Skip to main content
SpringerLink
Log in

Modeling and control of batch fermentation processes under conditions of uncertainty

  • Originals
  • Published:
Bioprocess Engineering Aims and scope Submit manuscript

Abstract

An approach of model-based control design of batch biotechnological processes combining the advantages of two different analytical descriptions (deterministic and fuzzy model) is proposed. The approach uses the kinetic unstructured model accounting for the basic process dependencies. Using the fuzzy optimal decomposition of the physiological space into fuzzy regions, a new model is derived as a fuzzy weighted sum of distinct subsystems with unstructured models describing the process dynamics in the respective region. The proposed model can be considered as a compromise between the simple fuzzy model (input-output process description) which does not take into account the analytical process characteristics and the unstructured deterministic model that is not suitable for the control design purpose. On-line linearizing control law on the basis of the developed model is also proposed. The theoretical results are illustrated for the example of batch xanthan gum fermentation of strain Xanthomonas campestris ITS-342.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

X g/kg:

biomass concentration

S g/kg:

limiting substrate concentration

P g/kg:

product concentration

μ(.) h−1 :

specific growth rate

ɛ(.) h−1 :

specific consumption rate

η(.) h−1 :

specific production rate

u :

process input

y :

process output

r :

marker vector

A :

vector, denoting the model coefficients

v :

weight coefficient

b i :

cluster (region) center

m :

number of fuzzy regions

n :

number of marker vector components

k :

discrete time

K :

number of the experimental data

H :

partition entropy

F :

partition coefficient

Ī :

averaged interactivity

I :

mutual interactivity between the clusters

μ ik :

membership function of the current process state in thek −th moment to thei −th cluster

y ⋆ :

set point of process output

e :

tracking error

T p h:

process time constant

λ=1/T p h−1 :

constant

T h:

sampling period

PS :

physiological state

PSN :

physiological situation

R :

fuzzy rule

i :

index, denotingi −th fuzzy region

1,s1,s2:

indexes, denoting iteration numbers

References

  1. Filev, D.: Fuzzy Modeling of Complex Systems. International J. of Approximate Reasoning. 5 (1991) 281–290

    Google Scholar 

  2. Hirota, K.;Pedricz, W.: Characterization of fuzzy clustering algorithms in terms of entropy of probabilistic sets. Pattern Recognition Letters. 2 (1984) 213–216

    Google Scholar 

  3. Sugeno, M.;Kang, G.: Structure identification of Fuzzy model. Fuzzy Sets and Systems. 28 (1988) 15–33

    Google Scholar 

  4. Patarinska, T.;Georgieva, O.: Modeling and control of xanthan gum production. Biotechnology and Biotechnological Equipment. 12 (1992) 12–18

    Google Scholar 

  5. Takagi, T.;Sugeno, M.: Fuzzy identification and its appplications to modeling and control. IEEE Transaction on System, Man and Cybernetics. SMC15 No1 (1985) 116–132

    Google Scholar 

  6. Yager, R.;Filev, D.: Unified structure and parameter identification of fuzzy models. Technical Report #MII-1211 Machine Intelligence Institute. New York. 1991

    Google Scholar 

  7. Bastin, G.;Dochain, D.; On-line estimation and adaptive control of bioreactors. Elsevier. Amsterdam. 1990

    Google Scholar 

  8. Yang, M-S.: A survey of fuzzy clustering. Mathematical and Computer Modeling. 18 (1993) No 11 1–162

    Google Scholar 

  9. Konstantinov, K.;Yoshida, T.: Physiological state control of fermentation processes. Biotechnology and Bioengineering. 33 (1989) 1145–1156

    Google Scholar 

  10. Staniskis, J.: Optimal control of biotechnical processes. Mokslas. Vilnius. 1984 (in Russian)

  11. Birukov, V.;Kantare, B.: Optimization of batch microbiological processes. Nauka. Moscow. 1985 (in Russian)

    Google Scholar 

  12. Takamatzu, T. et al.: A comparison of unstructured growth models of microorganisms. J. of Fermentation Technology. 59 No2 (1982)

  13. Pedrycz, W.: Fuzzy sets in pattern recognition: Methodology and Methods. Pattern Recognition. 23 No1/2 (1990) 121–146

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Control and System Research-Bulgarian Academy of Sciences, Acad. G. Bonchev St., bl.2, 1113, Sofia, Bulgaria

    O. Georgieva

  2. Center of Systems Engineering and Applied Mechanics Faculty of Applied Sciences, University Catholic of Louvain, Batiment Euler, 4-6, Georges Lemaitre Str., B-1348, Louvain-la-Neuve, Belgium

    T. Patarinska

Authors
  1. O. Georgieva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Patarinska
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

One of us (T. Patarinska) would like to thank the Belgium Science Policy Office for the opportunity to work at the Universite Catholique de Louvain, Louvain-la-Neuve, Belgium, where part of this work has been completed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Georgieva, O., Patarinska, T. Modeling and control of batch fermentation processes under conditions of uncertainty. Bioprocess Engineering 14, 299–306 (1996). https://doi.org/10.1007/BF00369473

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00369473

Keywords

Search

Navigation