Skip to main content
SpringerLink
Log in

Intelligent Fractional-Order Active Fault-Tolerant Sliding Mode Controller for a Knee Joint Orthosis

  • Short Paper
  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

Over the last few decades, the appearance of robot applications has been continuously increasing in rehabilitation treatment due to the increasing numbers of stroke patients. In this paper, a novel fractional-order active fault-tolerant controller (FOAFTC) based on an adaptive nonlinear observer is proposed to detect, estimate, and compensate faults of a knee joint orthosis. The controlling term is derived based on the fractional-order sliding mode control (FOSMC) approach, while the switching term of this controller is designed by the fractional-order interval type-2 fuzzy logic control (IT2FLC) technique. In this regard, a nonlinear disturbance observer (NDO) is combined with this controller to estimate the muscular torque inserted by the patient, while increasing the accuracy and speed of the system performance. Adopting the Lagrange equations, a unique model is presented for the orthosis and the human lower-limb. The proposed strategy reduces modeling difficulties and the chattering phenomenon of the SMC technique. Additionally, the number of rules in the fuzzy controller is decreased as well. Following on, the closed-loop system stability is proved theoretically. Finally, the system performance based on the suggested controller is evaluated and compared with the results of two other different controllers including the conventional SMC and the fractional-order terminal sliding mode controller. Implying the proposed controller to the system leads to the smaller frequency and magnitude of the chattering effects, which provides more convenience for patients. Moreover, the efficiency of the suggested controller is illustrated in the presence of both actuator and sensor faults.

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

Similar content being viewed by others

References

  1. Yan, T., Cempini, M., Oddo, C.M., Vitiell, N.: Review of assistive strategies in powered lower limb orthoses and exoskeletons. Robot. Auton. Syst. 64, 120–136 (2015)

    Article  Google Scholar 

  2. Huo, W., Mohammed, S., Moreno, J.C., Amirat, Y.: Lower limb wearable robots for assistance and rehabilitation: a state of the art. IEEE Syst. J. 10(3), 1068–1081 (2013)

    Article  Google Scholar 

  3. Jimenez-Fabian, R., Verlinden, O.: Review of control algorithms for robotic ankle systems in lower-limb orthoses, prostheses, and exoskeletons. Med. Eng. Phys. 34(4), 397–408 (2012)

    Article  Google Scholar 

  4. Mefoued, S.: A second order sliding mode control and a neural network to drive a knee joint actuated orthosis. Neurocomputing. 155, 71–79 (2015)

    Article  Google Scholar 

  5. Monje, C.A., Vinagre, B.M., Feliu, V., Chen, Y.Q.: Tuning and auto-tuning of fractional-order controllers for industry applications. Control Eng. Practice. 16(7), 798–812 (2008)

    Article  Google Scholar 

  6. Pashaei, S., Badamchizadeh, M.: A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances. ISA Trans. 63, 39–48 (2016)

    Article  Google Scholar 

  7. Chao, C., Teng, C.: A PD-like self-tuning fuzzy controller without steady-state error. Fuzzy Sets Syst. 87, 141–154 (1997)

    Article  Google Scholar 

  8. Mendel, J.M.: Type-2 fuzzy sets and systems: an overview. IEEE Comput Intell. 2(2), 20–29 (2007)

    Article  Google Scholar 

  9. Castillo, O., Melin, P.: Type-2 fuzzy logic: theory and application. Studfuzz. 223, 145–145 (2008)

    MATH  Google Scholar 

  10. Mendel, J.M., John, R.I., Feilong, L.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14, 808–821 (2006)

    Article  Google Scholar 

  11. Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems: theory and design. IEEE Trans. Fuzzy Syst. 8, 535–550 (2000)

    Article  Google Scholar 

  12. Hongyi, L., Chengwei, W., Peng, S.: Control of nonlinear networked systems with packet dropouts:interval type-2 fuzzy model-based approach. IEEE Transybern. 45, 2378–2389 (2015)

    Google Scholar 

  13. Mohadeszadeh, M., Delavari, H.: Synchronization of uncertain fractional-order hyper-chaotic systems via a novel adaptive interval type-2 fuzzy active sliding mode controller. Int J Dynamics Control. 5(1), 135–144 (2017)

    Article  MathSciNet  Google Scholar 

  14. Hongyi, L., Xingjian, S., Ligang, W., Lam, H.: State and output feedback control of aclass of fuzzy systems with mismatched membership functions. IEEE Trans. Fuzzy Syst. 23, 1943–1957 (2015)

    Article  Google Scholar 

  15. Heydarinejad, H., Delavari, H., Baleanu, D.: Fuzzy type-2 fractional Backstepping blood glucose control based on sliding mode observer. Int J Dynamics Control. 7, 341–354 (2019)

    Article  MathSciNet  Google Scholar 

  16. Khari, S., Rahmani, Z., Rezaie, B.: Designing fuzzy logic controller based on combination of terminal sliding mode and state feedback controllers for stabilizing chaotic behaviour in rod-type plasma torch system. Trans. Inst. Meas. Control. 38(2), 150–164 (2016)

    Article  Google Scholar 

  17. Rezaie, B., Ghasemi, H., Rahmani, Z.: Terminal Sliding Mode Controller Tuned Using Evolutionary Algorithms for Finite-Time Robust Tracking Control in a Class of Nonholonomic Systems. J. Inform. Technol. Control. 47(1), 26–44 (2018)

    Google Scholar 

  18. Bkekri, R., Benamor, A., Alouane, M.A., Fried, G., Messaoud, H.: robust adaptive sliding mode control for a human-driven knee joint orthosis. Indust. Robot. 45(3), 379–389 (2018)

    Article  Google Scholar 

  19. Mefoued, S., Eddine, D., Belkhiat, C.: A Robust Control Scheme Based on Sliding Mode Observer to Drive a Knee-Exoskeleton. Asian J. Control. 21(1), 439–455 (2019)

    Article  MathSciNet  Google Scholar 

  20. Isermann, R.: Model-based fault-detection and diagnosis – status and applications. Annu. Rev. Control. 29(1), 71–85 (2005)

    Article  Google Scholar 

  21. Zeghlache, S., Benslimane, T., Bouguerra, A.: Active fault-tolerant control based on interval type-2 fuzzy sliding mode controller and non linear adaptive observer for 3-DOF laboratory helicopter. ISA Trans. 71, 280–303 (2017)

    Article  Google Scholar 

  22. Zhang, Y.M., Jiang, J.: Bibliographical review on reconfigurable fault-tolerant control. Annu. Rev. Control. 32(2), 229–252 (2008)

    Article  Google Scholar 

  23. Xiang, Y., Jiang, J.: A survey of fault-tolerant controllers based on safety-related issues. Annu. Rev. Control. 39, 46–57 (2015)

    Article  Google Scholar 

  24. Mohammed, S., Huo, W., Huang, J., Rifaï, H., Amirat, Y.: Nonlinear disturbance observer based sliding mode control of a human-driven knee joint orthosis. Robot. Auton. Syst. 75, 41–49 (2016)

    Article  Google Scholar 

  25. Wu, J., Huang, J., Wnag, Y.J., Xing, K.X.: Nonlinear disturbance observer based dynamic surface control for trajectory tracking of pneumatic muscle system. IEEE Trans. Control Syst. Technol. 22(2), 440–455 (2014)

    Article  Google Scholar 

  26. A. Tepljakov, E. Petlenkov, J. Belikov.”Robust FOPI and FOPID controller design for FFOPDT plants in embedded control application susing frequency-domain analysis”. In: Proceedings of American control conference, Chicago,USA, pp. 3868–73, 2015

  27. Pourmahmood Aghababa, M.: Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems. Int. J. Control. 86, 1744–1756 (2013)

    Article  MathSciNet  Google Scholar 

  28. Yan, L., Chen, Y.Q., Podlubny, I.: Mittag–Leffler stability of fractional-order non-linear dynamic systems. Automatica. 45, 1965–1969 (2009)

    Article  MathSciNet  Google Scholar 

  29. Yan, L., Chen, Y.Q., Podlubny, I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Comput. Math. Appl. 59, 1810–1821 (2010)

    Article  MathSciNet  Google Scholar 

  30. Rifaï, H., Mohammed, S., Djouani, K.Y.A.: Toward lower limbs functional rehabilitation through a knee-joint exoskeleton. IEEE. Trans. Control Syst. Technol. 25(2), 712–719 (2017)

    Article  Google Scholar 

  31. El-Nagar, A.M., El-Bardini, M., El-Rabaie, N.M.: Intelligent control for nonlinear inverted pendulum based on interval type-2 fuzzy PD controller. Alexandria Eng. J. 1, 23–32 (2014)

    Article  Google Scholar 

  32. Castillo, O., Melin, P.: A review on the design and optimization of interval type-2 fuzzy controllers. Appl. Soft Comput. 12, 1267–1278 (2012)

    Article  Google Scholar 

  33. H. Delavari, R. Jokar. "Fractional-order adaptive fuzzy terminal sliding mode controller design for a knee joint orthosis with nonlinear disturbance observer." In Control, Instrumentation, and Automation (ICCIA), 2017 5th International Conference on, pp. 49–54. IEEE, 2017

  34. Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J.A.: Lyapunov functions for fractional-order systems. Commun. Nonlinear Sci. Numer. Simul. 19, 2951–2957 (2014)

    Article  MathSciNet  Google Scholar 

  35. Jiang, B., Staroswiecki, M., Cocquempot, V.: Fault accommodation for nonlinear dynamic systems. IEEETrans. Autom. Control. 51, 1587–1583 (2006)

    Article  MathSciNet  Google Scholar 

  36. Efe, M.O.: Fractional fuzzy adaptive sliding mode control of 2-DOF direct-drive robot arm. IEEE Trans Syst Man Cybern Part B Cybern. 38(6), 1561–1570 (2008)

    Article  Google Scholar 

  37. Delavari, H., Lanusse, P., Sabatier, J.: Fractional-order controller design for a flexible link manipulator robot. Asian J. Control. 15(3), 783–795 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Availability of Data and Materials

The data will be available by request after the publication of this paper.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Hamedan University of Technology, Hamedan, 65155, Iran

    Hadi Delavari & Roya Jokar

Authors
  1. Hadi Delavari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roya Jokar
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Hadi Delavari: Writing the original draft, editing and reviewing, methodology, conceptualization, and supervision. Roya Jokar: Writing the original draft, simulation programming, conceptualization, methodology.

Corresponding author

Correspondence to Hadi Delavari.

Ethics declarations

Ethical Approval

Not applicable.

Consent to Participate

Not applicable.

Consent to Publish

Authors give their consent to the Springer pulisher to publish this article in Jounral of intelligent and robotic systems.

Competing Interests

The authors declare no conflict of interest regarding the publication of this paper.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Delavari, H., Jokar, R. Intelligent Fractional-Order Active Fault-Tolerant Sliding Mode Controller for a Knee Joint Orthosis. J Intell Robot Syst 102, 39 (2021). https://doi.org/10.1007/s10846-021-01382-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-021-01382-6

Keywords

Search

Navigation