In all these works, reaction rates are estimated from the measurement of state variables
(i.e. concentrations). Some authors have used exit-gas analysis for the estimation of the
growth rates (Estler, 1995; Lubenova, 1999; Rothen et al., 1998).
An illustrative example is given in the study of Oliveira et al. (2000a) on software
sensors applications in a baker’s yeast production process. An estimation scheme
consisting of a Luenberger-type state estimator (Luenberger, 1971) and a second order
dynamic kinetics estimator (Oliveira et al., 1996) was developed with the major concern
of keeping the number of required (and easily available) on-line measurements as low as
possible. The overall estimation scheme allowed on-line tracking of 3 state variables
(biomass, glucose and ethanol concentrations) and 3 rates (specific growth rates related to
glucose oxidation, glucose fermentation, and ethanol oxidation), using on-line
measurements of only 2 state variables (concentrations of dissolved oxygen and of
dissolved carbon dioxide) and off-gas analysis. An interesting feature of this scheme is
related to on-line kinetics estimation: the “true” process kinetics could be tracked with a
second order dynamics convergence, as illustrated in Figure 3.8.
Classical controlClassical control theory relies on linear time-invariant process dynamics. Bioprocesses
are inherently non-linear and time-varying. Nevertheless, classic control strategies such
as
Figure 3.8 Specific growth ( ) rate
estimates (dotted lines) and “true” (full
line) in a baker’s yeast production
process. The kinetics estimator
imposes second order dynamics of
convergence from estimates to true
kinetics; τ and ζ are the natural period
of oscillation and damping coefficient
of the second order response.
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