New approach to the nonlinear analysis of a chemostat with impulsive state feedback control

Bioreactor control is an important area of research concerning continuous microorganism cultivation. The possible occurrence of the substrate inhibition phenomenon or substrate deficiency engenders the necessity to the control the substrate concentration. Moreover in order to maintain the dissolved oxygen content in an appropriate range, the biomass concentration should not exceed the set out level. To maintain the substrate and biomass concentration in certain desired ranges, a proposal of a new chemostat with pulse state feedback control is presented in the work. Then, a universal mathematical model of the chemostat is formulated, and the dynamic properties of the model including the existence and stability of the periodic solution are discussed. After this, in order to optimize the biomass production, two objective functions are introduced and the optimization is performed. The work shows that the proposed chemostat extends functionality of a chemostat providing in easy way the control of biomass and substrate concentration. The analytical results presented in the work are validated by numerical simulations. Copyright © 2010 The Berkeley Electronic Press. All rights reserved.