cultivations. A modified Contois model was applied by Jianlin et al. [48] and Zhao
et al. [53] in an UKF and CKF algorithm for biomass and substrate prediction,
respectively. The growth rate can also be represented by artificial neural networks.
However this kind of models is not applied often in combination with a KF. Zorzetto
and Wilson [27] have applied a hybrid model in an EKF algorithm which is based on
the theory of limited respiratory with using artificial neural network for predicting
the growth rates during fed-batch cultivation of S. cerevisiae.
Most of the process models which are reported in literature and are used in the
Kalman filter algorithms are considered to be ideal stirred tank reactors, whereas
production-scale operations are corrupted by noise. This problem is more sever in
large-scale operations than in laboratory-scale fermentations [35]. This can describe
why all applications of state estimation methods presented in Table 1 are performed
in laboratory-scale bioreactors (most cultivations are performed in a 2–5 L bioreactor
and one cultivation [57] have been performed in a 22 L bioreactor).
4 An Extended Kalman Filter for the Monitoring of a Yeast
Cultivation
The integration of gas sensor array data in a non-linear state estimator has not been
discussed previously in the literature. Yousefi-Darani et al. [69] have designed and
implemented a model-based calibrated gas sensor array for online measurement of
ethanol concentration in batch cultivation with the yeast S. cerevisiae. However the
predicted values are only available every 5 min. Therefore in this work, in order to
have continues values of ethanol concentration as well as the values of biomass,
glucose and the maximal growth rates, we have implemented an EKF. In addition,
the whole estimation producer could be considered as a digital twin of the baker’s
yeast batch cultivation process, which could be used for process optimization and
control.
4.1 The Cultivation Process
The cultivation of Saccharomyces cerevisiae (fresh baker’s yeast, Oma’s Ur-Hefe)
was carried out in a 2.5 L bioreactor (Minifors, Infors HT, Bottmingen, Switzerland)
with a vessel of stainless steel working volume of 1.35 L equipped with a temperature (set point of 30
C) and pH (set point pH ¼ 5) control unit. The aeration and
agitation rates were kept constant at 3.5 L min
À1 and 500 rpm, respectively. For the
pre-culture, 5 g of the baker’s yeast was suspended into 100 mL medium containing
0.34 g L
À1 MgSO 4 Á7H 2 O, 0.42 g L
À1 CaCl 2 Á2H 2 O, 4.5 g L
À1 (NH 4 ) 2 SO 4 , 1.9 g L
À1
(NH 4 ) 2 HPO 4 , 0.9 g L
À1 KCl. The inoculation was performed after 10 min of
shaking. The same medium supplemented with glucose to a final concentration of
110
A. Yousefi-Darani et al.
et al. [53] in an UKF and CKF algorithm for biomass and substrate prediction,
respectively. The growth rate can also be represented by artificial neural networks.
However this kind of models is not applied often in combination with a KF. Zorzetto
and Wilson [27] have applied a hybrid model in an EKF algorithm which is based on
the theory of limited respiratory with using artificial neural network for predicting
the growth rates during fed-batch cultivation of S. cerevisiae.
Most of the process models which are reported in literature and are used in the
Kalman filter algorithms are considered to be ideal stirred tank reactors, whereas
production-scale operations are corrupted by noise. This problem is more sever in
large-scale operations than in laboratory-scale fermentations [35]. This can describe
why all applications of state estimation methods presented in Table 1 are performed
in laboratory-scale bioreactors (most cultivations are performed in a 2–5 L bioreactor
and one cultivation [57] have been performed in a 22 L bioreactor).
4 An Extended Kalman Filter for the Monitoring of a Yeast
Cultivation
The integration of gas sensor array data in a non-linear state estimator has not been
discussed previously in the literature. Yousefi-Darani et al. [69] have designed and
implemented a model-based calibrated gas sensor array for online measurement of
ethanol concentration in batch cultivation with the yeast S. cerevisiae. However the
predicted values are only available every 5 min. Therefore in this work, in order to
have continues values of ethanol concentration as well as the values of biomass,
glucose and the maximal growth rates, we have implemented an EKF. In addition,
the whole estimation producer could be considered as a digital twin of the baker’s
yeast batch cultivation process, which could be used for process optimization and
control.
4.1 The Cultivation Process
The cultivation of Saccharomyces cerevisiae (fresh baker’s yeast, Oma’s Ur-Hefe)
was carried out in a 2.5 L bioreactor (Minifors, Infors HT, Bottmingen, Switzerland)
with a vessel of stainless steel working volume of 1.35 L equipped with a temperature (set point of 30
C) and pH (set point pH ¼ 5) control unit. The aeration and
agitation rates were kept constant at 3.5 L min
À1 and 500 rpm, respectively. For the
pre-culture, 5 g of the baker’s yeast was suspended into 100 mL medium containing
0.34 g L
À1 MgSO 4 Á7H 2 O, 0.42 g L
À1 CaCl 2 Á2H 2 O, 4.5 g L
À1 (NH 4 ) 2 SO 4 , 1.9 g L
À1
(NH 4 ) 2 HPO 4 , 0.9 g L
À1 KCl. The inoculation was performed after 10 min of
shaking. The same medium supplemented with glucose to a final concentration of
110
A. Yousefi-Darani et al.