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.
