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
, trying to control
near the maximum of biomass concentration. This is done to observe the response of the controlled reactor to a step change in
The "rates" plot shows the steady state, at which the specific growth rate becomes equal to the dilution rate
: substrate concentration (g/L) (orange line)
: specific growth rate (1/h) (yellow line)
: maximum specific growth rate (1/h)
: saturation constant (g/L)
: biomass concentration (g/L) (blue line)
: maximum biomass concentration (g/L) (green dashed line)
: proportional controller constant (
: integral control time constant (h)
: setpoint for cellular concentration (g/L) (red dashed line)
: dilution rate (1/h) (black line)
: biomass-substrate yield (kg/kg)
: feed substrate rate (L/h)
The specific growth rate
predicted by the Monod equation has the following form :
Consult either reference for the model for a continuous bioreactor.
The turbidometer is modeled by a proportional-integral control of the feed rate of substrate concentration and can be set by:
is the error and is represented by
takes the value zero, then
takes the value
and the process runs out of control .
Snapshot 1: turn off the controller (
). Note that
is influenced by the
at steady state.
Snapshot 2: turn on the controller (
). Note that
begins to approach
Snapshot 3: vary the integral control time constant to see its effect
Snapshot 4: vary the flow rate to see its effect
 P. M. Doran, Bioprocess Engineering Principles
, 2nd ed., Boston: Academic Press, 2013.
 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.