Short and Long Timescales in Recycles

A new awareness on modelling is growing in the control-oriented community recognising the fact that control is dominantly model based. Since control is about manipulating certain characteristics of the plant, it is no surprise that modelling for control focuses on extracting exactly those characteristics of the plant that are to be controlled. This invariably induces the use of time scale assumptions and consequently model reduction methods. These assumptions lead to a time-scale separation, which results in a layered control structure, with the control loops getting slower as one moves upwards in the hierarchy of time-scales. Recycle structures are very common. The components may be fast, but the overall structure including the loop is usually much slower because of the recycle. These structures thus lend themselves to the application of time-scale assumptions. We demonstrate that any of these structures can be analysed. Starting with a first-principle based representation that makes no particular assumption on the nature of the process except that of a large recycle and fast internal dynamics, we derive a first-order approximation of a system. The result is generic and not dependent on the particular nature of the individual processes other structural properties of the process.