Nonlinear Control of a Continuous Bioreactor Based on Cell Population Model
Saccharomyces cerevisiae (baker-s yeast) can exhibit
sustained oscillations during the operation in a continuous bioreactor
that adversely affects its stability and productivity. Because of
heterogeneous nature of cell populations, the cell population balance
models can be used to capture the dynamic behavior of such cultures.
In this paper an unstructured, segregated model is used which is
based on population balance equation(PBE) and then in order to
simulation, the 4th order Rung-Kutta is used for time dimension and
three methods, finite difference, orthogonal collocation on finite
elements and Galerkin finite element are used for discretization of the
cell mass domain. The results indicate that the orthogonal collocation
on finite element not only is able to predict the oscillating behavior of
the cell culture but also needs much little time for calculations.
Therefore this method is preferred in comparison with other methods.
In the next step two controllers, a globally linearizing control (GLC)
and a conventional proportional-integral (PI) controller are designed
for controlling the total cell mass per unit volume, and performances
of these controllers are compared through simulation. The results
show that although the PI controller has simpler structure, the GLC
has better performance.
[1] T. Munch, B. Sonnleitner, and A. Fiechter, "New insights into the
synchronization mechanism with forced synchronous cultures of
Saccharomyces cerevisiae", J. Biotechnol., 24, p299-313, 1992.
[2] S. J. Parulekar, G. B. Semones, M. J. Rolf, J. C. Lievense,
and H. C. Lim, "Induction and elimination of oscillations in continuous
cultures of Saccharomyces cerevisiae", Biotechn. Bioeng., 28, p700-710,
1986.
[3] P. R. Patnaik, "Oscillatory metabolism of Saccharomyces cerevisiae: an
overview of mechanisms and models", Biotechnology Advances, 21,
p183-192, 2003.
[4] C. Strassle, B. Sonnleitner, and A. Fiechter, "A predictive model for the
spontaneous synchronization of Saccharomyces cerevisiae grow in
continuous culture. II. Experimental verification", J. Biotechnal., 9,
p191-208, 1989.
[5] D. E. Porro, B. Martegani, M. Ranzi, and L. Alberghina, "Oscillations in
continuous cultures of budding yeasts: A segregated parameter analysis",
Biotechnol. Bioeng., 32, p411-417, 1988.
[6] T. Munch, B. Sonnleitner, and A. Fiechter, "The decisive role of the
Saccharomyces cerevisiae cell cycle behavior for dynamic growth
characterization", J. Biotechnol., 22, p329-352, 1992.
[7] M. Beuse, R. Bartling, A. Kopmann, H. Diekmann, and M. Thoma,
"Effect of the dilution rate on the mode of osillation in continuous
cultures of Saccharomyces cerevisiae", J. of Biotechnology, 61, p15-31,
1998.
[8] L. Cazzador, L. Mariani, E. Martegani, and L. Alberghina, "Structured
segregated models and analysis of self-oscillating yeast continuous
cultures", Bioprocess Eng., 5, p175-180, 1990.
[9] K. D. Jones, and D. S. Kompala, "Cybernetic model of the growth
dynamics of Saccharomyces cerevisiae in batch and continuous
cultures", J. Biotechnology, 71, p105-131, 1999.
[10] E. Martegani, D. Porro, B. M. Ranzi, and L. Alberghina, "Involvement
of a cell size control mechanism in the induction and maintenance of
oscillations in continuous cultures of budding yeast", Biotechnol.
Bioeng., 36, p453-459, 1990.
[11] C. Strassle, B. Sonnleitner, and A. Fiechter, "A predictive model for the
spontaneous synchronization of Saccharomyces cerevisiae grown in
continuous culture. I. Concept", J. Biotechnol., 7, p299-318, 1988.
[12] N. V. Mantzaris, F. Srienc, and P. Daoutidis, "Nonlinear productivity
control using a multi-stage cell population balance model", Chem. Eng.
Sci., 57, p1-14, 2002.
[13] A. G. Fredrickson, and N. V. Mantzaris, "A new set of population
balance equations for microbial and cell cultures", Chem. Eng. Sci., 57,
p2265-2278, 2002.
[14] D. Ramkrishna, D. S. Kompala., and G. T. Tsao, "Are microbes optimal
strategists?", Biotechnol. Prog., 3, p121-126, 1987.
[15] J. D. Sheppard, and P. S. Dawson, "Cell synchrony and periodic
behavior in yeast populations", Canadian J. Chem. Eng., 77, p893-902,
1999.
[16] Y. Zhang, M. A. Henson, and Y.G. Kevrekidis, "Nonlinear model
reduction for dynamic analysis of cell population models", Chem. Eng.
Sci., 58, p429-445, 2003.
[17] M. A. Henson, "Dynamic modeling and control of yeast cell populations
in continuous biochemical reactors", Comp. Chem. Eng., 27, p1185-
1199, 2003.
[18] N. V. Mantzaris, P. Daoutidis, "Cell population balance modeling and
control in continuous bioreactors", J. Process Control, 14, p775-784,
2004.
[19] G. Y. Zhu, A. M. Zamamiri, M. A. Henson, and M. A. Hjortso, "Model
predictive control of continuous yeast bioreactors using cell population
models", Chem. Eng. Sci., 55, p6155-6167, 2000.
[20] Y. Zhang, Dynamic modeling and analysis of oscillatory bioreactors,
PhD Theses, Louisiana State University, Chem. Eng. Department, 2002.
[21] M. A. Hjortso, and J. Nielsen, "A conceptual model of autonomous
oscillations in microbial cultures", Chem. Eng. Sci., 49, p1083-1095,
1994.
[22] M. A. Hjortso, and J. Nielsen, "Population balance models of
autonomous microbial oscillations", J. Biotechnol., 42, p255-269, 1995.
[23] N. V. Mantzaris, J. J. Liou, P. Daoutidis, and F. Srienc, "Numerical
solution of a mass structured cell population balance model in an
environment of changing substrate concentration", J. Biotechnol., 71,
p157-174, 1999.
[24] N. V. Mantzaris, P. Daoutidis, and F. Srienc, "Numerical solution of
multi-variable cell population balance models: I. Finite difference
methods", Comp. Chem. Eng., 25, p1411-1440, 2001.
[25] N. V. Mantzaris, P. Daoutidis, and F. Srienc, "Numerical solution of
multi-variable cell population balance models: II. Spectral methods",
Comp. Chem. Eng., 25, p1441-1462, 2001.
[26] N. V. Mantzaris, P. Daoutidis, and F. Srienc, "Numerical solution of
multi-variable cell population balance models: III. Finite element
methods", Comp. Chem. Eng., 25, p1463-1481, 2001.
[27] B. A. Finlayson, Nonlinear analysis in chemical engineering, McGraw-
Hill, 1980.
[28] M. J. Kurtz, G. Y. Zhu, A. M. Zamamiri, M. A. Henson, and M. A.
Hjortso, "Control of oscillating microbial cultures described by
population balance models", Ind. Eng. Chem. Research, 37, p4059-4070,
1998.
[29] Y. Zhang, A. M. Zamamiri, M. A. Henson, and M. A. Hjortso, "Cell
population models for bifurcation analysis and nonlinear control of
continuous yeast bioreactors", J. process control. ,12, p721-734, 2002.
[30] M. J. Kurtz, G. Y. Zhu, A. M. Zamamiri, M. A. Henson, and M. A.
Hjortso, "Control of oscillating microbial cultures described by
population balance models", Ind. Eng. Chem. Research, 37, p4059-4070,
1998.
[31] M. Shahrokhi, and M. A. Fanaei, "State estimation in a batch suspension
polymerization reactor", Iranian Polymer J., 10, p173-187, 2001.
[32] M. Soroush, and C. Kravaris, "Nonlinear control of a batch
polymerization reactor: An experimental study", AIChE J., 38, p1429-
1440, 1992.
[1] T. Munch, B. Sonnleitner, and A. Fiechter, "New insights into the
synchronization mechanism with forced synchronous cultures of
Saccharomyces cerevisiae", J. Biotechnol., 24, p299-313, 1992.
[2] S. J. Parulekar, G. B. Semones, M. J. Rolf, J. C. Lievense,
and H. C. Lim, "Induction and elimination of oscillations in continuous
cultures of Saccharomyces cerevisiae", Biotechn. Bioeng., 28, p700-710,
1986.
[3] P. R. Patnaik, "Oscillatory metabolism of Saccharomyces cerevisiae: an
overview of mechanisms and models", Biotechnology Advances, 21,
p183-192, 2003.
[4] C. Strassle, B. Sonnleitner, and A. Fiechter, "A predictive model for the
spontaneous synchronization of Saccharomyces cerevisiae grow in
continuous culture. II. Experimental verification", J. Biotechnal., 9,
p191-208, 1989.
[5] D. E. Porro, B. Martegani, M. Ranzi, and L. Alberghina, "Oscillations in
continuous cultures of budding yeasts: A segregated parameter analysis",
Biotechnol. Bioeng., 32, p411-417, 1988.
[6] T. Munch, B. Sonnleitner, and A. Fiechter, "The decisive role of the
Saccharomyces cerevisiae cell cycle behavior for dynamic growth
characterization", J. Biotechnol., 22, p329-352, 1992.
[7] M. Beuse, R. Bartling, A. Kopmann, H. Diekmann, and M. Thoma,
"Effect of the dilution rate on the mode of osillation in continuous
cultures of Saccharomyces cerevisiae", J. of Biotechnology, 61, p15-31,
1998.
[8] L. Cazzador, L. Mariani, E. Martegani, and L. Alberghina, "Structured
segregated models and analysis of self-oscillating yeast continuous
cultures", Bioprocess Eng., 5, p175-180, 1990.
[9] K. D. Jones, and D. S. Kompala, "Cybernetic model of the growth
dynamics of Saccharomyces cerevisiae in batch and continuous
cultures", J. Biotechnology, 71, p105-131, 1999.
[10] E. Martegani, D. Porro, B. M. Ranzi, and L. Alberghina, "Involvement
of a cell size control mechanism in the induction and maintenance of
oscillations in continuous cultures of budding yeast", Biotechnol.
Bioeng., 36, p453-459, 1990.
[11] C. Strassle, B. Sonnleitner, and A. Fiechter, "A predictive model for the
spontaneous synchronization of Saccharomyces cerevisiae grown in
continuous culture. I. Concept", J. Biotechnol., 7, p299-318, 1988.
[12] N. V. Mantzaris, F. Srienc, and P. Daoutidis, "Nonlinear productivity
control using a multi-stage cell population balance model", Chem. Eng.
Sci., 57, p1-14, 2002.
[13] A. G. Fredrickson, and N. V. Mantzaris, "A new set of population
balance equations for microbial and cell cultures", Chem. Eng. Sci., 57,
p2265-2278, 2002.
[14] D. Ramkrishna, D. S. Kompala., and G. T. Tsao, "Are microbes optimal
strategists?", Biotechnol. Prog., 3, p121-126, 1987.
[15] J. D. Sheppard, and P. S. Dawson, "Cell synchrony and periodic
behavior in yeast populations", Canadian J. Chem. Eng., 77, p893-902,
1999.
[16] Y. Zhang, M. A. Henson, and Y.G. Kevrekidis, "Nonlinear model
reduction for dynamic analysis of cell population models", Chem. Eng.
Sci., 58, p429-445, 2003.
[17] M. A. Henson, "Dynamic modeling and control of yeast cell populations
in continuous biochemical reactors", Comp. Chem. Eng., 27, p1185-
1199, 2003.
[18] N. V. Mantzaris, P. Daoutidis, "Cell population balance modeling and
control in continuous bioreactors", J. Process Control, 14, p775-784,
2004.
[19] G. Y. Zhu, A. M. Zamamiri, M. A. Henson, and M. A. Hjortso, "Model
predictive control of continuous yeast bioreactors using cell population
models", Chem. Eng. Sci., 55, p6155-6167, 2000.
[20] Y. Zhang, Dynamic modeling and analysis of oscillatory bioreactors,
PhD Theses, Louisiana State University, Chem. Eng. Department, 2002.
[21] M. A. Hjortso, and J. Nielsen, "A conceptual model of autonomous
oscillations in microbial cultures", Chem. Eng. Sci., 49, p1083-1095,
1994.
[22] M. A. Hjortso, and J. Nielsen, "Population balance models of
autonomous microbial oscillations", J. Biotechnol., 42, p255-269, 1995.
[23] N. V. Mantzaris, J. J. Liou, P. Daoutidis, and F. Srienc, "Numerical
solution of a mass structured cell population balance model in an
environment of changing substrate concentration", J. Biotechnol., 71,
p157-174, 1999.
[24] N. V. Mantzaris, P. Daoutidis, and F. Srienc, "Numerical solution of
multi-variable cell population balance models: I. Finite difference
methods", Comp. Chem. Eng., 25, p1411-1440, 2001.
[25] N. V. Mantzaris, P. Daoutidis, and F. Srienc, "Numerical solution of
multi-variable cell population balance models: II. Spectral methods",
Comp. Chem. Eng., 25, p1441-1462, 2001.
[26] N. V. Mantzaris, P. Daoutidis, and F. Srienc, "Numerical solution of
multi-variable cell population balance models: III. Finite element
methods", Comp. Chem. Eng., 25, p1463-1481, 2001.
[27] B. A. Finlayson, Nonlinear analysis in chemical engineering, McGraw-
Hill, 1980.
[28] M. J. Kurtz, G. Y. Zhu, A. M. Zamamiri, M. A. Henson, and M. A.
Hjortso, "Control of oscillating microbial cultures described by
population balance models", Ind. Eng. Chem. Research, 37, p4059-4070,
1998.
[29] Y. Zhang, A. M. Zamamiri, M. A. Henson, and M. A. Hjortso, "Cell
population models for bifurcation analysis and nonlinear control of
continuous yeast bioreactors", J. process control. ,12, p721-734, 2002.
[30] M. J. Kurtz, G. Y. Zhu, A. M. Zamamiri, M. A. Henson, and M. A.
Hjortso, "Control of oscillating microbial cultures described by
population balance models", Ind. Eng. Chem. Research, 37, p4059-4070,
1998.
[31] M. Shahrokhi, and M. A. Fanaei, "State estimation in a batch suspension
polymerization reactor", Iranian Polymer J., 10, p173-187, 2001.
[32] M. Soroush, and C. Kravaris, "Nonlinear control of a batch
polymerization reactor: An experimental study", AIChE J., 38, p1429-
1440, 1992.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:50805", author = "Mahdi Sharifian and Mohammad Ali Fanaei", title = "Nonlinear Control of a Continuous Bioreactor Based on Cell Population Model", abstract = "Saccharomyces cerevisiae (baker-s yeast) can exhibit
sustained oscillations during the operation in a continuous bioreactor
that adversely affects its stability and productivity. Because of
heterogeneous nature of cell populations, the cell population balance
models can be used to capture the dynamic behavior of such cultures.
In this paper an unstructured, segregated model is used which is
based on population balance equation(PBE) and then in order to
simulation, the 4th order Rung-Kutta is used for time dimension and
three methods, finite difference, orthogonal collocation on finite
elements and Galerkin finite element are used for discretization of the
cell mass domain. The results indicate that the orthogonal collocation
on finite element not only is able to predict the oscillating behavior of
the cell culture but also needs much little time for calculations.
Therefore this method is preferred in comparison with other methods.
In the next step two controllers, a globally linearizing control (GLC)
and a conventional proportional-integral (PI) controller are designed
for controlling the total cell mass per unit volume, and performances
of these controllers are compared through simulation. The results
show that although the PI controller has simpler structure, the GLC
has better performance.", keywords = "Bioreactor, cell population balance, finite difference,
orthogonal collocation on finite elements, Galerkin finite element,
feedback linearization, PI controller.", volume = "3", number = "3", pages = "127-10", }
