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RESEARCH ARTICLE

Predefined-time fractional-order terminal SMC for robot dynamics

Saim Ahmed1,2* ,  Ahmad Taher Azar1,2
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1 College of Computer and Information Sciences, Prince Sultan University, Riyadh, Saudi Arabia
2 Automated Systems and Computing Lab (ASCL), Prince Sultan University, Riyadh, Saudi Arabia
IJOCTA, 025060020 https://doi.org/10.36922/IJOCTA025060020
Received: 6 February 2025 | Revised: 9 April 2025 | Accepted: 17 April 2025 | Published online: 6 May 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This study presents an investigation into fractional-order predefined-time terminal sliding mode control (FoPtSMC) for robotic manipulators, particularly focusing on addressing uncertainties and external disturbances. The study introduces a new predefined-time fractional-order SMC method to ensure guaranteed predefined-time convergence and superior tracking performance. This approach also aims to mitigate control input chattering, a common issue in such systems. The Lyapunov analysis is used, and the study establishes the predefined time stability of the proposed closed system. Furthermore, the effectiveness of the proposed FoPtSMC technique is validated through computer simulations applied to a robotic manipulator system.

Keywords
Predefined-time control
Fractional-order SMC scheme
Robotic manipulator
Funding
This paper is funded by Prince Sultan University, Riyadh, Saudi Arabia. The authors would like to thank Prince Sultan University for paying the article processing fee for this paper.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
References
  1. Elhadidy MS, Abdalla WS, Abdelrahman AA, Elnaggar S, Elhosseini M. Assessing the accuracy and efficiency of kinematic analysis tools for sixdof industrial manipulators: The kuka robot case study. AIMS Mathematics.2024;9(6):13944–13979. https://doi.org/10.3934/math.2024678

 

  1. Joseph SB,  Dada  EG,  Abidemi  A,  Oye- wola  DO,  Khammas  Metaheuristic  algorithms  for  pid  controller parameters  tuning:   Review,  approaches and open   problems. Heliyon.2022;8(5):1-29. https://doi.org/10.1016/j.heliyon.2022.e09399

 

  1. Singh S, Azar AT, Ouannas A, Zhu Q, Zhang W, Na J. Sliding mode control technique for multi-switching synchronization of chaotic systems. 2017 9th International conference on modelling, identification and control (ICMIC). 2017;880–885. http://dx.doi.org/10.1109/ICMIC.2017.8321579

 

  1. Thanh HLNN, Vu MT, Mung NX, Nguyen NP, Phuong NT. Perturbation observer-based robust control using a multiple sliding surfaces for nonlinear systems with influences of matched and unmatched uncertainties. Mathe- matics.2020;8(8):1371. https://doi.org/10.3390/math8081371

 

  1. Li D, Slotine J-JE. On sliding control for multi-input multi-output nonlinear systems. 1987 American Control Conference. 1987;874–879.

 

  1. Almakhles D. The complex adaptive delta-modulator in sliding mode theory. 2020;22(8):1-11.https://doi.org/10.3390/e22080814

 

  1. Humaidi AJ, Ibraheem IK, Azar AT, Sadiq ME. A new adaptive synergetic control design for single link robot arm actuated by pneumatic muscles. Entropy. 2020;22(7):723. https://doi.org/10.3390/e22070723

 

  1. Chiliveri VR, Kalpana R, Subramaniam U, Muhibbullah M, Padmavathi L. Novel reaching law based predictive sliding mode control for lateral motion control of in-wheel motor drive electric vehicle with delay estimation. IET Intelligent Transport Systems. 2024;18(5):872–888. https://doi.org/10.1049/itr2.12474

 

  1. Elmorshedy MF, Selvam S, Mahajan SB, Al- makhles D. Investigation of high-gain two-tier converter with pi and super-twisting sliding mode control. ISA transactions.2023;138:628–638. https://doi.org/10.1016/j.isatra.2023.03.020

 

  1. Zhao D, Li S, Gao F. A new terminal sliding mode control for robotic manipulators. IFAC Proceedings Volumes. 2008;41(2):9888–9893. https://doi.org/10.3182/20080706-5-KR- 01673

 

  1. Boukattaya M, Gassara H. Time-varying nonsingular terminal sliding mode control for uncertain second-order nonlinear systems with prespecified time. International Journal of Adaptive Control and Signal Processing. 2022;36(8):2017–2040. https://doi.org/10.1002/acs.3445

 

  1. Feng Y, Yu X, Man Z. Non-singular terminal sliding mode control of rigid manipulators. Automatica. 2002;38(12):2159–2167. https://doi.org/10.1016/S0005-1098(02)00147-4

 

  1. Souissi S, Boukattaya M. Time-varying nonsingular terminal sliding mode control of autonomous surface vehicle with predefined convergence time. Ocean Engineering. 2022;263:112264. https://doi.org/10.1016/j.oceaneng.2022.112264

 

  1. Chen J, Zhang H, Tang Q, Zhang H. Adaptive fuzzy sliding mode control of the manipulator based on an improved super-twisting algorithm. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2024;238(10):4294–4306. http://dx.doi.org/10.1177/09544062231214835

 

  1. Yang L, Yang J. Nonsingular fast terminal sliding- mode control for nonlinear dynamical systems. International Journal of Robust and Nonlinear Control. 2011;21(16):1865–1879. http://dx.doi.org/10.1002/rnc.1666

 

  1. Ton C, Petersen C. Continuous fixed-time sliding mode control for spacecraft with flexible appendages. IFAC-PapersOnLine. 2018;51(12):1–5. https://doi.org/10.3934/mbe.2022106

 

  1. Chen J, Zhao C, Tang Q, Liu X, Wang Z, Tan C, Wu J, Long T. Low chattering trajectory tracking control of non-singular fast terminal sliding mode based on disturbance observer. International Journal of Control, Automation and Systems. 2023;21(2):440–451. https://doi.org/10.1007/s12555-021-0604-0

 

  1. Chen J, Tang Q, Zhao C, Zhang H. Adaptive sliding mode control for robotic manipulators with backlash. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2023;237(24):5842–5852. http://dx.doi.org/10.1177/09544062231167555

 

  1. Faraj MA, Maalej B, Derbel N. Design and analysis of nonsingular terminal super twisting sliding mode controller for lower limb rehabilitation exoskeleton contacting with ground. In State estimation and stabilization of nonlinear systems: Theory and applications. Springer. 2023;367–386. http://dx.doi.org/10.1007/978-3-031-37970-319

 

  1. Zaway I, Jallouli-Khlif R, Maalej B, Medhaffar H, Derbel N. From PD to fractional order PD controller used for gait rehabilitation. 2021 18th International Multi-Conference on Systems, Signals & Devices (SSD). 2021;948–953. http://dx.doi.org/10.1109/SSD52085.2021.9429318

 

  1. Gokyildirim A, Calgan  H,  Demirtas  Fractional-order sliding mode control of a 4d memristive chaotic system. Journal of Vibration and Control. 2024;30(7-8):1604–1620. http://dx.doi.org/10.1177/10775463231166187

 

  1. Chen Z, Wang X, Cheng Y. Adaptive finite-time disturbance observer based recursive fractional- order sliding mode control of redundantly actuated cable driving parallel robots under disturbances and input saturation. Journal of Vibration and Control. 2023;29(3-4):675–688. https://doi.org/10.1177/10775463211051460

 

  1. Bingi K, Rajanarayan Prusty B, Pal Singh A. A review on fractional order modelling and control of robotic manipulators. Fractal and Fractional. 2023;7(1):77. https://doi.org/10.3390/fractalfract7010077

 

  1. Mofid O, Amirkhani S, Din Su, Mobayen S, Vu MT, Assawinchaichote W. Finite-time convergence of perturbed nonlinear systems using adaptive barrier-function nonsingular sliding mode control with experimental validation. Journal of Vibration and Control. 2023;29(13- 14):3326–3339. http://dx.doi.org/10.1177/10775463221094889

 

  1. Rojsiraphisal T, Mobayen S, Asad JH, Vu MT, Chang A, Puangmalai J. Fast terminal sliding control of underactuated robotic systems based on disturbance observer with experimental validation. Mathematics. 2021;9(16):1935. http://dx.doi.org/10.3390/math9161935

 

  1. Ahmed S, Azar AT, Ibraheem IK. Model-free scheme using time delay estimation with fixed- time fsmc for the nonlinear robot dynamics. AIMS Mathematics. 2024;9(4):9989–10009. https://doi.org/10.3934/math.2024489

 

  1. Xue H, Liu X. A novel fast terminal sliding mode with predefined-time synchronization. Chaos, Solitons & Fractals. 2023;175:114049. http://dx.doi.org/10.1016/j.chaos.2023.114049

 

  1. Mazhar N, Malik FM, Raza A, Khan R. Predefined-time control of nonlinear systems: A sigmoid function based sliding manifold design approach. Alexandria Engineering Journal. 2022;61(9): 6831–6841. http://dx.doi.org/10.1016/j.aej.2021.12.030

 

  1. Mu˜noz-V´azquez AJ, S´anchez-Torres JD, Guti´errez-Alcal´a S, Jim´enez-Rodr´ıguez E, Loukianov AG. Predefined-time robust contour tracking of robotic manipulators. Journal of the Franklin Institute. 2019;356(5):2709–2722. http://dx.doi.org/10.1016/j.jfranklin.2019.01.041

 

  1. Ahmed S, Azar AT. Enhanced tracking control for n-dof robotic manipulators: A fixed-time terminal sliding mode approach with time delay estimation. Results in Engineering. 2024;24:102904. http://dx.doi.org/10.1016/j.rineng.2024.102904

 

  1. Yin C, Huang X, Chen Y, Dadras S, Zhong S-m, Cheng Y. Fractional-order exponential switching technique to enhance sliding mode control. Ap- plied Mathematical Modelling. 2017;44:705–726. https://doi.org/10.1016/j.apm.2017.02.034

 

  1. Grabcad community. accessed: Mar. 17, 2013. [online] : Https://grabcad.com/library/robot- puma-560. (n.d.).

 

  1. Armstrong B, Khatib O, Burdick J. The explicit dynamic model and inertial parameters of the puma 560 arm. Proceedings. 1986 IEEE international conference on robotics and automation. 1986;3:510–518. https://doi.org/10.1109/ROBOT.1986.1087644

 

  1. Nojavanzadeh D, Badamchizadeh M. Adaptive fractional-order nonsingular fast terminal sliding mode control for robot manipulators. IET Control Theory & Applications. 2016;10(13):1565–1572. http://dx.doi.org/10.1049/iet-cta.2015.1218
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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