Index of /skoge/publications/1990/unstable_halifax

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Abstract. The paper adresses dynamics and control of distillation columns which are operated at an open-loop unstable operating point. The fact that industrially operated distillation columns may be naturally unstable - even when the level and pressure loops are closed - has only recently been recognized. The main reason why this has been overlooked is that almost all work published in the field of distillation control has assumed the inputs (eg. reflux L and boilup V ) to be on a molar rate basis. Several authors have claimed, using models of different complexity, that in this case the responses will always be stable. However, in real columns the inputs are usually not on a molar basis, but rather on a mass or volume basis. It is shown that the transformation from mass or volume inputs to molar inputs may be singular. The results are independent of thermodynamic complexity, and applies also to homogeneous ideal distillation with constant molar flows. The singularity in this transformation implies that the column will have multiple steady-states, one of which will be unstable. In the paper we discuss the implications of unstable operating points with respect to distillation dynamics and control. It is shown that instability may be avoided by changing the control configuration. However, as we show, the instability will in most cases not cause any problems with regards to control. This is due to the fact that the unstable right half plane pole usually will be close to the imaginary axis ("goes slowly unstable"), thereby not affecting the high frequency behavior of the response which is most important for control. Results are also presented showing that previous results on distillation control design based on molar inputs in most cases will be valid for columns with other input units. This is true even for unstable operating points.
The paper includes an example showing that also models with molar inputs may exhibit multiple steady states and unstable solutions when the energy balance is included.