External versus internal open-loop unstable processes

This paper points out that there are two distinctly different types of open-loop unstable processes and that this leads to different methods for the selection and tuning of feedback controllers. Internal open-loop instability occurs when an individual unit operation is open-loop unstable, i.e., one or more open-loop eigenvalues with positive real parts. The classical chemical engineering example is the exothermic irreversible chemical reactor. External open-loop instability occurs when a collection of open-loop stable units are connected in such a way that the coupled system is open-loop unstable. The classical chemical example is a feed/effluent heat exchanger connected with an adiabatic exothermic chemical reactor. These two types of processes have different dynamic structures. The transfer function of an internal open-loop unstable process is typically of order 2 or higher. The transfer function of an external open-loop unstable process typically has a net order of zero. This difference explains the phenomenon described by Tyreus and Luyben (J. Process Control 1993, 3 (4), 241-251) of using reset action to improve dynamic control, which conflicts with conventional wisdom that adding reset or integral action degrades dynamic performance.