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. 2025 Jul 9;15:24650. doi: 10.1038/s41598-025-09336-w

Table 5.

Best gain values obtain by GWO, HHO and AOA algorithms using Benchmark errors for FLC-PI control.

MOTs—error type Rise time Setting time Overshoot Objective function Ki_VDCreg Kp_VDCreg Ki_Ireg Kp_Ireg K1 K2 K3 K4 K5 K6 K7 K8 K9 THD % Time taken
GWO -ITSE 228.87 330.09 1.52 21.66 210.20 2.60 21.72 0.30 0.89 0.94 0.97 0.71 0.54 0.70 1.38 0.15 0.68 3.97 248.60
HHO -ISE 105.79 1547.21 54.03 423.45 409.94 3.29 20.10 0.30 0.90 0.66 0.65 0.33 0.67 0.93 0.90 0.36 0.82 3.88 171.66
AOA -ITAE 228.87 330.09 1.52 549.90 210.20 2.60 21.72 0.30 0.89 0.94 0.97 0.71 0.54 0.70 1.38 0.15 0.68 3.97 249.70