Manuel Gräber
LK Energy GmbH, Germany
Jörg Fritzsche
olkswagen AG, Germany
Wilhelm Tegethoff
Institut für Thermodynamik, TU Braunschweig, Germany
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http://dx.doi.org/10.3384/ecp17132249Published in: Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017
Linköping Electronic Conference Proceedings 132:26, p. 249-254
Published: 2017-07-04
ISBN: 978-91-7685-575-1
ISSN: 1650-3686 (print), 1650-3740 (online)
Based on a specific application example - the thermal management system of an internal combustion engine - a toolchain is presented for formulating and solving of nonlinear optimal control problems. Starting from graphical modeling of the thermal management system with the Modelica library TIL, the model is exported to the standardized model exchange format Functional Mock-up Interface (FMI). Furthermore, it is imported to the optimal control software package MUSCOD-II. Python is used as scripting language for the problem formulation, the numerical solution and the processing of results. By using FMI as an interface, models from any simulation and modeling tools can be used if there is an FMI model export and the models fulfill certain mathematical requirements (smoothness).
Optimal control, Functional mock-up interface, thermal management, cooling system
Åkesson, Johan, Karl-Erik Årzén, Magnus Gäfvert, Tove Bergdahl, and Hubertus Tummescheit. 2010. “Modeling and Optimization with Optimica and JModelica.org--Languages and Tools for Solving Large-Scale Dynamic Optimization Problems.” Computers & Chemical Engineering 34 (11): 1737–49. doi: https://doi.org/10.1016/j.compchemeng.2009.11.011.
Albersmeyer, Jan. 2010. “Adjoint Based Algorithms and Numerical Methods for Sensitivity Generation and Optimization of Large Scale Dynamic Systems.” Ruprecht-Karls-Universität Heidelberg.
Albersmeyer, Jan, and Moritz Diehl. 2010. “The Lifted Newton Method and Its Application in
Optimization.” SIAM Journal on Optimization 20(3): 1655–84. http://epubs.siam.org/doi/abs/10.1137/080724885.
Bauer, Irene. 1999. “Numerische Verfahren Zur Lösung von Anfangswertaufgaben Und Zur Generierung von Ersten Und Zweiten Ableitungen Mit Anwendungen Bei Optimierungsaufgaben in Chemie Und Verfahrenstechnik.” Universität Heidelberg. doi: https://doi.org/10.1159/000328458.
Betts, John T. 2001. Practical Methods for Optimal Control Using Nonlinear Programming. Society for Industrial and Applied Mathematics. Biegler, L. 2007. “An Overview of Simultaneous Strategies for Dynamic Optimization.” Chemical Engineering and Processing: Process Intensification 46 (11): 1043–53.
Blochwitz, T., M. Otter, J. Akesson, M. Arnold, C. Clauß, H. Elmqvist, M. Friedrich, et al. 2012. “Functional Mockup Interface 2.0: The Standard for Tool Independent Exchange of Simulation Models.” In 9th International Modelica Conference.
Bock, H. G., and K. J. Plitt. 1984. “A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems.” In Proc. of the 9th IFAC World Congress Budapest, 243–47. Pergamon Press.
Bock, Hans Georg. 1987. Randwertproblemmethoden Zur Parameteridentifizierung in Systemen Nichtlinearer Differentialgleichungen. Universität Bonn.
Bryson, Arthur E., and Yu-Chi Ho. 1979. Applied Optimal Control: Optimization, Estimation, and Control. John Wiley & Sons Inc.
Diehl, Moritz. 2001. “Real-Time Optimization for Large Scale Nonlinear Processes.” Universität Heidelberg.
Franke, Rüdiger. 2002. “Formulation of Dynamic Optimization Problems Using Modelica and Their Efficient Solution.” In 2nd International Modelica Conference, 315–23. Oberpfaffenhofen.
Gräber, Manuel. 2013. “Energieoptimale Regelung von Kälteprozessen.” TU Braunschweig.
Gräber, Manuel, Kai Kosowski, Christoph Richter, and Wilhelm Tegethoff. 2010. “Modelling of Heat Pumps with an Object-Oriented Model Library for Thermodynamic Systems.” Mathematical and Computer Modelling of Dynamical Systems 16 (3): 195–209. doi: https://doi.org/10.1080/13873954.2010.506799.
Imsland, L., P. Kittilsen, and T. S. Schei. 2010. “Model-Based Optimizing Control and Estimation Using Modelica Models.” Modeling, Identification and Control 31 (3): 107–21. doi:10.4173/mic.2010.3.3.
Leineweber, D B, I Bauer, A A S Schäfer, H G Bock, and J P Schlöder. 2003. “An Efficient Multiple Shooting Based Reduced SQP Strategy for Large-Scale Dynamic Process Optimization (Parts I and II).” Computers and Chemical Engineering 27: 157–74.
Richter, Christoph. 2008. “Proposal of New Object-Oriented Equation-Based Model Libraries for Thermodynamic Systems.” Technische Universität Braunschweig.
Schulze, C. 2013. “A Contribution to Numerically Efficient Modelling of Thermodynamic Systems.” Technische Universität Braunschweig.
