# Optimized Dissolved Oxygen Fuzzy Control for Recombinant _Escherichia coli_ Cultivations
## 1 Introduction
As an alternative to the traditional control perspective, the Knowledge-Based (KB) methodologies were introduced in order to deal with uncertainties and nonlinearities of complex biological systems [PERSON] et al. (2018). [PERSON] et al. (2018); [PERSON] et al. (2018); [PERSON] et al. (2018) designed a hybrid system aiming to control DOC in a bioreactor. The DOC controller was a single module in a complete automation system for monitoring and controlling cultivations called SUPERSYS_HCDC. The hybrid system was developed by combining a digital PID controller (manipulating agitation speed) and a pseudocode based on a decision tree (manipulating air and oxygen flow rates). Results showed that, on average, it was possible to keep DOC levels near its setpoint value [PERSON] et al. (2018); [PERSON] et al. (2018); [PERSON] et al. (2018). However, further analysis showed that the decision tree did no provide smooth responses for the manipulated variables, thus revealing the need for improvements. Fuzzy control is one of the best-known KB methodologies, and it is formed by the combination of fuzzy sets theory and fuzzy logic, applied to control problems [PERSON] et al. (2018); [PERSON] et al. (2018). [PERSON] and [PERSON] (2018) designed a DOC controller based on fuzzy logic. The input variables were \"Error\" and \"Change in error\" of dissolved oxygen concentration (with \"error\" been defined as the difference between the current dissolved oxygen concentration value and its setpoint value). Output variables were air flow and agitation speed variations. To test the fuzzy controller and tune its parameters, simulations were conducted (based on previous cultivation data collected under specific conditions in order to represent the desired controller behavior). Results showed that DOC was kept near its setpoint value of 30% [PERSON] and [PERSON] (2018). In a previous work, [PERSON] et al. (2018) started applying fuzzy reasoning, aiming to improve the dissolved oxygen control module from [PERSON] et al. (2018); [PERSON] et al. (2018); [PERSON] et al. (2018). For the development of the fuzzy controller, the pseudocode of the decision tree was fuzzified using _E. coli_ cultivation data and via MATLAB software. Parameters were determined via Adaptive Neuro-Fuzzy Inference System (ANFIS) tool. To test the controller, a simulator was designed by coupling the fuzzy controller with a neural network model of the process. Simulation results showed that the fuzzy controller provided smoother air and oxygen flow rates compared with the decision tree. It also kept DOC near its optimum value of 30% [26]. This sketch is one on the few recent applications to employ fuzzy reasoning in DOC control [27]. Under the light of these facts, this work aims to develop, implement and validate an optimized fuzzy DOC controller, based on the sketch presented by [PERSON] et al. [26]. It is important to emphasize that the cited sketch was focused only on evaluating (through computational simulations) the potential of the fuzzy controller. Present work, in turn, is much more robust, bringing new (unpublished) simulation results and experimental validation. Nevertheless, the sketch in [PERSON] et al. [26] paved the way for the final version of the DOC fuzzy controller presented here. During the development process, the extensive simulations were essential to upgrade the subroutines (via improved selection of the input variables for the fuzzy system and refinement of their granulation). The modifications were necessary to raise the controller to an implementation level and bring the experimental validation results to this publication. For the new simulations, we adjusted the controller parameters and tested it with neural network models. To validate the controller, we implemented it in the SUPERSY_HCDC software (adapting the MATLAB coded controller to a LabVIEW graphic language) and conducted _E. coli_ cultivations. Batch cultivations were performed in a 5 L bioreactor with a chemically-defined medium.