Novel Nonlinear Control in a Chaotic Continuous Flow Enzymatic–Fermentative Bioreactor

Fermentative processes are considered one of the most important technological developments in the modern transforming industry, due to this, the applied research to reach high performance standards with a crucial focus on system intensification, which is the the analysis, optimization, and control issues, are a cornerstone. The goal of this proposal is to show a novel nonlinear feedback control structure to assure a stable closed-loop operation in a continuous flow enzymatic–fermentative bioreactor with chaotic dynamic behavior. The proposed structure contains an adaptive-type gain, which, coupled with a proportional term of the named control error, can lead the feedback control trajectories of the bioreactor to the required reference point or trajectory. The Lyapunov method is used to present the stability analysis of the system within a closed loop, where an adequate choice of the controller gains assures asymptotic stability. Moreover, analyzing the dynamic equation of the control error, under some properties of boundedness of the system, shows that the control error can be diminished to close to zero. Numerical experiments are carried out, where a well-tuned standard proportional–integral (PI) controller is also implemented for comparison purposes, the satisfactory performance of the proposed control scheme is observed, including the diminishing offsets, overshoots, and settling times in comparison with the PI controller.