Abstract
The purpose of this paper is an experimental proof-of-concept of the application of NMPC for large scale systems using specialized dynamic optimization strategies. For this aim we investigate the application of modern, computationally efficient NMPC schemes and realtime optimization techniques to a nontrivial process control example, namely the control of a high purity binary distillation column. All necessary steps are discussed, from formulation of a DAE model with 164 states up to the final application to the experimental apparatus. Especially an efficient real-time optimization scheme based on the direct multiple shooting method is introduced. It is characterized by an initial value embedding strategy, that allows to immediately respond to disturbances, and real-time iterations, that dovetail the optimization iterations with the real process development. Using this scheme, sampling times of 10 seconds are feasible on a standard PC. This shows that an efficient NMPC scheme based on large scale DAE models is feasible for the real-time control of a pilot scale distillation column.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Allgöwer, T. A. Badgwell, J. S. Qin, J. B. Rawlings, and S. J. Wright. Nonlinear predictive control and moving horizon estimation — An introductory overview. In P. M. Frank, editor, Advances in Control, Highlights of ECC’99, pages 391–449. Springer, 1999.
F. Allgöwer and J. Raisch. Multivariable controller design for an industrial distillation colunm. In N.K Nichols and D.H. Owens, editors, The Mathematics of Control Theory. Clarendon Press, Oxford, 1992.
I. Bauer. Numerische Verfahren zur Lösung von Anfangswertaufgaben und zur Generierung von ersten und zweiten Ableitungen mit Anwendungen bei Optimierungsaufgaben in Chemie und Verfahrenstechnik. PhD thesis, University of Heidelberg, 2000.
T. Binder, L. Blank, H. G. Bock, R. Bulirsch, W. Dahmen, M. Diehl, T. Kronseder, W. Marquardt, J. P. Schlöder, and O. von Stryk. Introduction to model based optimization of chemical processes on moving horizons. In to be announced. Springer, 2001.
H. G. Bock, M. Diehl, D. Leineweber, and J. P. Schlöder. A direct multiple shooting method for real-time optimization of nonlinear DAE processes. In F. Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 245–268. Birkhäuser, 2000.
H. G. Bock, M. Diehl, J. P. Schlöder, F. Allgöwer, R. Findeisen, and Z. Nagy. Realtime optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. In ADCHEM2000 — International Symposium on Advanced Control of Chemical Processes, volume 2, pages 695–703, Pisa, 2000.
H. G. Bock, E. Eich, and J. P. Schlöder. Numerical solution of constrained least squares boundary value problems in differential-algebraic equations. In K. Strehmel, editor, Numerical Treatment of Differential Equations. Teubner, Leipzig, 1988.
L. Biegler. Efficient solution of dynamic optimization and NMPC problems. In F. Allgöwer and A. Zheng, editors, Nonlinear Predictive Control. Birkhäuser, 2000.
H. G. Bock. Numerical treatment of inverse problems in chemical reaction kinetics. In K. H. Ebert, P. Deuflhard, and W. Jäger, editors, Modelling of Chemical Reaction Systems, volume 18 of Springer Series in Chemical Physics. Springer, Heidelberg, 1981.
H. G. Bock and K. J. Plitt. A multiple shooting algorithm for direct solution of optimal control problems. In Proc. 9th IFAC World Congress, Budapest, 1984.
H. Chen and F. Allgöwer. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 34(10):1205–1218, 1998.
M. Diehl, H. G. Bock, D. B. Leineweber, and J. P. Schlöder. Efficient direct multiple shooting in nonlinear model predictive control. In F. Keil, W. Mackens, H. Voß, and J. Werther, editors, Scientific Computing in Chemical Engineering II, volume 2, pages 218–227, Berlin, 1999. Springer.
M. Diehl, H. G. Bock, J. P. Schloeder, R. Findeisen, Z. Nagy, and F. Allgoewer. Real-time optimization and nonlinear model predictive control of processes governed by large-scale DAE. J. Proc. Contr., 2001.
M. Diehl. Real-Time Optimization for Large Scale Nonlinear Processes. PhD thesis, University of Heidelberg, 2001.
G. De Nicolao, L. Magni, and R. Scattolini. Stabilizing nonlinear receding horizon control via a nonquadratic terminal state penalty. In Symposium on Control, Optimization and Supervision, CESA’96 IMACS Multiconference, pages 185–187, Lille, 1996.
G. de Nicolao, L. Magni, and R. Scattolini. Stability and robustness of nonlinear receding horizon control. In F. Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 3–23. Birkhäuser, 2000.
R. Findeisen, F. Allgöwer, M. Diehl, H. G. Bock, J. P. Schlöder, and Z. Nagy. Efficient nonlinear model predictive control. Submitted to 6th International Conference on Chemical Process Control — CPC VI, 2000.
R. Henrion, P. Li, A. Moeller, M. Wendt, and G. Wozny. Optimal control of a continuous distillation process under probabilistic constraints. In M. Groetschel, S. O. Krumke, and J. Rambau, editors, Online Optimization of Large Scale Systems: State of the Art. Springer, 2001.
D. B. Leineweber. Efficient reduced SQP methods for the optimization of chemical processes described by large sparse DAE models, volume 613 of Fortschr. -Ber. VDI Reihe 3, Veifahrenstechnik. VDI Verlag, Düsseldorf, 1999.
K. J. Plitt. Ein superlinear konvergentes Mehrzielverfahren zur direkten Berechnung beschränkter optimaler Steuerungen. Master’s thesis, University of Bonn, 1981.
V. H. Schulz, H. G. Bock, and M. C. Steinbach. Exploiting invariants in the numerical solution of multipoint boundary value problems for daes. SIAM J. Sci. Comp., 19:440–467, 1998.
S. J. Wright. Applying new optimization algorithms to model predictive control. In J. C. Kantor, C. E. Garcia, and B. Carnahan, editors, Fifth International Conference on Chemical Process Control — CPC V, pages 147–155. American Institute of Chemical Engineers, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Diehl, M. et al. (2001). Real-Time Optimization for Large Scale Processes: Nonlinear Model Predictive Control of a High Purity Distillation Column. In: Grötschel, M., Krumke, S.O., Rambau, J. (eds) Online Optimization of Large Scale Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04331-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-662-04331-8_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07633-6
Online ISBN: 978-3-662-04331-8
eBook Packages: Springer Book Archive