Application to the Chemostat

Abstract

This chapter is devoted to the stabilization of chemostats under measurement delays. Continuous stirred microbial bioreactors, often called chemostats, cover a wide range of applications; specialized “pure culture” biotechnological processes for the production of specialty chemicals (proteins, antibiotics, etc.) as well as large-scale environmental technology processes of mixed cultures such as wastewater treatment. The dynamics of the chemostat is often adequately represented by a simple dynamic model involving two state variables, the microbial biomass X and the limiting organic substrate s [55]. For control purposes, one input is usually considered: the dilution rate D. A general model for microbial growth on a limiting substrate in a chemostat is of the form:

$$ \begin{array}{l}\overset{.}{X}=\left(\mu (s)- D\right) X\\ {}\overset{.}{s}= D\left({S}_0- s\right)-{\gamma}^{-1}\mu (s) X\end{array} $$

where S ₀ is the feed substrate concentration, μ(s) is the specific growth rate, and $\gamma >0$ is a biomass yield factor (constant). As seen in what follows, one important example is anaerobic digestion, which finds many applications, e.g., in wastewater treatment, sludge management, and energy from biomass.