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.

Structured H∞‐control of infinite‐dimensional systems

“…We apply our frequency‐sampled H ∞ ‐synthesis method to control a continuous cooling crystallizer, shown schematically in Figure . The process uses fines dissolution and product removal and is governed by a population balance and a molar balance equation (see Vollmer and Raisch and Rachah et al).…”

Characterization of branched polymers by size exclusion chromatography coupled with multiangle light scattering detector. I. Size exclusion chromatography elution behavior of branched polymers

“…Our second study uses the model of a continuous crystallizer presented by Vollmer and Raisch 27 (see Figure 7), where crystal growth is modelled by mole and population balance equations. The mole balance is with initial condition and the population balance with initial and boundary conditions Here c ( t ) is the solute concentration and n ( L, t ) the crystal size distribution (no.…”

“… Continuous crystallizer model from 27. Ideal mixing is assumed, particle breakage and agglomeration are neglected.…”

“…In industrial crystallizers operated in open loop, the crystal size distribution (CSD) may exhibit bad damping or sustained oscillations (see Figure 8 left, and Figure 10 top), which affect product quality, hence the need for feedback control. The challenge addressed in 27 (study 1 in Table VII) was to control the system based on measuring only solute concentration c ( t ) and by acting on the solute feed rate c f ( t ) alone, while older strategies control the process through the fines dissolution rate R 1 ( t ).…”

A mathematical model for continuous crystallization

“…The function h p .L/ describes the profile of the product removal filter, which removes large particles with a certain probability according to size. In the ideal case, assumed, for example, in [23], one has…”