The extension to the ordinary Monod model for μ E is applied, so that the
transformation from glucose consumption to ethanol consumption is modelled. In
Tables 2, 3, and 4 the parameters of the model as well as the initial values for the
state equations and the initial values of the estimation error covariance are presented.
The Matlab code as well as the measured off- and online data of this example can
be found in the appendix.
4.6 Results
In Fig. 4 the online and offline measured values of ethanol, the offline measured
values of biomass and glucose as well as all the Kalman filter estimated values of all
three bioprocess variables can be seen.
Figure 4 indicates the typical diauxic growth pattern of baker’s yeast on glucose
is obtained. First the glucose is consumed and biomass and ethanol are produced,
Table 2 Parameter values used for the simulation model
Parameter
Value
Description
K G
0.1 gL
À1
Monod constant glucose
K E
0.1 gL
À1
Monod constant ethanol
Y GX
0.17 gg
À1
Conversion factor glucose to biomass
Y GE
0.46 gg
À1
Conversion factor glucose to ethanol
Y EX
0.6 gg
À1
Conversion factor ethanol to biomass
Table 3 Initial conditions for the extended Kalman filter
Parameter Value
Description
X t ¼ 0
2.4 gL
À1
Initial biomass
concentration
G t ¼ 0
5.0 gL
À1
Initial glucose
concentration
E t ¼ 0
0.1 gL
À1
Initial ethanol
concentration
μ max, G
0.14 h
À1
Initial maximal
growth rate on
glucose
μ max, E
0.07 h
À1
Initial maximal
growth rate on
ethanol
P t ¼ 0
0:02 g
2 L
2
0
0
0
0
0
0 :02 g
2 L
2
0
0
0
0
0
0 :02 g
2 L
À2
0
0
0
0
0
0 :02 h
À2
0
0
0
0
0
0 :02 h
À2
0
B
B
B
B
B
B
@
1
C
C
C
C
C
C
A
Initial estimation
error covariance
matrix
114
A. Yousefi-Darani et al.