Modelling and optimization of a continuous stirred tank reactor with feedback control and pulse feeding

Abstract The work is a presentation of the use of a continuous stirred tank reactor with feedback control to maintain the biomass concentration in desired range. Through analysis of the model’s nonlinear dynamics and numerical performance simulations, conditions are obtained for the existence of the system’s positive period-1 solution. The analysis also indicates that the system is not chaotic. Based on the model’s analysis, it is demonstrated that the selection of suitable operating conditions for the continuous stirred tank reactor can be simplified. This offers the possibility of establishing more general and systematic operations and control strategies that are based on the counteraction of the mechanisms which underlie the adverse effects of the bioreactor dynamics. Moreover, in the article the new objective function is introduced and the aspect of advanced optimization of the biomass productivity is presented.

[1]  Yang Kuang,et al.  Limit cycles in a Chemostat-related model , 1989 .

[2]  A. Novick,et al.  Description of the chemostat. , 1950, Science.

[3]  Lansun Chen,et al.  Modelling and simulation of a continuous process with feedback control and pulse feeding , 2010, Comput. Chem. Eng..

[4]  Lansun Chen,et al.  Universal modelling and qualitative analysis of an impulsive bioprocess , 2011, Comput. Chem. Eng..

[5]  Lansun Chen,et al.  Density-dependent birth rate, birth pulses and their population dynamic consequences , 2002, Journal of mathematical biology.

[6]  Lansun Chen,et al.  Periodic solution of a turbidostat system with impulsive state feedback control , 2009 .

[7]  Lansun Chen,et al.  Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect , 2011, Biosyst..

[8]  Guangzhao Zeng,et al.  Existence of periodic solution of order one of planar impulsive autonomous system , 2006 .

[9]  Sanyi Tang,et al.  Modelling and analysis of integrated pest management strategy , 2004 .

[10]  Guifang Fu,et al.  Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake , 2005 .

[11]  Sigurd Skogestad,et al.  Comparison of various control configurations for continuous bioreactors , 1997 .

[12]  Alain Pavé,et al.  Monod's bacterial growth model revisited , 1992, Bulletin of mathematical biology.

[13]  Lansun Chen,et al.  Dynamic behaviors of Monod type chemostat model with impulsive perturbation on the nutrient concentration , 2007 .

[14]  F. Menkel,et al.  A Biological Approach on Modelling a Variable Biomass Yield , 1995 .

[15]  Yuan Tian,et al.  Nonlinear Modelling and Qualitative Analysis of a Real Chemostat with Pulse Feeding , 2010 .

[16]  Kaibiao Sun,et al.  New Approach to the Nonlinear Analysis of a Chemostat with Impulsive State Feedback Control , 2010 .

[17]  Robert D. Tanner,et al.  THE EFFECT OF THE SPECIFIC GROWTH RATE AND YIELD EXPRESSIONS ON THE EXISTENCE OF OSCILLATORY BEHAVIOR OF A CONTINUOUS FERMENTATION MODEL , 1980 .

[18]  Sanyi Tang,et al.  The effect of seasonal harvesting on stage-structured population models , 2004, Journal of mathematical biology.

[19]  Xianning Liu,et al.  Complex dynamics of Holling type II Lotka–Volterra predator–prey system with impulsive perturbations on the predator ☆ , 2003 .

[20]  Jesus Alvarez,et al.  On the existence of sustained oscillations in a class of bioreactors , 2009, Comput. Chem. Eng..

[21]  Andrzej Kasperski,et al.  Optimization of pulsed feeding in a Baker's yeast process with dissolved oxygen concentration as a control parameter , 2008 .

[22]  Guirong Jiang,et al.  Chaos and its control in an impulsive differential system , 2007 .

[23]  Hal L. Smith,et al.  Feedback control for chemostat models , 2003, Journal of mathematical biology.

[24]  Arthur E. Humphrey,et al.  Study of the dynamic behavior of the chemostat system , 1967 .

[25]  D. Tempest,et al.  The status of YATP and maintenance energy as biologically interpretable phenomena. , 1984, Annual review of microbiology.

[26]  Andrés Aguilera,et al.  Relationship between growth, fermentation, and respiration rates in Saccharomyces cerevisiae: A study based on the analysis of the yield Ypx , 1988 .

[27]  Lansun Chen,et al.  Periodic solution of a chemostat model with Monod growth rate and impulsive state feedback control. , 2009, Journal of theoretical biology.

[28]  Lansun Chen,et al.  Nonlinear modelling of a synchronized chemostat with impulsive state feedback control , 2010, Math. Comput. Model..

[29]  Robert D. Tanner,et al.  Hopf bifurcations for a variable yield continuous fermentation model , 1982 .

[30]  David F. Ollis,et al.  Biochemical Engineering Fundamentals , 1976 .

[31]  Karl Schügerl,et al.  Bioreaction Engineering: Modeling and Control , 1987 .

[32]  Duduku Krishnaiah,et al.  Chemical and bioprocess engineering: A special issue of Journal of Applied Sciences , 2007 .

[33]  G. Andrews.  Estimating cell and product yields , 1989, Biotechnology and bioengineering.

[34]  Lansun Chen,et al.  PERMANENCE AND COMPLEXITY OF THE ECO-EPIDEMIOLOGICAL MODEL WITH IMPULSIVE PERTURBATION , 2008 .

[35]  D. Bainov,et al.  Impulsive Differential Equations: Periodic Solutions and Applications , 1993 .

[36]  Guirong Jiang,et al.  Complex dynamics of a Holling type II prey–predator system with state feedback control , 2007 .

[37]  Andrzej Kasperski,et al.  Modelling of Cells Bioenergetics , 2008, Acta biotheoretica.

[38]  Xinzhu Meng,et al.  PERMANENCE AND GLOBAL STABILITY IN AN IMPULSIVE LOTKA–VOLTERRA N-SPECIES COMPETITIVE SYSTEM WITH BOTH DISCRETE DELAYS AND CONTINUOUS DELAYS , 2008 .

[39]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[40]  Y. H. Lee,et al.  A model for energy‐sufficient culture growth , 1990, Biotechnology and bioengineering.

[41]  Lansun Chen,et al.  Studies on the dynamics of a continuous bioprocess with impulsive state feedback control , 2010 .