Parameter continuation and numerical bifurcation analysis are two methods from Nonlinear Dynamics which have successfully been applied to chemical process models. While these methods have become established tools, a shift can be detected in the way these techniques are used in the chemical engineering community.
Early applications of applied Nonlinear Dynamics to chemical processes focused on gaining insight into the fundamental chemical and physical interactions and their impact on stability or on dynamics in general. In contrast, some more recent articles focus on obtaining information that is not merely meant to deepen the understanding of a given chemical process, but to aid process design. Information on the location of saddle-node, Hopf, and other bifurcation points is valuable to a design engineer, for example, as it allows to avoid parameter regions that correspond to unstable or otherwise undesired process behavior. In this sense, a shift is taking place in the chemical engineering community from Nonlinear Dynamics analysis for a deeper understanding towards analysis for design. As an example of analysis for design, the present paper demonstrates the use of bifurcation analysis in controller design. By generalizing some of the results obtained for this case study, a procedure for bifurcation-based controller tuning can be derived.
Despite being very powerful, a numerical bifurcation analysis becomes tedious or even impossible for models with many parameters. The application of an analysis to guide the design of chemical processes is therefore limited to models with only a few parameters. To overcome this limitation, a new approach has been developed that incorporates information on the location of bifurcation points into optimization-based process design. This novel approach does not rely on analyzing, visualizing, and interpreting the visualized information on the location of critical points in the process parameter space and is therefore, at least in principle, not restricted with respect to the number of process parameters. The present paper summarizes the progress made in the development of this constructive Nonlinear Dynamics method and gives two illustrative examples.
Nonlinear Dynamics of Production Systems, Wiley-VCH, Weinheim, Germany, pp. 503-526 (2004)