Linearized Stability Analysis of Continuous Fermentor

Biochemical Engineering

Problem Statement: The following equations describe a continuous bioreactor. 
  dx
  -- = (u-D)*x
  dt

  ds              u*x
  -- = D*(sf-s) - ---
  dt               Y

  where   u(s)=0.3*s/(50+s+0.01*s2)    Y(s)=0.004+0.001*s
          s in (g/liter)  and  u in (h-1)
Map out the stability regions in the operating domain (i.e., for various values of D and sf.

Solution:

See a related problem on the optimum dilution rate for maximum cell productivity. Dynamic simulation of the same set of equations verifies the findings here based on linearlized analysis.

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Biochemical Engineering -- Linearized Stability Analysis of Continuous Fermentor
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