Extracellular DNA accumulation in recirculating bioprocesses inhibits microbial growth and reduces productivity. We consider a continuous bioreactor with a recirculating loop and an electrophoretic filtration unit for selective DNA removal, and develop a feedback control framework combining online state and parameter estimation via an Unscented Kalman Filter with an adaptive Model Predictive Controller that jointly optimizes dilution rate and filtration activation. Closed-loop simulations under nominal and perturbed conditions show that the addition of the filtration unit enables the proposed control strategy to achieve significantly higher cumulative profit while keeping DNA concentration below the inhibition threshold.

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