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

Table 3.

Simulation results of the applied HHO algorithm in case of using benchmark errors (IAE, ISE, ITAE, and ITSE).

FLC-PI _HHO_(IAE, ISE, ITAE, ITSE)
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
IAE 124.23 330.07 2.91 2438.15 248.26 2.95 19.08 0.24 0.62 0.59 0.53 0.74 0.39 0.58 0.78 0.27 0.79 4.00 260.83
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
ITAE 124.23 330.07 2.91 568.97 248.26 2.95 19.08 0.24 0.62 0.59 0.53 0.74 0.39 0.58 0.78 0.27 0.79 4.00 266.51
ITSE 289.20 330.08 1.85 77.79 242.30 2.68 20.28 0.29 0.97 0.68 0.95 0.51 0.16 0.94 0.90 0.26 0.89 3.98 216.06