H∞-Control of a continuous crystallizer

Abstract

Robustly stabilizing control of an open loop oscillatory crystallization process is considered. The crystallizer is described by a population balance model. From this distributed parameter model an irrational transfer function is obtained which has infinitely many poles and thus represents the infinite-dimensional nature of the system. An infinite-dimensional Hoc controller synthesis method is applied to solve the weighted mixed sensitivity problem for this transfer function. This procedure results in an irrational controller. For practical implementation, the controller needs to be approximated by a rational transfer function. The effectiveness of the controller is demonstrated in simulations.

Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics

“…At the concluding stage, the growth of each particle influences the evolution of neighbouring crystals so that Ostwald ripening, coagulation and fragmentation processes are capable of occurring [13][14][15][16][17]. Let us especially note that such processes as external electromagnetic fields [18], buoyancy forces [19], polymerization [9,20] and withdrawal mechanisms of product crystals from a crystallizer [21][22][23][24] may essentially change the dynamics of particulate assemblages in a metastable liquid as well.…”

A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals

“…The dependence h(r) can be connected with the classification of crystals inside a crystallizer. For the sake of simplicity, we assume that h = q/V is constant (q and V are, respectively, the feed rate and total volume of a crystallizer) [44,45] where θ and θ 0 should be replaced by C and C 0 , respectively, in the case of supersaturated solutions. Here, θ 0 represents the initial supercooling and the nucleation rate I has the form [22,29]…”

Influence of zone formation on stability of continuous fluidized bed layering granulation with external product classification

“…These oscillations result in varying product properties, which are usually not acceptable. Oscillations can be avoided by suitable selection of operating and design parameters in the stable regime, or by means of stabilizing feedback control applied in the unstable regime (Bück, Palis, & Tsotsas, 2015;Chiu & Christofides, 1999;Christofides, 2002;Palis & Kienle, 2012, 2014Vollmer & Raisch, 2001, 2002. The first strategy requires reliable prediction of parameter combinations leading to instability.…”