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

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 , 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 [1].
Notation
: 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)
Kinetics
The specific growth rate predicted by the Monod equation has the following form [1]:
.
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:
where is the error and is represented by . If takes the value zero, then takes the value and the process runs out of control [2].
Suggestions for Use
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
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.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.