PID Controller Design for an E. coli Fed-Batch Fermentation Process System Using Chaotic Electromagnetic Field Optimization

Abstract

This paper presents an optimal tuning of a proportional integral differential (PID) controller used to maintain glucose concentration at a desired set point. The PID controller synthesizes an appropriate feed rate profile for an E. coli fed-batch cultivation process. Mathematical models are developed based on dynamic mass balance equations for biomass, substrate, and product concentration of the E. coli BL21(DE3)pPhyt109 fed-batch cultivation for bacterial phytase extracellular production. For model parameter identification and PID tuning, a hybrid metaheuristic technique—chaotic electromagnetic field optimization (CEFO)—is proposed. In the hybridization, a chaotic map is used for the generation of a new electromagnetic particle instead of the electromagnetic field optimization (EFO) search strategy. The CEFO combines the exploitation capability of the EFO algorithm and the exploration power of ten different chaotic maps. The comparison of the results with classical EFO shows the superior behaviour of the designed CEFO. An improvement of 30% of the objective function is achieved by applying CEFO. Based on the obtained mathematical models, 10 PID controllers are tuned. The simulation experiments show that the designed controllers are robust, resulting in a good control system performance. The closed-loop transient responses for the corresponding controllers are similar to the estimated models. The settling time of the control system based on the third PID controller for all estimated models is approximately 9 min and the overshoot is approximately 15%. The proposed CEFO algorithm can be considered an effective methodology for mathematical modelling and achievement of high quality and better performance of the designed closed-loop system for cultivation processes.