4.4 Offline Measurements
For offline analysis, samples were regularly taken from the bioreactor and placed in
pre-weighed and pre-dried micro centrifuge tubes. For biomass determination, the
sample without supernatant were dried for 24 h at 103
C and after cooling for 30 min
weighed. Using the filtrated supernatant (pore size filter, 0.45 μm, polypropylene
membrane, VWR, Darmstadt, Germany), glucose and ethanol were determined by
HPLC (ProStar, Variant, Walnut Creek, CA, USA); injection of 20 μL into a Rezex
ROA-organic acid H+ (8%) column (Phenomenex, Aschaffenburg, Germany) and
operated at 70
C with 5 mM H 2 SO 4 as an eluent at 0.6 mL min
À1
flow rate; software
GalaxieTM Chromatography (Varian, Walnut Creek, CA, USA). The offline values
were not used during the estimation of the state variables and are only taken to show
that the estimates are accurate.
4.5 State Equations of the Cultivation Process
As bioreactor an ideal stirred tank reactor was assumed. As state variables, the
biomass, glucose and ethanol concentrations as well as the maximal specific growth
rate on glucose and ethanol were applied. Therefore, the following state equations
are obtained:
d
dt
X
G
E
μ max ,G
μ max ,E
2
6
6
6
6
6
6
4
3
7
7
7
7
7
7
5
¼
μ G þ μ E
ð
Þ X
À
μ G
Y GX
X
μ G
Y GE
À
μ E
Y EX
X
0
0
2
6
6
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
7
7
5
ð19Þ
were μ G and μ E are given as
μ G ¼
μ max ,G ∙ G
K G þ G
ð20Þ
μ E ¼
μ max ,E ∙ E
K E þ E
∙ 1 À
μ G
μ max ,G
2
ð21Þ
As one can see from the state equation, the Kalman filter is used to estimate the
maximum specific growth rate on glucose μ max, G and on ethanol μ max, E . The
importance of the specific growth rate for the assessment of a cultivation is discussed
by Galvanauskas et al. [70].
The Kalman Filter for the Supervision of Cultivation Processes
113
For offline analysis, samples were regularly taken from the bioreactor and placed in
pre-weighed and pre-dried micro centrifuge tubes. For biomass determination, the
sample without supernatant were dried for 24 h at 103
C and after cooling for 30 min
weighed. Using the filtrated supernatant (pore size filter, 0.45 μm, polypropylene
membrane, VWR, Darmstadt, Germany), glucose and ethanol were determined by
HPLC (ProStar, Variant, Walnut Creek, CA, USA); injection of 20 μL into a Rezex
ROA-organic acid H+ (8%) column (Phenomenex, Aschaffenburg, Germany) and
operated at 70
C with 5 mM H 2 SO 4 as an eluent at 0.6 mL min
À1
flow rate; software
GalaxieTM Chromatography (Varian, Walnut Creek, CA, USA). The offline values
were not used during the estimation of the state variables and are only taken to show
that the estimates are accurate.
4.5 State Equations of the Cultivation Process
As bioreactor an ideal stirred tank reactor was assumed. As state variables, the
biomass, glucose and ethanol concentrations as well as the maximal specific growth
rate on glucose and ethanol were applied. Therefore, the following state equations
are obtained:
d
dt
X
G
E
μ max ,G
μ max ,E
2
6
6
6
6
6
6
4
3
7
7
7
7
7
7
5
¼
μ G þ μ E
ð
Þ X
À
μ G
Y GX
X
μ G
Y GE
À
μ E
Y EX
X
0
0
2
6
6
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
7
7
5
ð19Þ
were μ G and μ E are given as
μ G ¼
μ max ,G ∙ G
K G þ G
ð20Þ
μ E ¼
μ max ,E ∙ E
K E þ E
∙ 1 À
μ G
μ max ,G
2
ð21Þ
As one can see from the state equation, the Kalman filter is used to estimate the
maximum specific growth rate on glucose μ max, G and on ethanol μ max, E . The
importance of the specific growth rate for the assessment of a cultivation is discussed
by Galvanauskas et al. [70].
The Kalman Filter for the Supervision of Cultivation Processes
113