Journal of Control Science and Engineering / 2012 / Article / Tab 1

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 πœ† 𝐷 πœ‡ controller parameters.

(Z-N) IAE ISE ITAE
π‘˜ 𝑐 π‘Ÿ = 1 . 1 2 Γ— 1 0 βˆ’ 5 , 𝑇 𝑐 π‘Ÿ = 2 8 4
𝑃 𝐼 𝐷 𝑃 𝐼 𝐷 𝑃 𝐼 πœ† 𝐷 πœ‡ 𝑃 𝐼 𝐷 𝑃 𝐼 πœ† 𝐷 πœ‡ 𝑃 𝐼 𝐷 P 𝐼 πœ† 𝐷 πœ‡

π‘˜ 𝑝 0 . 6 π‘˜ 𝑐 π‘Ÿ = 6 . 7 βˆ— 1 0 βˆ’ 6 1 . 4 4 βˆ— 1 0 βˆ’ 5 5 . 6 7 βˆ— 1 0 βˆ’ 5 1 . 2 6 9 2 βˆ— 1 0 βˆ’ 5 1 . 2 5 0 3 βˆ— 1 0 βˆ’ 4 1 . 2 6 5 2 βˆ— 1 0 βˆ’ 5 6 . 9 8 βˆ— 1 0 βˆ’ 5
π‘˜ 𝑖 1 . 2 π‘˜ 𝑐 π‘Ÿ / 𝑇 𝑐 π‘Ÿ = 5 . 0 9 βˆ— 1 0 βˆ’ 8 8 . 4 3 βˆ— 1 0 βˆ’ 8 4 . 4 5 βˆ— 1 0 βˆ’ 8 1 . 7 2 βˆ— 1 0 βˆ’ 7 5 . 6 2 0 9 βˆ— 1 0 βˆ’ 6 6 . 5 4 βˆ— 1 0 βˆ’ 8 3 . 0 7 7 3 8 1 0 βˆ’ 8
π‘˜ 𝑑 4 . 8 π‘˜ 𝑐 π‘Ÿ / 𝑇 𝑐 π‘Ÿ = 2 . 0 3 6 4 βˆ— 1 0 βˆ’ 7 0.001260.02560.002330.08011 8 . 0 0 2 0 βˆ— 1 0 βˆ’ 4 0.03688
πœ† 111.2010.0111.25
πœ‡ 111.5111.7711.55

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