On concentration control of fast reactions in slowly-mixed plants with slow inputs

Fast reactions, taking place in a relatively slowly-mixed environment, are a common phenomenon. In the past, model-based control frequently used Wiener models for such processes. This paper gives a link between first-principle models for processes including arbitrary dynamics of the hydraulics and arbitrary reactions and a Wiener-model description of the same process. The derivation introduces two key assumptions, (i) the reactions are fast compared to the process hydraulics and (ii) control is slow compared to the process hydraulics. The first assumption creates an index problem, which when solved results in a separation of the dynamic hydraulics of the process and the event dynamic of the reactions. The second assumption allows for the linearisation of the dynamics describing the process hydraulics. The assumptions are essential and thus need to be checked before the model is used for control. The derivation is independent of the particular structure of the hydraulics and chemical reactions. The result allows separate identification of the hydraulics and reactions. Adaptive control of such systems can thus, once the hydraulic is known, focus on the on-line identification of the static gain only.