Mathematical modelling, parameter identification and adaptive control of single cell protein processes in tower loop bioreactors

In recent years a new type of bioreactors, the tower loop reactor has successfully been applied for production of single cell protein (SCP). For an improved economical operation of these processes — and other applications of this type of reactors — a detailed mathematical modelling is necessary. The large dimension of the production plants used leads to distributed-parameter models; in other words, the balances are formulated as partial differential equations.

[1]  J. Aubin.  Approximation of Elliptic Boundary-Value Problems , 1980 .

[2]  A. G. Butkovskiĭ,et al.  Distributed control systems , 1969 .

[3]  R. Goodson,et al.  A definition and some results for distributed system observability , 1970 .

[4]  G. R. Walsh,et al.  Methods Of Optimization , 1976 .

[5]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[6]  F. Magelli,et al.  A contribution to the analysis of tower fermentation systems , 1977 .

[7]  A. Clamen,et al.  The relationship of substrate, growth rate, and maintenance coefficient to single cell protein production , 1973, Biotechnology and bioengineering.

[8]  Arthur E. Humphrey,et al.  Computer Applications in Fermentation Technology , 1979 .

[9]  A. Aziz,et al.  Control theory of systems governed by partial differential equations , 1977 .

[10]  A. Balakrishnan.  Applied Functional Analysis , 1976 .

[11]  Wolf D. Deckwer,et al.  Blasensäulen-Reaktoren - ihre modellmäßige Erfassung und Berechnung , 1977 .

[12]  L. Fan,et al.  On the merits of partial fluid mixing in the biochemical reactor system , 1972 .

[13]  Jose C. Merchuk,et al.  Distributed parameter model of an airlift fermentor , 1980 .

[14]  C. Cooney,et al.  Microbial utilization of methanol. , 1972, Advances in applied microbiology.

[15]  C. G. Sinclair,et al.  Models for the continuous culture of microorganisms under both oxygen and carbon limiting conditions , 1975 .

[16]  R. Curtain.  Infinite-Dimensional Linear Systems Theory , 1978 .

[17]  L. Fan,et al.  Pressure drop, gas hold‐up, and oxygen transfer in tower systems , 1977 .

[18]  W. Deckwer,et al.  A comprehensive study on co2‐interphase mass transfer in vertical cocurrent and countercurrent gas‐liquid flow , 1978 .

[19]  Magdi S. Mahmoud,et al.  Hierarchical techniques for on-line microprocessor control of an industrial fermentation process , 1983 .

[20]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[21]  W. Sittig,et al.  Erfahrungen mit großtechnisch eingesetzten Bioreaktoren , 1977 .

[22]  H. P. Schwefel,et al.  Numerische Optimierung von Computermodellen mittels der Evo-lutionsstrategie , 1977 .

[23]  L. E. Erickson,et al.  Design and physical characteristics of a multistage, continuous tower fermentor , 1969 .

[24]  Dane W. Zabriskie.  REAL‐TIME APPLICATIONS OF COMPUTERS IN FERMENTATION PROCESSES , 1979 .

[25]  Heinz Schuchmann.  On the simulation of distributed parameter systems , 1970 .

[26]  Reiner Badura,et al.  Durchmischung in Blasensäulen , 1974 .

[27]  George A. Bekey.  Hybrid computation , 1968 .

[28]  R. Luttmann,et al.  Identification of mass‐transfer parameters and process simulation of SCP production process in airlift tower reactors with an external loop , 1982, Biotechnology and bioengineering.

[29]  H. Asthana,et al.  Growth of yeast on methanol as the sole carbon substrate , 1971 .

[30]  W. Harmon Ray,et al.  Distributed parameter systems: Identification, estimation, and control , 1978 .

[31]  L. Fan,et al.  Effect of mixing on the washout and steady‐state performance of continuous cultures , 1970, Biotechnology and bioengineering.

[32]  W. Harmon Ray,et al.  Some recent applications of distributed parameter systems theory - A survey , 1978, Autom..

[33]  Carlos S. Kubrusly,et al.  Distributed parameter system indentification A survey , 1977 .

[34]  W. Deckwer.  Non-isobaric bubble columns with variable gas velocity , 1976 .

[35]  L. Erickson,et al.  Oxygen‐transfer rates and efficiencies in one‐ and two‐stage airlift towers , 1979 .

[36]  R.E. Goodson,et al.  Parameter identification in distributed systems: A synthesizing overview , 1976, Proceedings of the IEEE.

[37]  Alain Bensoussan,et al.  Control theory, numerical methods, and computer systems modelling : international symposium, Rocquencourt, June 17-21, 1974 , 1975 .

[38]  G. T. Tsao,et al.  Extended Monod equation for batch cultures with multiple exponential phases , 1975 .

[39]  J. Seinfeld.  Identification of parameters in partial differential equations , 1969 .

[40]  Daniel I. C. Wang,et al.  Single-cell protein II , 1975 .

[41]  Wolfgang K. Giloi.  Principles of Continuous System Simulation , 1976 .

[42]  H. M. Tsuchiya,et al.  Mathematical Models for Fermentation Processes , 1970 .

[43]  M. Thoma,et al.  Model development, parameter identification, and simulation of the SCP production process in air lift tower bioreactors with external loop—I: Generalized distributed parameter model , 1983 .

[44]  Hiromu Ohno,et al.  Theory and practice of optimal control in continuous fermentation process , 1975 .

[45]  Stanley B. Gershwin,et al.  Applicability of adaptive control to real problems - trends and opinions , 1978, Autom..

[46]  Wen H. Chen,et al.  Estimation of parameters in distributed systems , 1974 .

[47]  S. M. Roberts,et al.  Two-point boundary value problems: shooting methods , 1972 .

[48]  Kok Lay Teo,et al.  Optimal control of distributed parameter systems , 1981 .

[49]  R. Showalter.  Hilbert Space Methods for Partial Differential Equations , 1979, Electronic Journal of Differential Equations.

[50]  Michimasa Kishimoto,et al.  On-line Optimal Control of Fed-batch Culture of Glutamic Acid Production : , 1981 .

[51]  Jacques-Louis Lions.  Some Aspects of the Optimal Control of Distributed Parameter Systems , 1987 .

[52]  C. Nelson Dorny,et al.  A Vector Space Approach to Models and Optimization , 1983 .

[53]  J. P. Yvon.  Some Optimal Control Problems for Distributed Systems and their Numerical Solutions , 1975 .

[54]  Arvo Lannus,et al.  Gas‐Liquid Reactions , 1970 .

[55]  R. Luttmann,et al.  A comprehensive study on the cultivation of yeast in a tower bioreactor , 1980 .

[56]  R. P. Jefferis.  Workshop Computer Applications in Fermentation Technology : 1976 : text of 11 reports presented to the workshop, 5 July 1976, Braunschweig-Stöckheim , 1977 .

[57]  S. Nakagiri,et al.  Identifiability of Spatially-Varying and Constant Parameters in Distributed Systems of Parabolic Type , 1977 .

[58]  George A. Bekey,et al.  System identification- an introduction and a survey , 1970 .

[59]  Aarne Halme,et al.  Modelling and control of biotechnical processes : proceedings of the First IFAC Workshop, Helsinki, Finland, August 17-19, 1982 , 1983 .

[60]  Robert Vichnevetsky.  Hybrid methods for partial differential equations , 1971 .

[61]  G. Chavent.  Identification of functional parameters in partial differential equations , 1974 .

[62]  A Survey of Optimization Methods in Optimal Control for Distributed Parameter Systems , 1975 .

[63]  A L Tannahill,et al.  Extended culture: The growth of Candida utilis at controlled acetate concentrations , 1970, Biotechnology and bioengineering.

[64]  F. Wagner,et al.  Mikrobielle Protein-Gewinnung auf Methanol-Basis , 1974 .

[65]  Raymond P. Jefferis.  PARAMETER ESTIMATION AND DIGITAL FILTER TECHNIQUES , 1979 .

[66]  Karl Schügerl,et al.  Characterization and performance of single- and multistage tower reactors with outer loop for cell mass production , 1982 .

[67]  Roland Glowinski,et al.  An introduction to the mathematical theory of finite elements , 1976 .

[68]  W. Gestrich,et al.  Der flüssigkeitsseitige Stoffübergangskoeffizient in Blasenschichten , 1976 .

[69]  Lothar Collatz,et al.  Numerische Behandlung von Differentialgleichungen , 1948 .

[70]  R. Bellman,et al.  Quasilinearization and nonlinear boundary-value problems , 1966 .

[71]  J. P. Babary,et al.  Adaptive open loop control for a class of distributed parameter systems , 1978, Autom..

[72]  Washout condition for a biochemical reactor with axial dispersion through a dynamic approach , 1975 .

[73]  O. Levenspiel.  Chemical Reaction Engineering , 1972 .

[74]  A. Aziz.  The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations , 1972 .

[75]  L E Erickson,et al.  Oxygen transfer and axial dispersion in an aeration tower containing static mixers , 1977, Biotechnology and bioengineering.

[76]  K. von Meyenburg,et al.  Automatic analysis of gas exchange in microbial systems , 1968 .

[77]  J. Lehmann,et al.  Application of tower bioreactors in cell mass production , 1978 .

[78]  P. V. Danckwerts.  Continuous flow systems , 1953 .

[79]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[80]  U. Faust,et al.  Methanol as Carbon Source for Biomass Production in a Loop Reactor , 1980, Products from Alkanes, Cellulose and other Feedstocks.

[81]  Lennart Ljung,et al.  Theory and applications of self-tuning regulators , 1977, Autom..

[82]  S. J. Pirt,et al.  Principles of microbe and cell cultivation , 1975 .

[83]  Hanns Hofmann,et al.  Modeling of chemical reactors — XVI Steady state axial heat and mass transfer in tubular reactors An analysis of the uniqueness of solutions , 1970 .

[84]  A. Constantinides.  APPLICATION OF RIGOROUS OPTIMIZATION METHODS TO THE CONTROL AND OPERATION OF FERMENTATION PROCESSES , 1979 .

[85]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .