Page 86 - IJOCTA-15-2

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.2, pp.281-293 (2025)
https://doi.org/10.36922/ijocta.1678

RESEARCH ARTICLE

Comparison of fractional order sliding mode controllers on robot
manipulator

¨
3
Mehmet Yavuz 1,2* , Muhammet Ozt¨urk , and Burcu Ya¸skıran 1
1 Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University,
42090 Konya, T¨urkiye
2 Department of Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University, Bishkek 720038,
Kyrgyzstan
3 Department of Aeronautical Engineering, Faculty of Aviation and Astronautics, Necmettin Erbakan
University, 42140 Konya, T¨urkiye
mehmetyavuz@erbakan.edu.tr, mozturk@erbakan.edu.tr, burcu.yaskiran89@gmail.com

ARTICLE INFO ABSTRACT
Article History: Challenging and time-consuming tasks performed by humans can today be
Received: September 11, 2024 performed faster and more efficiently by robot manipulators with the develop-
Accepted: January 21, 2025 ment of technology. Robotic manipulators are flexible, can fit in small spaces,
Published Online: April 4, 2025 and are very effective for tasks that require high precision. They are widely
used in the production lines of factories (handling, assembly, welding, etc.)
Keywords:
and in fields that require manpower, such as medicine and engineering. Since
Robot manipulator
it is used in tasks that require precision, its control is also important. Sliding
Sliding surface
modal control (SMC), one of the robust control methods, is a control method
Sliding mode control
used in nonlinear systems because it can be applied to unstable systems, is easy
Caputo fractional order operator
to design and, has high accuracy against parameter uncertainties. However,
AMS Classification: it produces an unstable control signal within a certain range and this discon-
26A33; 70Q05; 70E60; 93C85; tinuous control signal causes cracking in the system, which causes damage to
93C10 the system elements. Especially in recent years, one of the most recent and
successful methods used to reduce the chattering effect, which is the biggest
problem in the SMC approach, is the fractional order design of the sliding
surface. In the fractional order SMC (FOSMC) method, the derivative ex-
pression in the sliding surface is defined using the system variable’s error to
be controlled and the derivative of the error is computed fractionally. In this
paper, Caputo FOSMC (CFOSMC), defined with 3 different sliding surfaces
using the Caputo fractional operator, is compared with classical SMC for con-
trolling a 2-degree of-freedom (2-DOF) robot manipulator. According to the
results obtained from simulation comparisons, it is observed that approach 3
gives better results than the other two approaches and classical SMC in terms
of overshoot, settling and error value for some derivative orders.

1. Introduction manipulators require high precision, their con-
trol is very important. An appropriate control
Robot manipulators are widely used in in- method should be applied to increase their effi-
dustrial processes such as handling, assembly, ciency. Some of the methods used in the liter-
welding, etc., in fields such as medicine and ature for robot manipulator control are propor-
aerospace. Challenging and time-consuming tional–integral–derivative (PID), 1–3 fractional or-
tasks performed by humans can be done faster der PID, 4,5 sliding mode control (SMC), 6–8 frac-
and more efficiently thanks to robot manipu- tional order SMC (FOSMC). 9–12
lators. Since the tasks performed by robot
*Corresponding Author
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