A simple and effective procedure for control degrees of freedom

The focus of this paper is on one of the important steps in designing plant-wide control systems, namely, control degrees of freedom (CDOF). There appears to be no simple procedure to compute CDOF, the maximum number of flows that can be manipulated simultaneously, especially in the context of plant-wide control (PWC) of industrial processes. Hence, a simple and yet effective procedure to find CDOF is proposed and illustrated in this work. The key idea is to define ‘restraining number’ (i.e., the minimum number of flows that cannot be manipulated along with others in an unit, which is also an inherent characteristic of that unit) of an unit. We show that the restraining number is equal to the number of independent and overall material balances with no associated inventory 1 1 Inventory is used here to refer to ‘variable hold-up’ but not ‘fixed hold-up’. For example, gas phase (or gas–liquid phase) PFR is considered as the ‘unit with inventory’ as it contains ‘variable hold-up’ and liquid phase PFR is considered as the ‘unit without inventory’ as it contains ‘fixed hold-up’. in that particular unit. The concept of restraining number is then used to find CDOF of not only simple units but also highly integrated processes. One of the advantages is its generic nature, which facilitates its automation. Moreover, the proposed procedure implicitly takes care of number of phases and components involved in the unit. In addition, it needs just the basic understanding of simple units and one does not require all the mathematical equations involved.