Feedback Control of Cellular Concentration in a Continuous Bioreactor (Turbidostat)

​
proportional controller constant ​
6
m
/kg h
1.1
integral control time constant (h)
10
feed substrate rate ​
3
m
/h
0.2
fermentation time (h)
20
feed substrate concentration kg/
3
m
​
9
This Demonstration simulates feedback control of cellular concentration in a continuous bioreactor. The cellular concentration (turbidity) is controlled by the flow rate of the substrate into the vessel.

Details

The "dynamics and feedback control" plot shows the startup of the bioreactor, initially under batch growth conditions (between hour 0 and hour 3.5). Feeding of the substrate starts after hour 3.5. Between hour 3.5 and hour 15, the setpoint for cellular concentration is 2.8 g/L. After hour 15 the setpoint is
X
max
=
S
F
×
Y
XS
, trying to control
X
near the maximum of biomass concentration. This is done to observe the response of the controlled reactor to a step change in
X
set
.
The "rates" plot shows the steady state, at which the specific growth rate becomes equal to the dilution rate
μ=D
[1].
Notation
S
: substrate concentration (g/L) (orange line)
μ
: specific growth rate (1/h) (yellow line)
μ
max
: maximum specific growth rate (1/h)
K
sat
: saturation constant (g/L)
X
: biomass concentration (g/L) (blue line)
X
max
: maximum biomass concentration (g/L) (green dashed line)
K
prop
: proportional controller constant (
6
m
kgh
)
τ
int
: integral control time constant (h)
X
set
: setpoint for cellular concentration (g/L) (red dashed line)
D
: dilution rate (1/h) (black line)
Y
XS
: biomass-substrate yield (kg/kg)
F
0
: feed substrate rate (L/h)
Kinetics
The specific growth rate
μ
predicted by the Monod equation has the following form[1]:
μ=
μ
max
S
K
sat
+S
.
Consult either reference for the model for a continuous bioreactor.
Control Process
The turbidometer is modeled by a proportional-integral control of the feed rate of substrate concentration and can be set by:
F=
F
0
+
K
prop
ϵ+
K
prop
τ
int
∫ϵdt
where
ϵ
is the error and is represented by
X-
X
set
. If
K
prop
takes the value zero, then
F
takes the value
F
0
and the process runs out of control[2].
Suggestions for Use
Snapshot 1: turn off the controller (
K
prop
=0
). Note that
X
is influenced by the
F
0
at steady state.
Snapshot 2: turn on the controller (
K
prop
≠0
). Note that
X
begins to approach
X
set
.
Snapshot 3: vary the integral control time constant to see its effect
Snapshot 4: vary the flow rate to see its effect

References

[1] P. M. Doran, Bioprocess Engineering Principles, 2nd ed., Boston: Academic Press, 2013.
[2] I. J. Dunn, E. Heinzle, J. Ingham and J. E. Prvenosil, Biological Reaction Engineering: Dynamic Modelling Fundamentals with Simulation Examples, 2nd, completely rev. ed., Weinheim, Germany: VCH Verlagsgesellschaft mbH, 2003.

External Links

Feedback Control in a Stirred-Tank Reactor
Startup and Steady State in a Chemostat
Oxygen Dynamics in a Chemostat with Substrate Inhibition

Permanent Citation

R. Ricardo Sánchez
​
​"Feedback Control of Cellular Concentration in a Continuous Bioreactor (Turbidostat)"​
​http://demonstrations.wolfram.com/FeedbackControlOfCellularConcentrationInAContinuousBioreacto/​
​Wolfram Demonstrations Project​
​Published: November 30, 2021