# Optimized Dissolved Oxygen Fuzzy Control for Recombinant _Escherichia coli_ Cultivations
## 4 Results and Discussions
### DOC Fuzzy Controller Application in _E. coli_ Cultivations
#### 4.2.2 Adjustments in Princ1 and Princ2 Fuzzy Systems and Further _E. coli_ Tests  
Since QairIF is an important variable, that defines if pure oxygen should be enriched in the cultivation (therefore decreasing air flow rate), efforts were made to improve its performance. Initial experiments results pointed mild difficulties establishing whether maximum gas flow rate had been reached or even surpassed (as this limit changed during the cultivation). Therefore, three linguistic values (unsaturated, saturate, and supersaturate) for QairIF were determined and adjusted by ANFIS, as shown in Figure 9.  
With the new linguistic values, it was possible to establish clear limits between gas saturation levels, while keeping track of the maximum gas fluctuations during the cultivation. The three values were chosen based on the fuzzy control strategy and in the decision tree (Figure 1). At first, the system is unsaturated; therefore, air flow rate is continuously increased (with constant oxygen flow rate). When the system reached saturation (sum of air and oxygen flow rates equals the maximum gas flow rate), it gradually started to replace air flow rate with oxygen enrichment. As a protection mechanism, if the sum was greater than the maximum gas flow rate, both gas flow rate would be diminished (up till the saturation point). By applying completeness and consistency principles, ANFIS created 108 \"If-Then\" fuzzy rules for each inference system. Some of them are summarized in Table 4.  
Figure 9: QairIF linguistic values (Unsaturated, Saturated, and Supersaturated) and their respective membership functions, adjusted by ANFIS. The root mean squared errors of the training processes were 0.085 for Princ1 and 0.058 for Princ2. Once more, the training showed an almost perfect match between predicted and target values. Following the re-training of the fuzzy inference systems and their re-implementation in the SUPERSYS_HCDC software, other _E. coli_ cultivations were conducted. In one of them, the first 10 h were supervised by the decision tree, whilst the remaining period was overseen by the fuzzy controller. Analyzing the results, it was possible to obtain a final concentration of 35 g\({}_{\text{dry cell weight}}\)/L (with 2.41 g/(L * h) of productivity). Acetic acid production was neglectable (maximum concentration of 0.15 g/L, as shown in Figure 10a). Figure 10b,c show air and oxygen flow rates dynamics (respectively). By comparing these results with Figure 8a,b, it is possible to notice a smoother behavior of the manipulated variables. It also led to a less oscillatory DOC behavior during the cultivation. The exception was at around 13.5 h, when the glycerol pulse was injected in the system, causing an abrupt fall in DOC (Figure 10d). The fast recovery and stabilization of DOC around the set point value (30%) proved, once more, the robustness of the fuzzy controller. Figure 10e compares the simulation results for QairVar and QO\({}_{2}\)Var range values (used as initial condition set for the fuzzy controller) and their maximum variation range (heuristically determined during the experiment). Both values were close to the simulation results (maximum deviations of \(-0.31\) and \(+0.53\) from simulated values). Comparing Figures 8 and 10, the adjustments in the fuzzy controller showed improvements in the DOC control. The mild fluctuations observed in Figure 8c were attenuated. Statistically, in both Figures 8c and 10d, DOC mean was approximately 30%. The standard deviation in Figure 10d was smaller than in Figure 8c (3.93% and 5.59%, respectively), which was translated into an attenuation of DOC peaks in the latter. Although corrections in QairVar and QO\({}_{2}\)Var range values were necessary in both experiments, a clear reduction in the deviation was observed, pointing toward an increase in stability and performance.