Page 178 - IJOCTA-15-4

Oleiwi et al. / IJOCTA, Vol.15, No.4, pp.706-727 (2025)

Figure 10. The trajectories tracking of all angles of 3-links robot when initial value set to (0.2, −0.5, −0.8)
rad. “A” , “B”, and “C” are the positions tracking for Psi-1, Psi-2, and Psi-3, respectively. “D” is the end
effector x–y plot.
Abbreviations: Con-PID: Conventional proportional-integral-derivative control; NN: Neural network; STNN:
Self-tuning neural network.

(0.0, −0.7, −1) rad. All other controller and sys- 6.4. Overall efficiency
tem model parameters remained unchanged. This
The overall efficiency and robustness of the pro-
test evaluates the performance of the proposed
posed controllers were evaluated by simultane-
controllers under system parameter variations.
ously combining the conditions of altered ini-
The resulting ITSE values are reported in Table
tial values, external disturbances, and parameter
7, and the tracking performance of Psi-1, Psi-2,
variations. This comprehensive test represents
and Psi-3 for each control scheme is illustrated in
the most critical evaluation scenario, as it encom-
Figure 12.
passes all potential challenges that may affect the
control system. The resulting ITSE values are re-
Table 7. Integral time square error (ITSE) across ported in Table 8. Figure 13 illustrates the posi-
controllers under the condition of a 10% increase in tion tracking of Psi-1, Psi-2, and Psi-3, along with
M c and an initial values set to (0.0, −0.7, −1) rad
the trajectory followed by the 3-LRRM under the
combined test conditions for each controller.
Controller ITSE
Con-PID 0.022231 Table 8. Integral time square error (ITSE) across
STNN–PID 0.883710 controllers under the condition of a 10% increase in
NN–PID 0.001164 M c , an initial values set to (0.2, −0.5, −0.8) rad, and
Abbreviations: Con-PID, conventional disturbance
proportional-integral-derivative control;
NN, neural network; STNN, self-tuning Controller ITSE
neural network. Con-PID 0.0915603
STNN–PID 2.672754
NN–PID 0.073968
The results show that the NN–PID controller
achieves the lowest ITSE among all controllers un- Abbreviations: Con-PID, conventional
proportional-integral-derivative control;
der parameter variation. Furthermore, it records
NN, neural network; STNN, self-tuning
the fastest response and most accurately tracks
neural network.
the desired trajectories of Psi-1, Psi-2, and Psi-
3. In contrast, the STNN–PID controller ex- The results confirm that the NN–PID con-
hibits the poorest performance, yielding the high- troller achieves the lowest ITSE value, indicat-
est ITSE value. ing superior performance, while the STNN–PID
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