Skip to main content
Springer Nature Link
Log in

Evaluation of various controllers in fractional order non-linear systems with actuator fault

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

The tracking control of a non-linear fractional-order system (FOS) is highly tedious since cumulative approximation errors are encountered during the control process. Hence, to cope with that problem, several controllers have been adopted previously, such as backstepping controllers, sliding mode controllers, dynamic surface controllers, etc. These controllers have successfully reduced the approximation errors in the integer order non-linear system. However, the performance of those effective controllers in fractional-order non-linear systems is evaluated in this paper. The controllers such as the backstepping controller, sliding mode controller, dynamic surface controller and fuzzy dynamic surface controller are examined on FOS to verify the stability of control systems. As a result, the backstepping controller has performed better than other controllers in the case of actuator errors but still has the problem of the increased number of derivative terms and greater complexity in repeated calculations. The tracking error of the backstepping controller has been reduced to 0.0358 with 1.58 s of response time.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Data sharing is not applicable to this article.

References

  1. Sharma M, Rajpurohit BS, Agnihotri S, Rathore AK (2020) Development of fractional order modeling of voltage source converters. IEEE Access 8:131750–131759

    Article  Google Scholar 

  2. Sabatier J (2021) Fractional order models are doubly infinite dimensional models and thus of infinite memory: consequences on initialization and some solutions. Symmetry 13(6):1099

    Article  Google Scholar 

  3. Cheng H, Huang X, Li Z (2023) Unified neuroadaptive fault-tolerant control of fractional-order systems with or without state constraints. Neurocomputing 524:117–125

    Article  Google Scholar 

  4. Li S, Li Y, Zhao D, Zhang C (2020) Adaptive state of charge estimation for lithium-ion batteries based on implementable fractional-order technology. J Energy Storage 32:101838

    Article  Google Scholar 

  5. Shah ZM, Kathjoo MY, Khanday FA, Biswas K, Psychalinos C (2019) A survey of single and multi-component Fractional-Order Elements (FOEs) and their applications. Microelectron J 84:9–25

    Article  Google Scholar 

  6. Baskonus HM, Mekkaoui T, Hammouch Z, Bulut H (2015) Active control of a chaotic fractional order economic system. Entropy 17(8):5771–5783

    Article  Google Scholar 

  7. Song S, Zhang B, Song X, Zhang Z (2019) Adaptive neuro-fuzzy backstepping dynamic surface control for uncertain fractional-order non-linear systems. Neurocomputing 360:172–184

    Article  Google Scholar 

  8. Ma Z, Ma H (2019) Adaptive fuzzy backstepping dynamic surface control of strict-feedback fractional-order uncertain non-linear systems. IEEE Trans Fuzzy Syst 28(1):122–133

    Article  Google Scholar 

  9. Han S (2020) Fractional-order command filtered backstepping sliding mode control with fractional-order non-linear disturbance observer for non-linear systems. J Franklin Inst 357(11):6760–6776

    Article  MathSciNet  Google Scholar 

  10. Delavari H, Ghaderi R, Ranjbar A, Momani S (2010) Fuzzy fractional order sliding mode controller for non-linear systems. Commun Non-linear Sci Numer Simul 15(4):963–978

    Article  Google Scholar 

  11. Liu H, Pan Y, Li S, Chen Y (2017) Adaptive fuzzy backstepping control of fractional-order non-linear systems. IEEE Trans Syst Man Cybern Syst 47(8):2209–2217

    Article  Google Scholar 

  12. Li X, Wen C, Zou Y (2020) Adaptive backstepping control for fractional-order non-linear systems with external disturbance and uncertain parameters using smooth control. IEEE Trans Syst Man Cybern Syst 51(12):7860–7869

    Article  Google Scholar 

  13. Li YX, Wang QY, Tong S (2019) Fuzzy adaptive fault-tolerant control of fractional-order non-linear systems. IEEE Trans Syst Cybern Syst 51(3):1372–1379

    Google Scholar 

  14. Hu X, Song Q, Ge M, Li R (2020) Fractional-order adaptive fault-tolerant control for a class of general non-linear systems. Non-linear Dyn 101:379–392

    Article  Google Scholar 

  15. Li X, Zhan Y, Tong S (2022) Adaptive neural network decentralized fault-tolerant control for non-linear interconnected fractional-order systems. Neurocomputing 488:14–22

    Article  Google Scholar 

  16. Sweetha S, Sakthivel R, Almakhles DJ, Priyanka S (2022) Non-fragile fault-tolerant control design for fractional-order non-linear systems with distributed delays and fractional parametric uncertainties. IEEE Access 10:19997–20007

    Article  Google Scholar 

  17. Hua C, Ning J, Zhao G, Li Y (2018) Output feedback NN tracking control for fractional-order non-linear systems with time-delay and input quantization. Neurocomputing 290:229–237

    Article  Google Scholar 

  18. Ha S, Chen L, Liu H, Zhang S (2022) Command filtered adaptive fuzzy control of fractional-order non-linear systems. Eur J Control 63:48–60

    Article  MathSciNet  Google Scholar 

  19. Li YX, Wei M, Tong S (2021) Event-triggered adaptive neural control for fractional-order non-linear systems based on finite-time scheme. IEEE Trans Cybern 52(9):9481–9489

    Article  Google Scholar 

  20. Liu H, Wang H, Cao J, Alsaedi A, Hayat T (2019) Composite learning adaptive sliding mode control of fractional-order non-linear systems with actuator faults. J Franklin Inst 356(16):9580–9599

    Article  MathSciNet  Google Scholar 

  21. Liu H, Pan Y, Cao J, Wang H, Zhou Y (2020) Adaptive neural network backstepping control of fractional-order non-linear systems with actuator faults. IEEE Trans Neural Netw Learn Syst 31(12):5166–5177

    Article  MathSciNet  Google Scholar 

  22. Liu H, Pan Y, Cao J (2019) Composite learning adaptive dynamic surface control of fractional-order non-linear systems. IEEE Trans Cybern 50(6):2557–2567

    Article  Google Scholar 

  23. Gnucci M, Marino R (2021) Adaptive tracking control for underactuated mechanical systems with relative degree two. Automatica 129:109633

    Article  MathSciNet  Google Scholar 

  24. Verrelli CM (2022) Virtual control strategy and conditioning technique for tracking and learning controls under input restrictions. Annu Rev Control 53:187–198

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lovely Professional University, Phagwara, Punjab, 144001, India

    A. Narmada & Anuj Jain

  2. Symbiosis International (Deemed University), Symbiosis Institute of Technology, Pune, 412115, India

    Manoj Kumar Shukla

  3. NIMS University Jaipur, Shobha Nagar, Jaipur, Rajasthan, 303121, India

    Neeraj Kumar Mishra

Authors
  1. A. Narmada
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Anuj Jain
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Manoj Kumar Shukla
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Neeraj Kumar Mishra
    View author publications

    You can also search for this author inPubMed Google Scholar

Contributions

All authors read and approved the final manuscript.

Corresponding author

Correspondence to A. Narmada.

Ethics declarations

Ethical approval

This article does not contain any studies with human participants or animals performed by any authors.

Consent to participate

All the authors involved have agreed to participate in this submitted article.

Consent to publish

All the authors involved in this manuscript give full consent for publication of this submitted article.

Conflict of interest

Authors declare that they have no conflict of interest.

Additional information

Publisher's note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Narmada, A., Jain, A., Shukla, M.K. et al. Evaluation of various controllers in fractional order non-linear systems with actuator fault. Multimed Tools Appl 83, 64945–64962 (2024). https://doi.org/10.1007/s11042-023-18018-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-18018-6

Keywords