Real-Time PDE Constrained Optimal Control of a Periodic Multicomponent Separation Process

  • Malte Behrens
  • Hans Georg Bock
  • Sebastian Engell
  • Phawitphorn Khobkhun
  • Andreas PotschkaEmail author
Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)


We present a case study for a ternary separation process, for which structural and aleatoric model uncertainty must be taken into account. For the first time, we apply the control strategy of Modifier Adaptation to a PDE constrained optimization problem with challenging switched periodic boundary conditions in time. Numerically, real-time feasibility of the control scheme is possible by the use of a direct one-shot optimization method, whose efficiency is based on a two-grid Newton-Picard approach. We demonstrate real-time feasibility for a virtual plant with experimentally determined isotherm parameters under reasonable model-plant mismatch conditions. As a result, it is possible to drive the plant into its true optimum, i.e. to increase the productivity of the plant by 100 and 35 % in the two scenarios considered here.


Real-time control PDE constrained optimization Time-periodic 

Mathematics Subject Classification (2010)

35Q93 90C90 92E20 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Malte Behrens
    • 1
  • Hans Georg Bock
    • 2
  • Sebastian Engell
    • 1
  • Phawitphorn Khobkhun
    • 1
  • Andreas Potschka
    • 2
    Email author
  1. 1.Department of Biochemical and Chemical EngineeringTU DortmundDortmundGermany
  2. 2.Interdisciplinary Center for Scientific ComputingHeidelberg UniversityHeidelbergGermany

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