# Optimized Dissolved Oxygen Fuzzy Control for Recombinant _Escherichia coli_ Cultivations
## 4 Results and Discussions  
### Simulation Results  
Figures 6 and 7 illustrate the simulation results for the modeled processes, based on A16 and A12 datasets (respectively). The first simulation represents the base case (both fuzzy controller and neural networks were trained with the same A16 dataset). However, the second simulation is a robustness test, in order to test the fuzzy controller performance under a different simulated process (based on the A12 dataset). Figure 6: Simulation results for DOC fuzzy control using the simulator. The dashed line represents previously controlled cultivation data using the decision tree, whereas the solid line represents the simulated process, controlled by the fuzzy controller. Dynamics of air (**a**) and oxygen (**b**) flow rates comparing both controllers, dissolved oxygen results during fuzzy control compared with the decision tree (**c**), and limits for comparing QairVar and QO\({}_{2}\)Var to appropriate range values (**d**) to analyze if maintaining, increasing, or decreasing the previous QairP and QO\({}_{2}\)P flow rates. Figure 6a,b compare the fuzzy controller and the decision tree dynamics in relation to air and oxygen flow rates (respectively). The result was an improvement in stability, for both flow rates. It also affected DO_net results; in a way that a smooth behavior (that is, the dissolved oxygen peaks were soften) was observed (Figure 6c). The fixed QairVar and QO\({}_{2}\)Var range values (associated with Princl and Princ2 subroutines, respectively) were heuristically determined by balancing small deviations in air and oxygen flow rates (compared with the decision tree responses) and smoother DOC behavior (Figure 6d). Both final QairVar and QO\({}_{2}\)Var range values were smaller than the output target used during ANFIS training. Thus, with the fuzzy DOC controller, it was possible to maintain the dissolved oxygen concentration near its optimum value of 30%, with little offset. It is worth noticing that the standard deviation of the decision tree responses was 1.52 times higher than those provided by the fuzzy controller (2.72%), proving, statistically, that DOC peaks were softened. A second set of simulation run-ups was conducted aiming to test the fuzzy controller robustness. It is important to notice that no change in membership function parameters of fuzzy control was carried out for the new test. The second pair of trained neural networks (based on A12 dataset) were coupled with the simulator, and a new heuristic search for QairVar and QO\({}_{2}\)Var range values was performed. Figure 7a,b compare the fuzzy controller and the decision tree dynamics. The result was an improvement in stability, for air and oxygen flow rates, by applying fuzzy logic. It also affected DO_net results, in a way so that a smoother behavior of the output was observed (Figure 7c). The fixed QairVar and QO\({}_{2}\)Var range values were heuristically de  
Figure 7: Robustness tests results for DOC fuzzy control using the simulator. The dashed line represents previously controlled cultivation data using the decision tree, whereas the solid line represents the simulated process, controlled by the fuzzy controller. Dynamics of air (**a**) and oxygen (**b**) flow rates comparing both controllers, DOC results during fuzzy control compared with the decision tree (**c**), and limits for comparing QairVar and QO\({}_{2}\)Var to appropriate range values (**d**) to analyze if maintaining, increasing, or decreasing the previous QairP and QO\({}_{2}\)P flow rates. termined by balancing small deviations in gas flow rates and smoother DOC behavior (Figure 7d). Both final QairVar and QO\({}_{2}\)Var range values were smaller than the output target used during ANFIS training (especially QO\({}_{2}\)Var range values). The standard deviation of the decision tree responses was 2.45 times higher than the fuzzy controller (3.87%), proving, statistically, that DOC peaks were softened.