Plant-wide hierarchical optimal control of a crystallization process

Hierarchically coordinated economic MPC plantwide control of mixed continuous‐batch units in process industries with application to a beet sugar plant

“…) + 1 · 10 7 · max(0, (s − 1)) 0.8 · cc 0.8 (20) There is an explicit relation between the flux of crystallization (J cris ) used in (16) and the linear growth velocity G, which is shown in (19) and is calculated taking into account the density of sugar crystals and two shape factors relating the characteristic size L with the crystal surface (f s ) and volume (f v ). The nucleation term (B) is calculated by means of (20), by adding the contributions of primary and secondary nucleation. Primary nucleation is the mechanism that works in the absence of other crystals, whereas secondary nucleation accounts for the presence of an already crystallized mass of sugar resulting on its current concentration (cc).…”

“…Primary nucleation is the mechanism that works in the absence of other crystals, whereas secondary nucleation accounts for the presence of an already crystallized mass of sugar resulting on its current concentration (cc). The expression (20) has a form similar to the ones recommended in the work of Puel et al, 42 but the coefficients are chosen for the particular case at hand. The balance to the mass, which is evaporated from the boiling product and that shares the vessel volume with the latter could be described as in (21).…”

“…The accelerating/delaying factors P Fi act as the only decision variables. The h local function represent the model of the given crystallizer, as described, for example, in (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29). In general, as previously discussed, it is also required to enforce path and terminal constraints (see Equation 10).…”

“…The simulated case study used is described in the work of Mazaeda et al 19 and the solution adopted extends the previous work reported in conference proceedings. 20,21 This paper is organized as follows. Section 2 goes deeper into the problem of distributed optimal control, to establish, in a general framework, the characteristics of the type of problem specifically addressed here and the solution adopted.…”

Neural network adaptive real-time optimizing control of industrial processes

“…1 In a large-scale plant the implementation of RTO has proved to be profitable. 2,3,4 RTO drives operating condition towards the actual plant optimum in spite of model mismatch by adjusting selected optimization variables using measurement data. Problems face in RTO arise due to the inability to develop and adopt accurate models and the following are three different strategies which have been classified on how measurements are used to compensate the model uncertainty: model-parameter adaptation, modifier adaptation and input adaptation.…”