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. 2025 Aug 17;15:30128. doi: 10.1038/s41598-025-98976-z

Table 13.

Optimized PID controller gains for the test system in scenario D.

Techniques Kp1 Ki1 Kd1 Kp2 Ki2 Kd2 λ 1 λ 2 µ
CCMGO PID [Studied] - - - 1.000 1.000 1.000 - - -
CCMGO FOPI-FOPID [Studied] 0.010 0.010 - 0.900 0.900 0.010 0.010 0.900 0.900
CCMGO PD-PID [Studied] 0.010 - 0.010 1.000 1.000 0.010 - - -
CCMGO FOPID [Proposed] - - - 3.000 3.000 2.999 0.900 - 0.376