International Scholarly Research Notices

Research Article

Tuning and Retuning of PID Controller for Unstable Systems Using Evolutionary Algorithm

Table 5

Mathematical model of the bioreactor.
Operating regionState-space modelTransfer function model
Growth phase 𝐴 = 0 − 0 . 0 6 8 − 0 . 7 5 − 0 . 1 3 0 2 ; 𝐵 = − 0 . 9 9 5 1 2 . 4 8 7 8 ; 𝐶 = 1 0 ; D = [ 0 ] Δ 𝑋 ( 𝑠 ) = Δ 𝐷 ( 𝑠 ) − 0 . 9 9 5 1 𝑠 − 0 . 2 9 8 7 𝑠 2 + 0 . 1 3 0 2 𝑠 − 0 . 0 5 0 9
Stationary phase 𝐴 = 0 0 . 9 0 5 6 − 0 . 7 5 − 2 . 5 6 4 ; 𝐵 = − 1 . 5 3 0 1 3 . 8 2 5 5 ; 𝐶 = 1 0 ; D = [ 0 ] Δ 𝑋 ( 𝑠 ) = Δ 𝐷 ( 𝑠 ) − 1 . 5 3 𝑠 − 0 . 4 5 8 8 𝑠 2 + 2 . 5 6 4 𝑠 + 0 . 6 7 9 2