FAU Erlangen-Nuremberg

Optimal Control of Periodic Adsorption Processes via a Reduced Newton-Picard Scheme

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Project leaders

FB 6, Bio- u. Chemieingenieurwesen, Lehrst. f. Techn. Chemie B (TCB)
Uni Dortmund

Tel: 0231 755-2697
Fax: 0231 755-2698

Email: agar@bci.uni-dortmund.de


Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, INF 368
Uni Heidelberg

Tel: 06221 54-8237
Fax: 06221 54-5444

Email: bock@iwr.uni-heidelberg.de


FB 6, Bio- u. Chemieingenieurwesen, Lehrstuhl für Anlagensteuerungstechnik
Uni Dortmund

Tel: 0231 755-5127
Fax: 0231 755-5129

Email: s.engell@bci.uni-dortmund.de


Additional applicants

K.U. Leuven Optimization in Engineering Center (OPTEC)

Tel: +32 16-321884
Tel: +32 16-321709 (Sekr.)
Fax: +32 16-321970

Email: moritz.diehl@esat.kuleuven.be

Philipps Universität Marburg

Tel: 06421 28-25400
Tel: 06421 28-25489 (Sekr.)
Fax: 06421 28-28986

Email: kostina@mathematik.uni-marburg.de

Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, INF 368
Uni Heidelberg

Tel: 06221 54-8239
Fax: 06221 54-5444

Email: j.schloeder@iwr.uni-heidelberg.de

DFG funded assistant

Andreas Potschka (Uni Heidelberg)


Jan Albersmeyer (Uni Heidelberg)


Periodic adsorption processes are widely established in process engineering for the production of gases, fine chemicals or pharmaceuticals, and novel uses involve the combination of adsorption and reaction processes. Characteristic for all these processes are traveling concentration fronts of different species in a solid fixed bed, and periodic switching between different types of operation. The dynamics of each phase can be modelled by instationary partial differential algebraic equations (PDAE) in one or two spatial dimensions, so that the overall system is described by periodically switched PDAE. Following start-up, a periodic attractor, or Cyclic Steady State (CSS), is finally reached and used for production. This CSS should ideally be optimal with respect to operational costs and product specifications, and recent years have seen the development of a variety of novel process operation variants to improve efficiency. Two of these are the processes to be investigated in Dortmund: the simulated moving bed (SMB) with variable inlet concentrations (ModiCon-SMB) studied in the group of Prof. Engell and the entirely novel fixed bed catalytic reactor with desorptive cooling (in the following called "Desorptive cooling (DC)-Process") in the group of Prof. Agar. Due to the large scale of the process models and due to their periodic nature, only few model based optimisation approaches exist and their use for large scale applications is limited by prohibitive computation times. These computational costs are caused by the expensive solution of the periodicity (or CSS) constraints, that come on top of a large scale forward PDAE optimization problem.

Goal of the project is the development of practically applicable numerical methods for periodic optimal control of large, switched PDAE systems, and their application to the two processes in Dortmund. The methods we have in mind shall be based on novel ideas from the Heidelberg group for reduced Newton type methods that work with inexact jacobian matrices. In contrast to most existing approaches, only one accurate adjoint solve is required in each iteration, independent of the number of state inequalities. This framework shall allow to compute cheap inexact derivatives of the CSS constraint in some dominant directions only. A mixture of Newton and Picard iterates shall be used to exploit the fact that the jacobian matrix of the desired cyclic steady state constraint has most eigenvalues close to zero.

The following features shall characterise the methods to be developed within the project:

  • a simultaneous optimisation framework is chosen in which the discretised model equations enter the optimisation problem as nonlinear constraints
  • only one cycle is simulated and optimised, and periodicity is imposed in form of additional constraints
  • a time-domain decomposition is used to handle the intermediate switching and the enormous amount of data
  • a novel reduced SQP framework being able to cope with inexact Jacobians is used to solve the nonlinear programming problem resulting after discretisation of model equations and controls
  • a mixed Newton-Picard scheme is used to treat the periodicity constraints efficiently

The method development is driven by the requirements of the two processes in Dortmund. Final application aim of the project is the optimisation and experimental validation of the operating regime of the novel desorptive cooling (DC) process.

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