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African vultures optimization-based hybrid neural network–proportional-integral-derivative controller...
nonlinear, multi-input–multi-output (MIMO) na- exogenous model was introduced, integrating PD
ture, industrial robotic manipulators are suscep- and H∞ control methods. Likewise, Fani and
tible to nonlinear friction, payload variations, Shahraki 15 employed genetic algorithms and the
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and external disturbances. Consequently, design- estimation of distribution algorithm to select the
ing an optimal controller requires a comprehen- optimal coefficients for a FOPID controller. Nu-
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sive understanding of the system dynamics. Cur- merical results indicated that the FOPID scheme
rently, one of the most critical challenges for re- is more effective when applied to actual robot
searchers and engineers is to develop controllers models, especially when optimized using the par-
that provide optimal tracking performance. This ticle swarm optimization (PSO) algorithm. An-
challenge arises from the inherent complexity of waar et al. 16 applied the Nelder–Mead optimiza-
controlling the position, velocity, and orientation tion technique to enhance the FOPID controller’s
of nonlinear dynamical robotic manipulators. 5,6 ability to mitigate residual tracking errors. In an-
In recent years, numerous studies have pro- other study, Khalil and Sharkawy 17 introduced an
posed various control structures and hybrid adaptive hybrid PID control strategy for manip-
schemes for two-link rigid robotic manipulators ulators and compared its performance with SMC,
(2-LRRM) addressing the position tracking prob- demonstrating the effectiveness and reliability of
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lem. Mohamed et al. developed six control struc- the proposed approach. More recently, several
tures by integrating neural networks (NNs) with studies have extended the focus to control struc-
both integer- and fractional-order proportional- tures and hybrid controllers for 3-LRRM, aim-
integral-derivative (FOPID) controllers, opti- ing to solve the path tracking problem. In this
mized using the gorilla troops optimization algo- context, Vineet et al. 18 proposed a self-regulated
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rithm. Likewise, Saha et al. introduced an adap- fuzzy FOPID scheme optimized using a back-
tive framework combining proportional-integral- tracking search algorithm.
derivative (PID) and NN controllers for effective Ahmad et al. 19 presented an NN-based PID
trajectory control of robot manipulators. In the controller, where the proposed artificial NN, con-
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study by Mohammed et al., a novel hybrid con- sisting of two layers and utilizing feedforward
trol strategy was presented, integrating backstep- training, was trained using the back-propagation
ping control with nonlinear reduced-order active algorithm. In the study by Kumar et al., 20 a
disturbance rejection control. The global stability self-tuned fuzzy FOPID controller optimized via
of the proposed controller was rigorously verified the cuckoo search algorithm was employed to ad-
using the Lyapunov method. Similarly, Tlijani et dress the behavior of a nonlinear system. Mean-
al. 10 proposed a non-singular fast terminal slid- while, Tohma and Hamoudi 21 focused on design-
ing mode control (SMC) strategy, incorporating ing two types of controllers: an adaptive SMC
a wavelet NN observer to ensure precision and with a barrier function and a saturation func-
stability in joint control. The study by Bankole tion, and a standard SMC with the same com-
and Igbonoba 11 presented a hybrid control strat- ponents, aiming to mitigate the chattering phe-
egy that combined H-infinity (H) control method- nomenon. Zhu et al. 22 developed a hybrid control
ology with proportional-derivative (PD) control, scheme combining PID with a fuzzy NN, with pa-
demonstrating superior performance over stan- rameters tuned to enable simultaneous trajectory
dalone PD and H∞ controllers. Furthermore, Es- and contact force tracking. Similarly, Sathish Ku-
mail et al. 12 developed a reliable P-H∞ controller, mar et al. 23 proposed a fuzzy direct current lin-
which integrates proportional and H∞ elements ear servo controller for robotic arm control, opti-
to enhance disturbance rejection, position track- mized using the PSO technique. The study by
ing accuracy, and vibration suppression. G¨um¨u¸s et al. 24 introduced a cascade PD con-
Villa-Tiburcio et al. 13 proposed a novel intel- troller enhanced by the bees algorithm to reg-
ligent control algorithm for force/position control ulate a flexible robot arm and suppress tip vi-
of robotic manipulators, integrating traditional bration. Likewise, Nohooji 25 developed a novel
PID/proportional integral (PI) control schemes adaptive neural-based control scheme utilizing a
with back-propagation NNs. In this approach, simplified PID-like structure to manage a robot
the back-propagation NNs are responsible for es- subjected to external disturbances and incom-
timating and compensating for dynamic varia- plete dynamic modeling. Using a direct Lyapunov
tions in the automated fiber placement process method, the PID gains were determined, and un-
in real time, while the PID/PI controllers han- certainties were estimated through a radial ba-
dle the core control actions. In the study by sis function (RBF) NN. Additionally, the control
Bankole and Igbonoba, 14 a multilayer perceptron strategy is refined to ensure constrained behavior
NN structure based on a nonlinear autoregressive throughout system operation.
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