Page 87 - IJOCTA-15-2

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M. Yavuz, M. Ozt¨urk, B. Ya¸skıran / IJOCTA, Vol.15, No.2, pp.281-293 (2025)
With the developing technology, control sys- calculus has been extensively used in different ap-
tems have been used in many areas such as space plication areas such as control theory, 48–50 dis-
and air vehicles, 13,14 military systems, 15,16 and ease modelling, 51–53 and approximate-analytical
the automotive industry. 17,18 The purpose of us- techniques. 54–56
ing control systems is to ensure that the sys- Especially in recent years, fractional order cal-
tems automatically follow the reference signal culations have attracted increasing attention and
with minimum error against various reference sig- one of the most recent and successful methods
nals and that the system operates at maximum used to reduce the chattering effect, which is the
efficiency and is not affected by disturbances as biggest problem in the sliding mode control ap-
much as possible. proach, is the fractional order design of the slid-
ing surface. In this method, the derivative ex-
To eliminate parameter uncertainties and dis-
pression in the sliding surface is defined by using
turbance effects in the control of dynamic sys-
the system variable’s error to be controlled, and
tems, many studies have been carried out in en-
the derivative of the error is calculated fraction-
gineering fields in recent years and as a result
ally. In this case, if the sliding surface is properly
of these studies, significant progress has been
defined, the chattering effect can be eliminated
achieved in robust control approaches. Nonlin-
without reducing the robustness of the fractional
ear robust controller approaches such as adap-
tive control, 19–21 fuzzy control, 22–25 artificial neu- order sliding mode control approach.
ral network-based control, 26,27 SMC, 28–31 and In the FOSMC method, in addition to the free
FOSMC 32–35 have emerged. These control ap- selection of the controller gain coefficients as in
proaches can achieve their control objectives even integer degree controllers, the degrees of deriva-
in the presence of modeling errors, parameter un- tive and integral can also be freely selected de-
certainties, and disturbances. pending on the controller type. For this reason,
FOSMCs perform the control of the system more
The SMC approach, one of the robust control 57
successfully than integer-degree controllers. The
methods, has been easily applied to nonlinear sys-
superiority of FOSMC over SMC is observed in
tems because it is insensitive to disturbances and
the literature review. For instance; Zahraoui et
noise, can be applied to unstable systems, is easy 58
al. demonstrated that the proposed machine
to design, and has high accuracy against param- learning-based FOSMC for control of permanent
eter uncertainties. 36,37 SMC design is a two-step
magnet synchronous motor outperforms the con-
process. The first is to define a sliding surface
ventional SMC which is more widely used in in-
corresponding to the desired stable dynamics, and 59
dustry. Yuvapriya and Lakshmi showed that
the second is to obtain a control rule that achieves
FOSMC gives better results than other methods
the specified sliding surface using the Lyapunov
according to the simulation results of the con-
method. SMC was first proposed in 1950. Later,
trol methods they applied to improve the driv-
it was announced to the world by Utkin in books ing quality of the heavy-duty vehicle. In an-
and articles published in 1977 and 1992. 37,38 In other study, Musarrat and Fekih 60 proposed the
subsequent studies, different switching mecha- FOSMC approach for grid-connected photovoltaic
nisms and SMC rules for control strategy in linear systems and performed a comparative analysis
and nonlinear systems have been investigated by with a standard SMC approach and showed that
researchers. 39–42 SMC is widely used in engineer- FOSMC gives better results. Beniss et al. 61 con-
ing fields such as unmanned aerial vehicle, 43,44 ducted a comparative study between SMC and
wind turbine, 45,46 robotic manipulator, 8,47 etc.
FOSMC control strategies to improve the quality
The main disadvantage is that it produces an un-
of energy injected into the distribution grid by a
stable control signal within a certain range. This 62
wind energy conversion system. Basilio et al.
discontinuous control signal causes crackling in
applied SMC and FOSMC to control two nonlin-
the system, which in turn damages the physical
ear bi-stable vibration energy harvesting systems
system elements. 63
and compared them. Yavuz et al. discussed the
Although the beginning of fractional analysis comparison of classical SMC, Gr¨unwald-Letnikov
dates back to the 17th century, the reason why FOSMC and Caputo FOSMC for the control
it is not widely used can be considered as the of robot manipulator and showed that Caputo
lack of solution methods for fractional differen- FOSMC gives better results in simulation results.
tial equations. With technological advances, dif- The main contribution of this paper is to de-
ferent types of solution methods have been devel- termine the best sliding surface for controlling a 2-
oped for the approximate calculation of fractional DOF robot manipulator using Caputo fractional
derivatives and integrals. As a result, fractional order sliding mode controllers (CFOSMS) defined
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