Modeling, Analysis, and Intelligent Controller Tuning for a Bioreactor: A Simulation Study

Table 2

POLYMATH program for bioreactor simulation.

Lag phase	Growth phase	Stationary phase
𝑑(𝑥)/𝑑(𝑡)=(𝑢−𝐷)∗𝑥	𝑑(𝑥)/𝑑(𝑡)=(𝑢−𝐷)∗𝑥	𝑑(𝑥)/𝑑(𝑡)=(𝑢−𝐷)∗𝑥
𝑥(0)=0	𝑥(0)=0.125	𝑥(0)=1
𝑑(𝑠)/𝑑(𝑡)=𝐷∗(𝑠𝑓−𝑠)−(𝑢∗𝑥/𝑌)	𝑑(𝑠)/𝑑(𝑡)=𝐷∗(𝑠𝑓−𝑠)−(𝑢∗𝑥/𝑌)	𝑑(𝑠)/𝑑(𝑡)=𝐷∗(𝑠𝑓−𝑠)−(𝑢∗𝑥/𝑌)
𝑠(0)=1	𝑠(0)=1	𝑠(0)=1
𝑢=((𝑢𝑚∗𝑠)/(𝑘𝑚+𝑠))	𝑢=((𝑢𝑚∗𝑠)/(𝑘𝑚+𝑠))	𝑢=((𝑢𝑚∗𝑠)/(𝑘𝑚+𝑠))
𝑢𝑚=0.53	𝑢𝑚=0.53	𝑢𝑚=0.53
𝑘𝑚=0.12	𝑘𝑚=0.12	𝑘𝑚=0.12
𝐷=0.3	𝐷=0.3	𝐷=0.3
𝑠𝑓=4	𝑠𝑓=1.5122	𝑠𝑓=0.1746
𝑌=0.4	𝑌=0.4	𝑌=0.4
𝑡(0)=0	𝑡(0)=0	𝑡(0)=0
𝑡(𝑓)=10	𝑡(𝑓)=10	𝑡(𝑓)=10