Bai, Y., Cui, N.: Global smooth sliding mode controller for flexible air-breathing hypersonic vehicle with actuator faults. Aerosp. Sci. Technol. 92, 563–578 (2019)

    Article  Google Scholar 

  12. Riani, A., Madani, T., Benallegue, A., Djouani, K.: Adaptive integral terminal sliding mode control for upper-limb rehabilitation exoskeleton. control Eng. Pract. 75, 108–117 (2018)

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

    Article  MathSciNet  Google Scholar 

  14. Zong, Q., Zhao, Z., Zhang, J.: Higher order sliding mode control with self-tuning law based on integral sliding mode. IET Control Theory Appl. 4(7), 1282–1289 (2010)

    Article  MathSciNet  Google Scholar 

  15. Mondal, S., Mahanta, C.: Adaptive integral higher order sliding mode controller for uncertain systems. J. Control Theory Appl. 11(1), 61–68 (2013)

    Article  MathSciNet  Google Scholar 

  16. Zuo, Z., Tian, B., Defoort, M., Ding, Z.: Fixed-time consensus tracking for multiagent systems with high-order integrator dynamics. IEEE Trans. Autom. Control 63(2), 563–570 (2018)

    Article  MathSciNet  Google Scholar 

  17. Kim, S.K., Ahn, C.K.: Observer-based decentralized pole-zero cancellation tension control with gain booster and surface stabilizer for roll-to-roll systems. Nonlinear Dyn. 105(3), 2313–2326 (2021)

    Article  Google Scholar 

  18. Peng, J., Liu, Y., Wang, J.: Fuzzy adaptive output feedback control for robotic systems based on fuzzy adaptive observer. Nonlinear Dyn. 78(2), 789–801 (2014)

    Article  Google Scholar 

  19. Han, J.: The extended state observer of a class of uncertain systems. Control Decis. 10(1), 85–88 (1995)

    Google Scholar 

  20. Chen, M., Wu, Q., Cui, R.: Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems. ISA Trans. 52(2), 198–206 (2013)

    Article  Google Scholar 

  21. Xiao, B., Yin, S., Gao, H.: Reconfigurable tolerant control of uncertain mechanical systems with actuator faults: a sliding mode observer-based approach. IEEE Trans. Control Syst. Technol. 26(4), 1249–1258 (2018)

    Article  Google Scholar 

  22. Xiao, B., Cao, L., Xu, S., Liu, L.: Robust tracking control of robot manipulators with actuator faults and joint velocity measurement uncertainty. IEEE/ASME Trans. Mechatron. 25(3), 1354–1365 (2020)

    Article  Google Scholar 

  23. Li, B., Hu, Q., Yang, Y.: Continuous finite-time extended state observer based fault tolerant control for attitude stabilization. Aerosp. Sci. Technol. 84, 204–213 (2019)

    Article  Google Scholar 

  24. Cao, L., Xiao, B., Golestani, M.: Robust fixed-time attitude stabilization control of flexible spacecraft with actuator uncertainty. Nonlinear Dyn. 100(3), 2505–2519 (2020)

    Article  Google Scholar 

  25. Rabiee, H., Ataei, M., Ekramian, M.: Continuous nonsingular terminal sliding mode control based on adaptive sliding mode disturbance observer for uncertain nonlinear systems. Automatica 109, 108515 (2019)

    Article  MathSciNet  Google Scholar 

  26. Li, B., Gong, W., Yang, Y., Xiao, B., Ran, D.: Appointed-fixed-time observer based sliding mode control for a quadrotor uav under external disturbances. IEEE Trans. Aerosp. Electron. Syst. (2021). https://doi.org/10.1109/TAES.2021.3101562

  27. Andrieu, V., Praly, L., Astolfi, A.: Homogeneous approximation, recursive observer design, and output feedback. SIAM J. Control. Optim. 47(4), 1814–1850 (2008)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  29. Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57(8), 2106–2110 (2012)

    Article  MathSciNet  Google Scholar 

  30. Ba, D., Li, Y., Tong, S.: Fixed-time adaptive neural tracking control for a class of uncertain nonstrict nonlinear systems. Neurocomputing 363, 273–280 (2019)

    Article  Google Scholar 

  31. Polycarpou, M., Ioannou, P.: A robust adaptive nonlinear control design. Automatica 32(3), 423–427 (1996)

    Article  MathSciNet  Google Scholar 

  32. Basin, M., Shtessel, Y., Aldukali, F.: Continuous finite- and fixed-time high-order regulators. J. Franklin Inst. 353(18), 5001–5012 (2016)

    Article  MathSciNet  Google Scholar 

  33. Yang, F., Wei, C., Wu, R., Cui, N.: Non-recursive fixed-time convergence observer and extended state observer. IEEE Access 6, 62339–62351 (2018)

  34. Corradini, M.L., Cristofaro, A.: Nonsingular terminal sliding-mode control of nonlinear planar systems with global fixed-time stability guarantees. Automatica 95, 561–565 (2018)

    Article  MathSciNet  Google Scholar 

  35. Slotine, J.J.E., Coetsee, J.A.: Adaptive sliding controller synthesis for non-linear systems. Int. J. Control 43(6), 1631–1651 (1986)

    Article  Google Scholar 

  36. Plestan, F., Shtessel, Y., Brégeault, V., Poznyak, A.: New methodologies for adaptive sliding mode control. Int. J. Control 83(9), 1907–1919 (2010)

    Article  MathSciNet  Google Scholar 

  37. Li, B., Hu, Q., Yu, Y., Ma, G.: Observer-based fault-tolerant attitude control for rigid spacecraft. IEEE Trans. Aerosp. Electron. Syst. 53(5), 2572–2582 (2017)

    Article  Google Scholar 

  38. Song, T., Fang, L., Wang, H.: Model-free finite-time terminal sliding mode control with a novel adaptive sliding mode observer of uncertain robot systems. Asian J. Control. (2021). https://doi.org/10.1002/asjc.2542

  39. Chen, C.Y., Li, T.H.S., Yeh, Y.C., Chang, C.C.: Design and implementation of an adaptive sliding-mode dynamic controller for wheeled mobile robots. Mechatronics 19(2), 156–166 (2009)

    Article  Google Scholar 

  40. Ou, M., Du, H., Li, S.: Finite-time tracking control of multiple nonholonomic mobile robots. J. Franklin Inst. 349(9), 2834–2860 (2012)

    Article  MathSciNet  Google Scholar 

  41. Zhai, J., Song, Z.: Adaptive sliding mode trajectory tracking control for wheeled mobile robots. Int. J. Control 92(10), 2255–2262 (2019)

    Article  MathSciNet  Google Scholar 

  42. Ou, M., Sun, H., Li, S.: Finite time tracking control of a nonholonomic mobile robot with external disturbances. In: Proc. of the Chinese Control Conf., pp. 853–858 (2012)

  43. Zhang, Z., Leibold, M., Wollherr, D.: Integral sliding-mode observer-based disturbance estimation for euler-lagrangian systems. IEEE Trans. Control Syst. Technol. 28(6), 2377–2389 (2020)

    Article  Google Scholar 

  44. Basin, M., Guerra-Avellaneda, F.: Continuous fixed-time controller design for dynamic systems with unmeasurable states subject to unbounded disturbances. Asian J. Control 21(1), 194–207 (2019)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors sincerely appreciate to the editors and reviewers for their kind attention and valuable comments dedicated to this paper. This work was supported in part by National Natural Science Foundation of China (62073212, 61873207), and Project funded by China Postdoctoral Science Foundation (2019M661467).

Author information

Authors and Affiliations

  1. Institute of Logistics Science and Engineering, Shanghai Maritime University, Shanghai, 201306, China

    Bo Li, Haichao Zhang, Chenghu Wang & Yongsheng Yang

  2. School of Automation, Northwestern Polytechnical University, Xi’an, 710072, China

    Bing Xiao

Authors
  1. Bo Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haichao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chenghu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yongsheng Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bing Xiao.

Ethics declarations

Conflict of interest

The authors declare no potential conflict of interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 2484 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, B., Zhang, H., Xiao, B. et al. Fixed-time integral sliding mode control of a high-order nonlinear system. Nonlinear Dyn 107, 909–920 (2022). https://doi.org/10.1007/s11071-021-06984-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06984-1

Keywords

Search

Navigation