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Comparison of fractional order sliding mode controllers on robot manipulator
All controllers include a sudden control signal Acknowledgments
reaction except approach 2. This reaction occurs
None.
because of derivative terms. The SMC, approach
1, and approach 3 include derivatives for every α
Funding
value. However, approach 2 does not include a
derivative calculation for α = 0. Because of that, None.
the derivative of the initial error due to initial
conditions does not affect the approach 2 control Conflict of interest
signal. It is seen that the approach 2 control sig-
The authors declare that they have no conflict of
nal is very smooth for α = 0.1, in this way. But
interest regarding the publication of this article.
for α = 0.9, approach 2 has a similar control out-
put as in the other controllers. Author contributions
The given RMSE values in Table (2) show
Conceptualization: All authors
that approach 1 and approach 3 have close re-
Formal analysis: All authors
sults compared to classical SMC for α = 0.1. Un-
Investigation: All authors
der increasing α value, the fractional order SMC
Methodology: All authors
methods give better results. The main reason
Writing–original draft: All authors
for this improvement is the effect of derivatives.
As seen from Eq. (19, 35), approach 1 and ap- Writing–review & editing: All authors
proach 3 use a derivative parameter bigger than
1, and this causes noises due to numerical calcu-
Availability of data
lations. For this reason, the Kalman filter is used
for derivatives greater than 1. Not applicable.
As seen from Table (2), approaches 1 and 3
have very close results. The only difference be- References
tween approach 3 and approach 1 mathematical 1. Hern´andez-Guzm´an VM, Orrante-Sakanassi J.
equation is the ”µe(t)”. This is an error-based PID control of robot manipulators actuated by
term and the influence of the ”µe(t)” can be seen BLDC motors. Int J Control. 2021;94(2):267–276.
in Table (2). The effect of the error value can https://doi.org/10.1080/00207179.2019.1590648
be seen as small, but this affects the system’s 2. Kuc T-Y., Han W-G. An adaptive PID learn-
reaction time. It is seen in the Figures (2, 3) ing control of robot manipulators. Automatica,
that approach 3 gives the fastest reaction and 2000;36(5):717–725.
https://doi.org/10.1016/S0005-1098(99)00198-3
also produces small overshoots because of this
term. 3. Pan Y, Li X, Yu H. Efficient PID tracking con-
trol of robotic manipulators driven by compli-
ant actuators. IEEE Trans Control Syst Technol.
5. Conclusions 2019;27(2):915–922.
https://doi.org/10.1109/TCST.2017.2783339
This paper proposes using Caputo for three differ-
4. Angel L, Viola J. Fractional order PID for track-
ent fractional sliding surfaces as the main contri-
ing control of a parallel robotic manipulator type
bution. These sliding surfaces are used in Caputo-
delta. ISA Trans. 2018;79:172–188.
based FOSMCs and compared with each other for
https://doi.org/10.1016/j.isatra.2018.04.010
the control of a 2-DOF robot manipulator. Simu-
5. Sharma R, Gaur P, Mittal AP. Performance anal-
lation results show that two of the Caputo-based ysis of two-degree of freedom fractional order PID
FOSMCs those are approach 1 and approach 3 controllers for robotic manipulator with payload.
have better performance compared to classical ISA Trans. 2015;58:279–291.
SMC. These approaches will be tested in real-time https://doi.org/10.1016/j.isatra.2015.03.013
applications in the future, especially for air and 6. Baek J, Jin M, Han S. A New Adaptive Sliding-
space vehicles. It is known that derivative terms Mode Control Scheme for Application to Ro-
cause noise and are therefore difficult to imple- bot Manipulators. IEEE Trans Ind Electron.
ment in real systems. Especially air and space 2016;63(6):3628–3637.
vehicles are nonlinear and complex systems and https://doi.org/ 10.1109/TIE.2016.2522386
it is very important to eliminate sensor noise in 7. Kapoor N, Ohri J. Sliding Mode Control (SMC)
these vehicles. For this reason, it is planned to of Robot Manipulator via Intelligent Controllers.
test FOSMC structures in real-time applications J Inst Eng India Ser B. 2017;98(1):83–98.
https://doi.org/10.1007/s40031-016-0216-x
with Kalman filters in the future.
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