Abstract
The mathematical model of an aerobic culture of recombinant yeast presented in work by Zhang et al. (1997) is given by a differential-algebraic system. The classical nonlinear observer algorithms are generally based on ordinary differential equations. In this paper, first we extend the nonlinear observer synthesis to differential-algebraic dynamical systems. Next, we apply this observer theory to the mathematical model proposed in Zhang et al. (1997). More precisely, based on the total cell concentration and the recombinant protein concentration, the observer gives the online estimation of the glucose, the ethanol, the plasmid-bearing cell concentration and a parameter that represents the probability of plasmid loss of plasmid-bearing cells. Numerical simulations are given to show the good performances of the designed observer.
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Abbreviations
- C 1 :
-
activity of pacing enzyme pool for glucose fermentation (dimensionless)
- C 2 :
-
activity of pacing enzyme pool for glucose oxidation (dimensionless)
- C 3 :
-
activity of pacing enzyme pool for ethanol oxidation (dimensionless)
- E :
-
ethanol concentration (g/l)
- G :
-
glucose concentration (g/l)
- k a :
-
regulation constant for (g glucose/g cell h−1)
- k b :
-
regulation constant for (dimensionless)
- k c :
-
regulation constant for (g glucose/g cell h−1)
- k d :
-
regulation constant for (dimensionless)
- K m1 :
-
saturation constant for glucose fermentation (g/l)
- K m2 :
-
saturation constant for glucose oxidation (g/l)
- K m3 :
-
saturation constant for ethanol oxidation (g/l)
- L ( t):
-
time lag function (dimensionless)
- p :
-
probability of plasmid loss of plasmid-bearing cells (dimensionless)
- P :
-
recombinant protein concentration (mg/g cell)
- q G :
-
total glucose flux culture time (g glucose/g cell h)
- t :
-
culture time (h)
- t lag :
-
lag time (h)
- X :
-
total cell concentration (g/l)
- X + :
-
plasmid-bearing cell concentration (g/l)
- Y F X / G :
-
cell yield for glucose fermentation pathway (g cell/g glucose)
- Y O X / G :
-
cell yield for glucose oxidation pathway (g cell/g glucose)
- Y X / E :
-
cell yield for ethanol oxidation pathway (g cell/g ethanol)
- Y E / X :
-
ethanol yield for fermentation pathway based on cell mass (g ethanol·g cell)
- α 2 :
-
glucoamylase yield for glucose oxidation (units/g cell)
- α 3 :
-
glucoamylase yield for ethanol oxidation (units/g cell)
- µ 1 :
-
specific growth rate for glucose fermentation (h−1)
- µ 2 :
-
specific growth rate for glucose oxidation (h−1)
- µ 3 :
-
specific growth rate for ethanol oxidation (h−1)
- µ 1max :
-
maximum specific growth rate for glucose fermentation (h−1)
- µ 2max :
-
maximum specific growth rate for glucose oxidation (h−1)
- µ 3max :
-
maximum specific growth rate for ethanol oxidation (h−1)
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El Assoudi, A., El Yaagoubi, E.H. & Hammouri, H. Observer design for differential-algebraic model of an aerobic culture of a recombinant yeast. Bioprocess Biosyst Eng 26, 27–35 (2003). https://doi.org/10.1007/s00449-003-0331-3
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DOI: https://doi.org/10.1007/s00449-003-0331-3