Abstract
As we have seen in previous chapters of this book, bioreactors models can
predict operational problems that manifest themselves essentially in the form
of input and output multiplicities, and the occurrence of oscillatory behavior.
Input multiplicities arise when different values of a manipulated input variable
produce the same value of a desired controlled output variable. The occurrence
of such behavior is known to affect the closed-loop performance, regardless of
the selected control scheme [308]. Output multiplicities arise when the same
value of an input variable produces different values of the output variable.
The hysteresis phenomenon is the most common form of output multiplicity
and is associated with the existence of a region of open-loop unstable behavior. Output multiplicities are also known to adversely affect the control
performance of the bioreactor [292]. The study of the operability (interactions
between design and control) is a useful task. An early detection of difficult
operating regions in bioreactors would allow the removal or at least the reduction of these operational problems in the early stage of process design, and
this would ultimately improve the operability of the bioreactor. The detection
of operational problems in bioreactors is best carried out through the study
of the behavior of the open-loop process. This task requires two elements: a
good model and adequate tools for the analysis. The singularity theory was
proved to be a useful tool for this task. The theory, which was successfully
used to study the operability of chemical reactors [109, 120, 308, 309, 325],
can help to delineate how the design and operating parameters influence the
operating characteristics of the bioreactor.