Difference between revisions of "Bioreactor"

From mintOC
Jump to: navigation, search
Line 1: Line 1:
−
The bioreactor example is an easy bioreactor with an enzyme-substrate reaction. It has three states and a control that is describing the feed concentration of substrate. It is taken from the examples folder of the ACADO toolkit described in:
+
The bioreactor example is an easy bioreactor with an substrate that is converted to a product by the biomass in the reactor. It has three states and a control that is describing the feed concentration of substrate. It is taken from the examples folder of the ACADO toolkit described in:
  
 
  Houska, Boris, Hans Joachim Ferreau, and Moritz Diehl. "ACADO toolkit—An open‐source framework for automatic control and dynamic optimization."
 
  Houska, Boris, Hans Joachim Ferreau, and Moritz Diehl. "ACADO toolkit—An open‐source framework for automatic control and dynamic optimization."
 
  Optimal Control Applications and Methods 32.3 (2011): 298-312.
 
  Optimal Control Applications and Methods 32.3 (2011): 298-312.
 +
 +
Originally it seems to be taken from:
 +
 +
VERSYCK, KARINA J., and JAN F. VAN IMPE. "Feed rate optimization for fed-batch bioreactors: From optimal process performance to optimal parameter estimation."
 +
Chemical Engineering Communications 172.1 (1999): 107-124.
  
 
== Model Formulation ==
 
== Model Formulation ==
Line 18: Line 23:
 
</p>
 
</p>
  
−
 
+
The three states describe the concentration of the enzyme (<math>X</math>), the substrate (<math>S</math>), and the product (<math>P</math>) in the reactor. In steady state the feed and outlet are eaqual and dilute all three concentrations with a ratio <math>D</math>. The enzyme
  
 
In this section the dynamic model, that describes the physical or technical process of interest, should be described. First the differential equation should be written down. Then the states, inputs, and parameters should be declared (Dimension, Type (integer, real, binary, ...)). Finally the parameters that are not free in the optimization and the coefficients should be stated in an extra table or list. All equations and functions are defined over an interval <math>I \subset \R</math>. Initial values and free parameters are taken into account later in the Optimal Control Problem.
 
In this section the dynamic model, that describes the physical or technical process of interest, should be described. First the differential equation should be written down. Then the states, inputs, and parameters should be declared (Dimension, Type (integer, real, binary, ...)). Finally the parameters that are not free in the optimization and the coefficients should be stated in an extra table or list. All equations and functions are defined over an interval <math>I \subset \R</math>. Initial values and free parameters are taken into account later in the Optimal Control Problem.

Revision as of 15:28, 8 December 2015

The bioreactor example is an easy bioreactor with an substrate that is converted to a product by the biomass in the reactor. It has three states and a control that is describing the feed concentration of substrate. It is taken from the examples folder of the ACADO toolkit described in: 

Houska, Boris, Hans Joachim Ferreau, and Moritz Diehl. "ACADO toolkit—An open‐source framework for automatic control and dynamic optimization."
Optimal Control Applications and Methods 32.3 (2011): 298-312.

Originally it seems to be taken from: 

VERSYCK, KARINA J., and JAN F. VAN IMPE. "Feed rate optimization for fed-batch bioreactors: From optimal process performance to optimal parameter estimation."
Chemical Engineering Communications 172.1 (1999): 107-124.

Model Formulation

The dynamic model is an ODE model:

\begin{array}{rcl} \dot{X}&=&-DX+\mu X \\ \dot{S}&=& D(S_{f}-S)-\mu /Y_{xs} X \\ \dot{P}&=&-DP+ (\alpha \mu +\beta) X \end{array}

The three states describe the concentration of the enzyme (X), the substrate (S), and the product (P) in the reactor. In steady state the feed and outlet are eaqual and dilute all three concentrations with a ratio D. The enzyme

In this section the dynamic model, that describes the physical or technical process of interest, should be described. First the differential equation should be written down. Then the states, inputs, and parameters should be declared (Dimension, Type (integer, real, binary, ...)). Finally the parameters that are not free in the optimization and the coefficients should be stated in an extra table or list. All equations and functions are defined over an interval I \subset \R. Initial values and free parameters are taken into account later in the Optimal Control Problem.


The parameter (coefficient) p could be stated in a table, if it is fixed.

Parameter(s)
Name Symbol Value Unit
Parameter p 23 [-]

This would result in an right hand side function f(x,u) in this case, because there are no free parameters. Of course one could also specify an implicit DAE system (F(\dot{x},x,u,p,t)=0), where it just hast to be said which states are differential and which are algebraic.

Retrieved from "https://mintoc.de/index.php?title=Bioreactor&oldid=871"