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Proportional integral derivative plus control for nonlinear discrete-time state-dependent parameter. . .
of robotic manipulators. The proposed MRAC- choosing the right value of parameters to obtain
NNTDE approach demonstrates superior perfor- stability and convergence.
mance in handling uncertainties and disturbances In summary, the proposed MRAC-NNTDE
in robotic manipulator control. The capability approach possesses great promise for improv-
of the proposed method in rapid convergence, ing the tracking quality and resilience of nonlin-
as well as good tracking with no need for a re- ear systems, particularly against external distur-
gression matrix, shows its efficiency and flexibil- bances. With wide relevance to numerous control
ity. These findings support that MRAC-NNTDE engineering problems, the paper provides original
is a promising approach for controlling complex contributions to the design and application of the
robotic systems in realistic applications where un- MRAC-NNTDE method.
certain dynamics and external disturbances pre-
vail. 6. Conclusion
Remark 2 The proposed MRAC scheme
For the uncertain robot manipulator’s unknown
adaptively adjusts the control gains, TDE esti-
dynamics under unknown external disturbances,
mates the unknown system dynamics, and a neu-
the proposed MRAC-NNTDE scheme is intro-
ral network compensates for the estimation error.
duced. TDE replaces the known regression ma-
Compared to the existing control scheme, this ap-
trix and steady-state error to estimate unknown
proach provides superior performance in handling
dynamics, resulting in model-free control and
nonlinearities and uncertainties, resulting in en-
hanced tracking and robustness. high-tracking performance in terms of conver-
gence. Simulation results of the proposed scheme,
which is applied to a 2-DOF robotic manipu-
5. Discussion lator, demonstrate the performance of MRAC-
NNTDE. The resulting simulations demonstrate
The proposed MRAC-NNTDE technique is in- that the MRAC-NNTDE has effectively achieved
tended to control the nonlinear dynamical robotic better control inputs, including robust compen-
systems under external disturbances. The goal sation of uncertain unknown dynamics under ex-
of this study is to increase tracking and transient ternal perturbations, minimal steady-state error,
features while retaining the robustness of a closed- precise joint position tracking, and rapid response
loop system. The MRAC-NNTDE approach aims speed. For further research work, the proposed
to achieve quick convergence, and the Lyapunov control scheme can be used with fractional-order
technique was utilized to demonstrate stability. control for the practical application of the robotic
The simulation results demonstrate that the system.
MRAC-NNTDE technique efficiently handles the
dynamics of a robotic manipulator with external Acknowledgments
disturbances. Figures 3-4 exhibit the variables q 1 ,
q 2 , and the tracking errors e 1 , e 2 , indicating the This paper is derived from a research grant funded
successful control performance and the capacity of by the Research, Development, and Innovation
the proposed system to reduce the tracking error Authority (RDIA), Kingdom of Saudi Arabia,
to zero quickly. The control input in Figure 5 has with grant number 13382-psu-2023-PSNU-R-3-1-
desirable characteristics such as smoothness and EI-. The authors would like to acknowledge
satisfactory tracking performance, efficiently sup- Prince Sultan University, Riyadh, Saudi Arabia,
pressing the effects of external disturbances. The for their support of this publication. This re-
benefits of the MRAC-NNTDE approach, includ- search is supported by the Automated Systems
ing improved responsiveness, reduced tracking er- and Computing Lab (ASCL), Prince Sultan Uni-
ror, and enhanced control of nonlinear dynamics, versity, Riyadh, Saudi Arabia.
are emphasized by the simulation that graphically
demonstrates and confirms the theoretical analy- Funding
sis.
This work is funded by Prince Sultan University,
Constraints of the given controller parameters Riyadh, Saudi Arabia.
and stability proofs are discussed in this study. In
order to achieve the stability of the overall system
Conflict of interest
and convergence of error in a specified time, the
appropriate parameters for the MRAC-NNTDE The authors declare that the research was con-
technique were selected. The study allows for ducted in the absence of any commercial or fi-
easier selection of acceptable values and speeds nancial relationships that could be construed as a
up convergence by emphasizing the necessity of potential conflict of interest.
735