Page 54 - IJOCTA-15-3

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.3, pp.426-434 (2025)
https://doi.org/10.36922/IJOCTA025060020

RESEARCH ARTICLE

Predefined-time fractional-order terminal SMC for robot dynamics

Saim Ahmed 1,2* and Ahmad Taher Azar 1,2

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
sahmed@psu.edu.sa, aazar@psu.edu.sa
ARTICLE INFO ABSTRACT

Article History:
Received: February 6, 2025 This study presents an investigation into fractional-order predefined-time ter-
Revised: April 9, 2025 minal sliding mode control (FoPtSMC) for robotic manipulators, particularly
focusing on addressing uncertainties and external disturbances. The study in-
Accepted: April 17, 2025
troduces a new predefined-time fractional-order SMC method to ensure guar-
Published Online: May 6, 2025
anteed predefined-time convergence and superior tracking performance. This
Keywords: approach also aims to mitigate control input chattering, a common issue in
Predefined-time control, such systems. The Lyapunov analysis is used, and the study establishes the
Fractional-order SMC scheme predefined time stability of the proposed closed system. Furthermore, the ef-
Robotic manipulator fectiveness of the proposed FoPtSMC technique is validated through computer
AMS Classification 2010: simulations applied to a robotic manipulator system.
93D05; 93C95; 93C10; 70E60

1. Introduction disturbances has solidified its popularity in con-
trolling complex systems, especially in the context
Precisely controlling robotic manipulators is cru- of real-world robots with intricate dynamics that
cial for automating tasks in various industries. are difficult to model accurately. 5–9 Terminal Slid-
However, it can be challenging due to their com- ing Mode Control (TSM), an extension of SMC,
plex and unpredictable movements. Unknown provides the additional benefit of ensuring state
disturbances and uncertainties can compromise convergence within a predetermined time frame,
1
precise motions and stable performance. Tradi- leading to enhanced precision and resilience for
tional control methods rely on complex mathe- robots following a planned trajectory. 10,11 How-
matical models to predict robot behavior and de- ever, the literature suggests that TSM may
sign control strategies. Real-world robots may demonstrate slower convergence compared to al-
behave differently due to manufacturing varia- ternative methods. 12–14 Moreover, specific TSM
tions, resulting in unexpected behaviors or un- implementations can present design complexities,
modeled dynamics that can significantly impact necessitating careful attention. 15–18 Research en-
control performance, leading to errors, instabil- deavors have concentrated on enhancing the ro-
ity, or safety hazards. 2,3 This sensitivity to un- bustness and responsiveness of TSM. 19,20 One
certainties underscores the increasing need for ro- promising strategy is fractional-order SMC, which
bust control approaches in robotics, which priori- combines SMC with the fractional-order control
tize maintaining expected tracking performance scheme, offering several advantages. 21 Fractional-
and closed-loop stability even under unknown order SMC has the potential to enhance the sys-
factors. 4 tem’s response speed and path-following accuracy
The effectiveness of sliding mode control while reducing control jitters. 22 By having these
(SMC) in managing uncertainties and external advantages, fractional-order SMC emerges as a
*Corresponding Author
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