Skip to main content
SpringerLink
Log in

Nonlinear robust controller design for an upper limb rehabilitation robot via variable gain super twisting sliding mode

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

Rehabilitation robots have an effective role in helping patients with physical disabilities. Therefore, improving their performance is very important. In this paper, a robust nonlinear controller is proposed for the upper limb rehabilitation robot. The proposed controller has time-varying gains, which this property allows the gains to be adjusted online to external disturbances. The variable gain super twisting algorithm (VGSTA) controller is designed based on Lyapunov stability analysis, and the variable gains of the controller are determined by examining the bounds of the perturbation. Also, the convergence time is calculated. To demonstrate the desired performance of the VGSTA controller, it is compared with the fixed gain super-twisting controller and PID controller. The results show that the proposed controller ensures accurate tracking, finite-time convergence, robustness against uncertainty, internal (external) perturbations with an unknown bound, reduced chattering, and stability. The simulation results show that minimum values of RMS, Mean, and Sd of tracking error in different conditions correspond to the VGSTA controller.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

Availability of data and material

Not applicable.

Code availability (software application or custom code)

Not applicable.

References

  1. De Morand A (2014) Pratique de la rééducation neurologique. Elsevier Masson

    Google Scholar 

  2. Miao Q, Zhang M, Cao J, Xie SQ (2018) Reviewing high-level control techniques on robot-assisted upper-limb rehabilitation. Adv Robot 32(24):1253–1268

    Article  Google Scholar 

  3. Rahman MH, Saad M, Kenné J-P, Archambault PS (2013) Control of an exoskeleton robot arm with sliding mode exponential reaching law. Int J Control Autom Syst 11(1):92–104

    Article  Google Scholar 

  4. Crea S, Cempini M, Moise M, Baldoni A, Trigili E, Marconi D, Cortese M, Giovacchini F, Posteraro F, Vitiello N (2016) A novel shoulder-elbow exoskeleton with series elastic actuators. pp. 1248–1253

  5. Sharma MK, Ordonez R (2016) Design and fabrication of an intention based upper-limb exo-skeleton. pp. 1–6

  6. Kali Y, Saad M, Benjelloun K (2021) Nonsingular fast terminal second-order sliding mode for robotic manipulators based on feedback linearization. Int J Dyn Control. https://doi.org/10.1007/s40435-021-00810-7

    Article  Google Scholar 

  7. Nghia VBV, Van Thien T, Son NN, Long MT (2021) Adaptive neural sliding mode control for two wheel self balancing robot. Int J Dyn Control. https://doi.org/10.1007/s40435-021-00832-1

    Article  Google Scholar 

  8. Wang S, Yin X, Li P, Zhang M, Wang X (2020) Trajectory tracking control for mobile robots using reinforcement learning and PID. Iran J Sci Technol Trans Electr Eng 44(3):1059–1068

    Article  Google Scholar 

  9. Dávila A, Moreno JA, Fridman L (2010) Variable gains super-twisting algorithm: a Lyapunov based design. pp 968–973

  10. Miranda ABW, Forner-Cordero A (2013) Upper limb exoskeleton control based on sliding mode control and feedback linearization. pp 1–6

  11. Labbadi M, Cherkaoui M (2020) Novel robust super twisting integral sliding mode controller for a quadrotor under external disturbances. Int J Dyn Control 8(3):805–815

    Article  MathSciNet  Google Scholar 

  12. Labbadi M, Boukal Y, Cherkaoui M (2020) Path following control of quadrotor UAV with continuous fractional-order super twisting sliding mode. J Intell Rob Syst 100(3):1429–1451

    Article  Google Scholar 

  13. Gonzalez T, Moreno JA, Fridman L (2011) Variable gain super-twisting sliding mode control. IEEE Trans Autom Control 57(8):2100–2105

    Article  MathSciNet  MATH  Google Scholar 

  14. Labbadi M, Boudaraia K, Elakkary A, Djemai M, Cherkaoui M (2022) A continuous nonlinear sliding mode control with fractional operators for quadrotor UAV systems in the presence of disturbances. J Aerosp Eng 35(1):04021122

    Article  Google Scholar 

  15. Mirrashid N, Rakhtala SM, Ghanbari M (2018) Robust control design for air breathing proton exchange membrane fuel cell system via variable gain second-order sliding mode. Energy Sci Eng 6(3):126–143

    Article  Google Scholar 

  16. Cruz D, Ballesteros M, Salgado I, Chairez I (2015) Assisted rehabilitation by robotic orthosis of spinal cord and back injuries. pp 242–245

  17. Aziz HMW, Iqbal J (2016) Flexible joint robotic manipulator: Modeling and design of robust control law. pp. 63–68.

  18. Xu G, Song A, Li H (2011) Control system design for an upper-limb rehabilitation robot. Adv Robot 25(1–2):229–251

    Article  Google Scholar 

  19. Qin F, Zhao H, Zhen S, Zhang Y (2020) Adaptive robust control for lower limb rehabilitation robot with uncertainty based on Udwadia-Kalaba approach. Adv Robot 34(15):1012–1022

    Article  Google Scholar 

  20. Fellag R, Hamerlain M, Laghrouche S, Guiatni M, Achour N (2019) Homogeneous Finite time higher order sliding mode control applied to an upper limb exoskeleton robot. pp 355–360

  21. Rahmani M, Rahman MH (2020) Adaptive neural network fast fractional sliding mode control of a 7-DOF exoskeleton robot. Int J Control Autom Syst 18(1):124–133

    Article  Google Scholar 

  22. Nair AS, Ezhilarasi D (2020) Performance analysis of super twisting sliding mode controller by ADAMS–MATLAB co-simulation in lower extremity exoskeleton. Int J Precis Eng Manuf Green Technol. https://doi.org/10.1007/s40684-020-00202-w

    Article  Google Scholar 

  23. Wu Q, Wang X, Chen B, Wu H (2018) Design and fuzzy sliding mode admittance control of a soft wearable exoskeleton for elbow rehabilitation. IEEE Access 6:60249–60263

    Article  Google Scholar 

  24. Wang Y, Chen J, Yan F, Zhu K, Chen B (2019) Adaptive super-twisting fractional-order nonsingular terminal sliding mode control of cable-driven manipulators. ISA Trans 86:163–180

    Article  Google Scholar 

  25. Rosales Y, Lopez R, Rosales I, Salazar S, Lozano R (2015) Design and modeling of an upper limb exoskeleton. pp 266–272

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

    Article  MathSciNet  MATH  Google Scholar 

  27. Moreno JA, Osorio M (2008) A Lyapunov approach to secondorder sliding mode controllers and observers. In: 47th IEEE conference on decision and control, pp 2856–2861

  28. Moreno JA, Osorio M (2012) Strict Lyapunov functions for the super-twisting algorithm. IEEE Trans Autom Control 57(4):1035–1040

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

    Naghmeh Mirrashid & Esmail Alibeiki

  2. Faculty of Engineering, Department of Electrical Engineering, Golestan University, Gorgan, Iran

    Seyed Mehdi Rakhtala

Authors
  1. Naghmeh Mirrashid
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Esmail Alibeiki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seyed Mehdi Rakhtala
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Naghmeh Mirrashid: Investigation, Methodology, Software, Validation, Writing - original draft. Esmail Alibeiki and Seyed Mehdi Rakhtala: Investigation, Methodology, Supervision, Writing - review & editing.

Corresponding author

Correspondence to Esmail Alibeiki.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mirrashid, N., Alibeiki, E. & Rakhtala, S.M. Nonlinear robust controller design for an upper limb rehabilitation robot via variable gain super twisting sliding mode. Int. J. Dynam. Control 10, 1996–2010 (2022). https://doi.org/10.1007/s40435-021-00902-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-021-00902-4

Keywords

Search

Navigation