Fractional-Order Control of a Nonlinear Time-Delay System: Case Study in Oxygen Regulation in the Heart-Lung Machine

Table 2

Indices of the system time response due to using 𝑃𝐼𝐷 and 𝑃𝐼^𝜆𝐷^𝜇controllers.

	(Z-N)	IAE		ISE		ITAE
	𝑃𝐼𝐷	𝑃𝐼𝐷	𝑃𝐼^𝜆𝐷^𝜇	𝑃𝐼𝐷	𝑃𝐼^𝜆𝐷^𝜇	𝑃𝐼𝐷	𝑃𝐼^𝜆𝐷^𝜇
Rise time	245 sec	98 sec	45 sec	35 sec	26 sec	115 sec	31 sec
Settling time	1783 sec	300 sec	100 sec	612 sec	565 sec	300 sec	115 sec
Overshot %	50%	16.8%	18%	26.18%	26.5%	10.12%	28%
Reached criteria value	—	9816.3	4626.4	769840	327900	868350	465820