Steffen Hofmann

Optimal control of multidimensional population balance systems for crystal shape manipulation

Abstract Optimal control of multidimensional particulate processes for crystal shape manipulation based on the minimum principle and the method of characteristics is discussed. The posed optimal control problems consist in achieving a desired morphology for a seed crystal population within a free or a limited time scope, while minimizing the net mass of the nucleated crystal particles. An ODE system is obtained by neglecting the natural feedback of the nucleation mass into the crystallization kinetics. Optimal solutions resulting thereof reduce to boundary value problems in only one or two unknown parameters. Moreover, for the original optimal control problem, involving the full process dynamics, a simple feasible sub-optimal solution and an upper bound for the cost function are proposed. The proposed computational approach is compared with dynamic optimization techniques in terms of the efficiency and accuracy by means of a numerical example.

A Worst-Case Observer for Impurities in Enantioseparation by Preferential Crystallization

Abstract In this contribution, we show how a model is used to obtain worst-case estimates for product impurities in preferential crystallization of enantiomers. The estimates can be obtained for either a simple batch process in a single vessel, or for a coupled mode of operation of two vessels. We demonstrate, supported by a case study, how the estimates enable the use of a combined control strategy consisting of continuous feedback control and process stopping when critical impurity constraints are hit.

Approximate ODE models for population balance systems

Abstract We propose an approximate polynomial method of moments for a class of first-order linear PDEs (partial differential equations) of hyperbolic type, involving a filtering term with applications to population balance systems with fines removal terms. The resulting closed system of ODEs (ordinary differential equations) represents an extension to a recently published method of moments which utilizes least-square approximations of factors of the PDE over orthogonal polynomial bases. An extensive numerical analysis has been carried out for proof-of-concept purposes. The proposed modeling scheme is generally of interest for control and optimization of processes with distributed parameters.

Inversionsbasierte optimale Steuerung von Batch-Kristallisationsprozessen zur Enantiomertrennung

Zusammenfassung In diesem Beitrag wird zunächst eine inversionsbasierte Steuerung zur Realisierung vorgegebener Kristallgrößenverteilungen beim simultanen Batchbetrieb der bevorzugten Kristallisation in zwei gekoppelten Gefäßen unter symmetrischen Bedingungen behandelt. Anschließend wird ein Verfahren zur Minimierung der Batchdauer bei gegebener Reinheit und Produktmenge vorgestellt, welches auf der orbitellen Flachheit eines idealisierten Modells basiert. Die vorgeschlagene Methode wird anhand eines Beispiels mittels eines rechenintensiveren Verfahrens überprüft.