FAU Erlangen-Nuremberg

Optimal Control of Periodic Adsorption Processes

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Project leaders

Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Uni Heidelberg

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

Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Uni Heidelberg

DFG funded assistants

There are currently two positions available. Please contact one of the project leaders for details.


Andreas Potschka (Uni Heidelberg)

Jan Albersmeyer (Uni Heidelberg)

Achim Küpper (Uni Dortmund)


Periodic adsorption processes are widely established in process engineering as a separation procedure, e.g., for fine chemicals or pharmaceuticals. Recent variants also involve a combination of adsorption and reaction processes. Characteristic of such processes are moving concentrations profiles of different species in a solid fixed bed, and periodic controls that involve switching between different types of operation.

The dynamics of each phase can be modeled by non-stationary partial differential equations (PDE) in one or two spatial dimensions, so that the overall system is described by periodically switched PDE. Following start-up, a periodic attractor, or stable Cyclic Steady State (CSS), is finally reached and used for production, which should be optimal with respect to operational costs and product specifications. Recent years have seen the development of a variety of process operation variants to improve efficiency. Two of these are investigated in this project: the simulated moving bed with variable inlet concentrations ('ModiCon-SMB') and the novel fixed bed catalytic reactor with desorptive cooling ('DC process').

Due to the complexity of the process models and their periodic operation, only few model based online optimization approaches exist; and their use for large-scale applications is still limited by prohibitive computation times. The aim of this project is to develop new efficient numerical methods for the optimization of periodic adsorption processes described by periodically switched and non-stationary PDE, which are capable of online application to the process in the presence of perturbations. These methods combine Newton type optimization methods with a Newton-Picard approach to cope efficiently with the periodicity constraints.

The following features characterize the new methods, the development of which is driven by the requirements of the two processes investigated in Dortmund:

  • An adequate modeling of the ModiCon-SMB and DC processes as 1D and 2D non-stationary periodic PDE, and of the corresponding constrained process optimization problems
  • A simultaneous and direct optimization framework, in which the discretized model equations enter the optimization problem as non-linear constraints
  • Novel SQP and Gauss-Newton methods for the resulting inequality constrained non-linear programming problem, which can handle coarse approximations of the constraint Jacobians of Newton-Picard type that capture only derivativeswith respect to slow or unstable modes.
  • A time domain decomposition by multiple shooting, and an adaptation of the discretization mesh based on dual weighted residual (DWR) a-posteriori error estimates
  • A generalization of non-linear feedback control algorithms of Non-linear Model Predictive Control (NMPC) type to optimal periodic control problems to cope with process perturbations and model inaccuracies
  • Ultimately, the optimization and experimental validation of the optimal operating regime for the simulated moving bed and the desorptive cooling process.
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