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) Regulatory layer
SP UB LB If PV > SP If PV = SP If PV < SP
PV conditioning PID parameters PV conditioning PID parameters PV conditioning PID parameters
$$Kp$$ $$Ki$$ (h−1) $$Kd$$ (h) $$Kp$$ $$Ki$$ (h−1) $$Kd$$ (h) $$Kp$$ $$Ki$$ (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
2 (2.2) 4 10 2 PV = PV + SP 0.62 0.56 0 PV = PV 0.62 0.56 0 PV = PV − SP 0.62 0.11 0
2 (2.3) 4 10 2 PV = PV + SP 0.62 0.56 0 PV = PV 0.62 0.56 0 PV = PV − SP 0.80 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
1. aThe regulatory layer in Fermentation 4, included a rate controller to prevent abrupt responses caused by noisy measurements
2. 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