Research Article

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

Table 1

Optimum setting of 𝑃 𝐼 𝐷 and 𝑃 𝐼 𝜆 𝐷 𝜇 controller parameters.

(Z-N) IAE ISE ITAE
𝑘 𝑐 𝑟 = 1 . 1 2 × 1 0 5 , 𝑇 𝑐 𝑟 = 2 8 4
𝑃 𝐼 𝐷 𝑃 𝐼 𝐷 𝑃 𝐼 𝜆 𝐷 𝜇 𝑃 𝐼 𝐷 𝑃 𝐼 𝜆 𝐷 𝜇 𝑃 𝐼 𝐷 P 𝐼 𝜆 𝐷 𝜇

𝑘 𝑝 0 . 6 𝑘 𝑐 𝑟 = 6 . 7 1 0 6 1 . 4 4 1 0 5 5 . 6 7 1 0 5 1 . 2 6 9 2 1 0 5 1 . 2 5 0 3 1 0 4 1 . 2 6 5 2 1 0 5 6 . 9 8 1 0 5
𝑘 𝑖 1 . 2 𝑘 𝑐 𝑟 / 𝑇 𝑐 𝑟 = 5 . 0 9 1 0 8 8 . 4 3 1 0 8 4 . 4 5 1 0 8 1 . 7 2 1 0 7 5 . 6 2 0 9 1 0 6 6 . 5 4 1 0 8 3 . 0 7 7 3 8 1 0 8
𝑘 𝑑 4 . 8 𝑘 𝑐 𝑟 / 𝑇 𝑐 𝑟 = 2 . 0 3 6 4 1 0 7 0.001260.02560.002330.08011 8 . 0 0 2 0 1 0 4 0.03688
𝜆 111.2010.0111.25
𝜇 111.5111.7711.55