Skip to main content

2014 | OriginalPaper | Buchkapitel

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

verfasst von : Malte Behrens, Hans Georg Bock, Sebastian Engell, Phawitphorn Khobkhun, Andreas Potschka

Erschienen in: Trends in PDE Constrained Optimization

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat T. Ahmad, G. Guichon, Effect of the mobile phase composition on the adsorption behavior of tryptophan in reversed-phase liquid chromatography. J. Chromatograph. A 1114, 111–122 (2006)CrossRef T. Ahmad, G. Guichon, Effect of the mobile phase composition on the adsorption behavior of tryptophan in reversed-phase liquid chromatography. J. Chromatograph. A 1114, 111–122 (2006)CrossRef
2.
Zurück zum Zitat M. Behrens, S. Engell, Iterative set-point optimization of continuous annular electro-chromatography, in Proceedings of the 18th IFAC World Congress, 2011 – 28. 08 – 02.09.2011, Milano/Italy, Paper ID 3008, 2011 M. Behrens, S. Engell, Iterative set-point optimization of continuous annular electro-chromatography, in Proceedings of the 18th IFAC World Congress, 2011 – 28. 08 – 02.09.2011, Milano/Italy, Paper ID 3008, 2011
3.
Zurück zum Zitat M. Behrens, Y. Yu, S. Engell, Parameter estimation and iterative set-point optimization of continuous annular electrochromatography, in Proceedings of the IEEE, International Conference on Industrial Technology (Athens, Greece, 2012), pp. 236–241, 2012 M. Behrens, Y. Yu, S. Engell, Parameter estimation and iterative set-point optimization of continuous annular electrochromatography, in Proceedings of the IEEE, International Conference on Industrial Technology (Athens, Greece, 2012), pp. 236–241, 2012
4.
Zurück zum Zitat H.G. Bock, Numerical treatment of inverse problems in chemical reaction kinetics, in Modelling of Chemical Reaction Systems, ed. by K.H. Ebert, P. Deuflhard, W. Jäger. Springer Series in Chemical Physics, vol. 18 (Springer, Heidelberg, 1981), pp. 102–125 H.G. Bock, Numerical treatment of inverse problems in chemical reaction kinetics, in Modelling of Chemical Reaction Systems, ed. by K.H. Ebert, P. Deuflhard, W. Jäger. Springer Series in Chemical Physics, vol. 18 (Springer, Heidelberg, 1981), pp. 102–125
5.
Zurück zum Zitat H.G. Bock, W. Egartner, W. Kappis, V. Schulz, Practical shape optimization for turbine and compressor blades by the use of PRSQP methods. Optim. Eng. 3(4), 395–414 (2002)CrossRefMATHMathSciNet H.G. Bock, W. Egartner, W. Kappis, V. Schulz, Practical shape optimization for turbine and compressor blades by the use of PRSQP methods. Optim. Eng. 3(4), 395–414 (2002)CrossRefMATHMathSciNet
6.
Zurück zum Zitat H.G. Bock, K.J. Plitt, A multiple shooting algorithm for direct solution of optimal control problems, in Proceedings of the 9th IFAC World Congress, Budapest (Pergamon Press, 1984), pp. 242–247 H.G. Bock, K.J. Plitt, A multiple shooting algorithm for direct solution of optimal control problems, in Proceedings of the 9th IFAC World Congress, Budapest (Pergamon Press, 1984), pp. 242–247
7.
Zurück zum Zitat H.G. Bock, A. Potschka, S. Sager, J.P. Schlöder, On the connection between forward and optimization problem in one-shot one-step methods, in Constrained Optimization and Optimal Control for Partial Differential Equations, ed. by G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich, S. Ulbrich. International Series of Numerical Mathematics, vol. 160 (Springer, Basel, 2011), pp. 37–49 H.G. Bock, A. Potschka, S. Sager, J.P. Schlöder, On the connection between forward and optimization problem in one-shot one-step methods, in Constrained Optimization and Optimal Control for Partial Differential Equations, ed. by G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich, S. Ulbrich. International Series of Numerical Mathematics, vol. 160 (Springer, Basel, 2011), pp. 37–49
8.
Zurück zum Zitat S. Engell, Feedback control for optimal process operation. J. Process Control 17, 203–219 (2007)CrossRef S. Engell, Feedback control for optimal process operation. J. Process Control 17, 203–219 (2007)CrossRef
9.
Zurück zum Zitat W. Gao, S. Engell, Iterative set-point optimization of batch chromatography. Comput. Chem. Eng. 29, 1401–1410 (2005)CrossRef W. Gao, S. Engell, Iterative set-point optimization of batch chromatography. Comput. Chem. Eng. 29, 1401–1410 (2005)CrossRef
10.
Zurück zum Zitat A. Griewank, Projected Hessians for preconditioning in one-step one-shot design optimization, in Large-Scale Nonlinear Optimization. Nonconvex Optimization and Its Applications, vol. 83 (Springer, New York, 2006), pages 151–171 A. Griewank, Projected Hessians for preconditioning in one-step one-shot design optimization, in Large-Scale Nonlinear Optimization. Nonconvex Optimization and Its Applications, vol. 83 (Springer, New York, 2006), pages 151–171
11.
12.
Zurück zum Zitat C. Grossmann, G. Ströhlein, M. Morari, M. Morbidelli, Optimizing model predictive control of the chromatographic multi-column solvent gradient purification (MCSGP) process. J. Process Control 20, 618–629 (2010)CrossRef C. Grossmann, G. Ströhlein, M. Morari, M. Morbidelli, Optimizing model predictive control of the chromatographic multi-column solvent gradient purification (MCSGP) process. J. Process Control 20, 618–629 (2010)CrossRef
13.
Zurück zum Zitat S.B. Hazra, V. Schulz, J. Brezillon, N.R. Gauger, Aerodynamic shape optimization using simultaneous pseudo-timestepping. J. Comput. Phys. 204(1), 46–64 (2005)CrossRefMATHMathSciNet S.B. Hazra, V. Schulz, J. Brezillon, N.R. Gauger, Aerodynamic shape optimization using simultaneous pseudo-timestepping. J. Comput. Phys. 204(1), 46–64 (2005)CrossRefMATHMathSciNet
14.
Zurück zum Zitat P. Khobkun, Iterative set-point optimization of the multi column solvent gradient purification process, Master’s thesis, TU Dortmund University, 2013 P. Khobkun, Iterative set-point optimization of the multi column solvent gradient purification process, Master’s thesis, TU Dortmund University, 2013
15.
Zurück zum Zitat A. Küpper, Optimization, state estimation, and model predictive control of simulated moving bed processes, PhD thesis, TU Dortmund University, 2010 A. Küpper, Optimization, state estimation, and model predictive control of simulated moving bed processes, PhD thesis, TU Dortmund University, 2010
16.
Zurück zum Zitat D.N. Lopez, Handling uncertainties in process optimization, PhD thesis, University of Valladolid, 2013 D.N. Lopez, Handling uncertainties in process optimization, PhD thesis, University of Valladolid, 2013
17.
Zurück zum Zitat K. Lust, D. Roose, A. Spence, A. R. Champneys, An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions. SIAM J. Sci. Comput. 19(4), 1188–1209 (1998)CrossRefMATHMathSciNet K. Lust, D. Roose, A. Spence, A. R. Champneys, An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions. SIAM J. Sci. Comput. 19(4), 1188–1209 (1998)CrossRefMATHMathSciNet
18.
Zurück zum Zitat A. Marchetti, B. Chachuat, D. Bovin, A dual modifier approach for real-time optimization. J. Process Control 20, 1027–1037 (2010)CrossRef A. Marchetti, B. Chachuat, D. Bovin, A dual modifier approach for real-time optimization. J. Process Control 20, 1027–1037 (2010)CrossRef
19.
Zurück zum Zitat A. Potschka, A direct method for the numerical solution of optimization problems with time-periodic PDE constraints, PhD thesis, Heidelberg University, 2011 A. Potschka, A direct method for the numerical solution of optimization problems with time-periodic PDE constraints, PhD thesis, Heidelberg University, 2011
20.
Zurück zum Zitat A. Potschka, M.S. Mommer, J.P. Schlöder, H.G. Bock, Newton-Picard-based preconditioning for linear-quadratic optimization problems with time-periodic parabolic PDE constraints. SIAM J. Sci. Comp. 34(2), 1214–1239 (2012)CrossRef A. Potschka, M.S. Mommer, J.P. Schlöder, H.G. Bock, Newton-Picard-based preconditioning for linear-quadratic optimization problems with time-periodic parabolic PDE constraints. SIAM J. Sci. Comp. 34(2), 1214–1239 (2012)CrossRef
21.
Zurück zum Zitat H. Schmidt-Traub, Preperative Chromatography of Fine Chemicals and Pharmaceutical Agents (Wiley-VCH, Weinheim, 2012) H. Schmidt-Traub, Preperative Chromatography of Fine Chemicals and Pharmaceutical Agents (Wiley-VCH, Weinheim, 2012)
22.
Zurück zum Zitat G. Ströhlein, L. Aumann, M. Mazzotti, M. Morbidelli, A continuous, counter-current multi-column chromatographic process incorporating modifier gradients for ternary separations. J. Chromatograph. A 1126, 338–346 (2006)CrossRef G. Ströhlein, L. Aumann, M. Mazzotti, M. Morbidelli, A continuous, counter-current multi-column chromatographic process incorporating modifier gradients for ternary separations. J. Chromatograph. A 1126, 338–346 (2006)CrossRef
23.
Zurück zum Zitat P. Tatjewski, Iterative optimization set-point control – the basic principle redesigned, in Proceedings of the 15th IFAC World Congress, Barcelona, 2002 P. Tatjewski, Iterative optimization set-point control – the basic principle redesigned, in Proceedings of the 15th IFAC World Congress, Barcelona, 2002
24.
Zurück zum Zitat A. Toumi, S. Engell, Optimization and control of chromatography. Comput. Chem. Eng. 29, 1243–1252 (2005)CrossRef A. Toumi, S. Engell, Optimization and control of chromatography. Comput. Chem. Eng. 29, 1243–1252 (2005)CrossRef
25.
Zurück zum Zitat J. Wloka, Partielle Differentialgleichungen: Sobolevräume u. Randwertaufgaben (B.G. Teubner, Stuttgart, 1982) J. Wloka, Partielle Differentialgleichungen: Sobolevräume u. Randwertaufgaben (B.G. Teubner, Stuttgart, 1982)
Metadaten
Titel
Real-Time PDE Constrained Optimal Control of a Periodic Multicomponent Separation Process
verfasst von
Malte Behrens
Hans Georg Bock
Sebastian Engell
Phawitphorn Khobkhun
Andreas Potschka
Copyright-Jahr
2014
DOI
https://doi.org/10.1007/978-3-319-05083-6_33