Table 3 Overview of the different control schemes. The set-points (SP), upper and lower boundaries (UB and LB, respectively), the parameters in the proportional (\(Kp\)), integral (\(Ki\)) and differential (\(Kd\)) control algorithm (PID) and the process variable (PV) conditioning according to the set-point are shown for each fermentation
Fermentation (controller)
Set-point and boundaries (g/L)
If PV > SP
If PV = SP
If PV < SP
PV conditioning
\(Kp\)
\(Ki\) (h−1)
\(Kd\) (h)
1 (1) 10 12 8 PV = PV + SP 1.00 0.50 0.05 PV = PV 1.00 0.50 0.05 PV = PV − SP 1.00 0.50 0.05
2 (2.1) 4 10 2 PV = PV + SP 0.31 0.56 0 PV = PV 0.31 0.56 0 PV = PV − SP 0.31 0.11 0
3 (3) 4 10 2 PV = PV + SP 0.72 0.56 0 PV = PV 0.72 0.56 0 PV = PV—SP 0.72 0.11 0
4 (4)a 4b 10 2 PV = PV + SP 0.72 0.56 0 PV = PV 0.72 0.56 0 PV = PV − SP 0.72 0.11 0
aThe regulatory layer in Fermentation 4, included a rate controller to prevent abrupt responses caused by noisy measurements
bThe PLS model predicted the glucose concentration with a bias of 5 g/L, resulting in a real SP of 9 g/L and not 4 g/L