Abstract
A nonlinear model predictive control (NMPC) formulation is used to prevent an exothermic fed-batch chemical reactor from thermal runaways even in the case of total cooling failure. Detailed modeling of the reaction kinetics and insight into the process dynamics led to the formulation of a suitable optimization problem with safety constraints which is then successively solved within the NMPC scheme. Although NMPC control-loops can exhibit a certain degree of inherent robustness, an explicit consideration of process uncertainties is preferable not only for safety reasons. This is approached by reformulating the open-loop optimization problem as a min-max problem. This corresponds to a worst-case approach and leads to even more cautious control moves of the NMPC in the presence of uncertain process parameters. All results are demonstrated in simulations for the esterification process of 2-butyl.
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
Bauer I, Bock HG, Schiöder JP (1999) “DAESOL—a BDF-code for the numerical solution of differential algebraic equations”, Internal report IWR-SFB 359, Universität Heidelberg
Benuzzi A and Zaldivar JM (eds) (1991) “Safety of Chemical Reactors and Storage Tanks”, Kluwer Academic Publishers, Dordrecht, The Netherlands
Bock HG and Plitt KJ (1984) “A multiple shooting algorithm for direct solution of optimal control problems”, Proc. 9th IFAC World Congress Budapest
Chen H, Scherer CW, Allgöwer F (1997) “A game theoretic approach to nonlinear robust receding horizon control of constraint systems”, American Control Conference, Albuquerque, USA: 3073–3077
DeNicolao G, Magni L, Scattolini R (2000) “Stability and robustness of nonlinear receding horizon control”. In: Allgöwer F, Zheng A (eds) Nonlinear Model Predictive Control. Birkhäuser Basel.
Diehl M, Bock HG, Schiöder JP, Findeisen R, Nagy Z, Allgöwer F (2002) “Realtime optimization and Nonlinear Model Predictive Control of Processes governed by differential-algebraic equations”, J. of Proc. Control 12:577–585
Diehl M, Findeisen R, Bock HG, Schiöder JP, Allgöwer F (2005) “Nominal stability of the real-time iteration scheme for nonlinear model predictive control”, IEE Proc. Contr. Theory & Appl. 152(3):296–308
Diehl M, Bock HG, Kostina E (2005) “An approximation technique for robust nonlinear optimization”, Mathematical Programming B (accepted)
Hugo P, Steinbach J, Stoessel F (1988) “Calculation of the maximum temperature in stirred reactors in case of a breakdown of cooling”, Chemical Eng. Science 43:2147–2152
Körkel S, Kostina E, Bock HG, Schiöder JP (2004) “Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes”, Optimization Methods & Software 19:327–338
Lee JH, Yu Z (1997) “Worst-case formulations of model predictive control for systems with bounded parameters”, Automatica 33(5):763–781
Leineweber DB, Bauer I, Bock HG, Schiöder JP (2003) “An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization —part I: theoretical aspects”, Comp. & Chem. Eng. 27:157–166
Li P, Wendt M, Wozny G (2002) “A probabilistically constrained model predictive controller”, Automatica, 38: 1171–1176
Magni L, Nijmeijer H, van der Schaft AJ (2001) “A receding-horizon approach to the nonlinear H-infinity control problem”, Automatica 37:429–435
Nagy Z, Braatz RD (2004) “Open-loop and closed-loop robust optimal control of batch processes using distributional and worst-case analysis”, Journal of Process Control 14:411–422
Sahinidis NV (2004) “Optimization under uncertainty: state-of-the-art and opportunities”, Comp. & Chem. Eng. 28:971–983
Ubrich O, Srinivasan B, Lerena P, Bonvin D, Stoessel F (1999) “Optimal feed profile for a second order reaction in a semi-batch reactor under safety constraints —experimental study”, J. of Loss Prev. 12:485–493
Westerterp KR, Molga E (2004) “No more Runaways in Fine Chemical Reactors”, Ind. Eng. Chem. Res. 43:4585–4594
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kühl, P., Diehl, M., Milewska, A., Molga, E., Bock, H.G. (2007). Robust NMPC for a Benchmark Fed-Batch Reactor with Runaway Conditions. In: Findeisen, R., Allgöwer, F., Biegler, L.T. (eds) Assessment and Future Directions of Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72699-9_37
Download citation
DOI: https://doi.org/10.1007/978-3-540-72699-9_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72698-2
Online ISBN: 978-3-540-72699-9
eBook Packages: EngineeringEngineering (R0)