Control adjustments and heuristics

Several adjustments were made to provide better performance for the control system. The first modification was the insertion of an 80-point moving average filter [59] on the input variables: inlet pressure (P_in), outlet temperature (T_out), outlet oxygen fraction (yO2,out), outlet carbon dioxide fraction (yCO2,out), inlet oxygen fraction (yO2,in), and inlet carbon dioxide fraction (yCO2,in). This was done in order to maintain system stability and protect the equipment (e.g.: mass flow controllers, peristaltic pump) against sudden changes or oscillations [26]. The second adjustment was the addition of a control delay with Δt_lag = 60 s. This value refers to the time interval required for a given change in the gas stream composition to travel through the entire piping system and to be detected by the gas analyzer.

The pseudo-code of the RQ control implemented in the FMC cultivation is shown in Box ​Box3.3. It can be separated into three conditions, as follows.

In condition (1), the heuristics first determine if the on-line calculated RQ (RQCA) is between the established boundaries. If this statement is true, JSMC and JO2MC are updated along with F and Q_AIR (Box ​(Box2,2, Eqs. B2.1 and B2.3, respectively). If the statement in (1) is false, then conditions (2) and (3) are examined.

Condition (2) is true when RQCA is lower than the lower boundary, with the heuristics then calculating JCO2CA at an instant (n) (JCO2CA _new) and comparing it to JCO2CA at an instant (n-1) (JCO2CA _previous). If JCO2CA _n < JCO2CA _n−1 is true, the last JSMC, JO2MC, Q_AIR, and F are maintained. If false, it means that respiration might be under increasing activation. So, JO2MC is decremented by 0.5 mmol g_MS⁻¹ h⁻¹ to increase RQ at the next iteration, and JSMC, Q_AIR, and F are updated. The RQCA’s lower boundary is based on the 90% region of the maximum JEtOHMM (explained in Methods Metabolic Models Simulations).

Condition (3) is true when RQCA is higher than the upper boundary. In this case, JO2MC undergoes an increment of 0.5 mmol g_MS⁻¹ h⁻¹, to decrease RQ at the next iteration, and JSMC, Q_AIR, and F are also updated. The RQCA’s upper boundary was established due to the mass flow meters operational restrictions.