Manuel Gräber
Technische Universität Braunschweig, Braunschweig, Germany
Christian Kirches
Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Germany
Dirk Scharff
TLK-Thermo GmbH, Braunschweig, Germany
Wilhelm Tegethoff
Technische Universität Braunschweig, Braunschweig/TLK-Thermo GmbH, Braunschweig, Germany
Ladda ner artikel
http://dx.doi.org/10.3384/ecp12076781Ingår i: Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany
Linköping Electronic Conference Proceedings 76:80, s. 781-790
Publicerad: 2012-11-19
ISBN: 978-91-7519-826-2
ISSN: 1650-3686 (tryckt), 1650-3740 (online)
Based on the standardized model exchange format Functional Mock-up Interface (FMI) an software framework is presented for prototyping of nonlinear model predictive control (NMPC) loops. Arising optimal control problems are solved by an efficient implementation of the direct multiple shooting method; which is especially suitable for nonlinear and stiff system models. Using co-simulation optimizer; plant and estimator can be coupled to a closed NMPC loop. Several stages of a control design process are supported: from virtual simulation experiments to real plants with prototype NMPC controllers. Energy efficient control of vapor compression cycles is presented as example application of the proposed methods.
[1] Johan Åkesson. Languages and Tools for Optimization of Large-Scale Systems. Phd thesis; Lund University; 2007.
[2] Johan Åkesson; Karl-Erik Årzén; Magnus Gäfvert; Tove Bergdahl; and Hubertus Tummescheit. Modeling and optimization with Optimica and JModelica.org–Languages and tools for solving large-scale dynamic optimization problems. Computers & Chemical Engineering; 34(11):1737–1749; November 2010.
doi: 10.1016/j.compchemeng.2009.11.011.
[3] T. Blochwitz; M. Otter; M. Arnold; C. Bausch; C. Clauß; H. Elmqvist; A. Junghanns; J. Mauss; M. Monteiro; T. Neidhold; D. Neumerkel; H. Olsson; J.-V. Peetz; and S. Wolf. The Functional Mockup Interface for Tool independent Exchange of Simulation Models. In 8th International Modelica Conference; Dresden; 2011.
[4] H. G. Bock and K. J. Plitt. A Multiple Shooting algorithm for direct solution of optimal control problems. In Proceedings 9th IFAC World Congress Budapest; pages 243–247. Pergamon Press; 1984.
[5] 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; pages 102–125. Springer; Heidelberg; 1981.
[6] Jonathan Brembeck; Martin Otter; and Dirk Zimmer. Nonlinear Observers based on the Functional Mockup Interface with Applications to Electric Vehicles. In 8th International Modelica Conference; Dresden; 2011.
[7] Francesco Casella; Filippo Donida; and Marco Lovera. Beyond Simulation: Computer-Aided Control System Design using Equation-based Object-oriented Modelling for the Next Decade. Simulation News Europe; 19(1):29–41; 2009.
[8] M. Diehl; H. G. Bock; J. P. Schlöder; R. Findeisen; Z. Nagy; and F. Allgöwer. Real-time optimization and Nonlinear Model Predictive Control of Processes governed by differential-algebraic equations. Journal of Process Control; 12(4):577–585; 2002.
doi: 10.1016/S0959-1524(01)00023-3.
[9] Moritz Diehl. Real-Time Optimization for Large Scale Nonlinear Processes. Phd thesis; Universität Heidelberg; 2001.
[10] Moritz Diehl; Hans Joachim Ferreau; and Niels Haverbeke. Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation. In Lalo Magni; Davide Martino Raimondo; and Frank Allgöwer; editors; Nonlinear Model Predictive Control; Lecture Notes in Control and Information Sciences; pages 391–417. Springer; Berlin; Heidelberg; New York; 2009.
doi: 10.1007/978-3-642-01094-1_32.
[11] R. Fourer; D. M. Gay; and B. W. Kernighan. AMPL: A Modelling Language for Mathematical Programming. Books/Cole—Thomson Learning; 2nd edition; 2003.
[12] Rüdiger Franke. Formulation of dynamic optimization problems using Modelica and their efficient solution. In 2nd International Modelica Conference; pages 315–323; Oberpfaffenhofen; 2002.
[13] Manuel Gräber; Christian Kirches; Johannes P. Schlöder; and Wilhelm Tegethoff. Nonlinear Model Predictive Control of a Vapor Compression Cycle based on First Principle Models. In MATHMOD; 7th Vienna International Conference on Mathematical Modelling; 2012.
[14] Manuel Gräber; Nils Christian Strupp; and Wilhelm Tegethoff. Moving boundary heat exchanger model and validation procedure. In EUROSIM Congress on Modelling and Simulation; Prague; 2010.
[15] William Gropp and Jorge J. Moré. Optimization environments and the NEOS Server. In M. D. Buhmann and A. Iserles; editors; Approximation Theory and Optimization; pages 167–182. Cambridge University Press; 1997.
[16] L. Imsland; P. Kittilsen; and T. S. Schei. Model-based optimizing control and estimation using Modelica models. Modeling; Identification and Control; 31(3):107–121; 2010.
doi: 10.4173/mic.2010.3.3.
[17] Jørgen Bauck Jensen and Sigurd Skogestad. Optimal operation of simple refrigeration cycles Part I: Degrees of freedom and optimality of sub-cooling. Computers & Chemical Engineering; 31(5-6):712–721; May 2007.
doi: 10.1016/j.compchemeng.2006.12.003.
[18] C. Kirches. A numerical method for nonlinear robust optimal control with implicit discontinuities and an application to powertrain oscillations. Diploma thesis; Ruprecht–Karls–Universität Heidelberg; October 2006.
[19] Christian Kirches and Sven Leyffer. TACO – A Toolkit for AMPL Control Optimization. Preprint ANL/MCS-P1948-0911; Mathematics and Computer Science Division; Argonne National Laboratory; October 2011.
[20] Roland Kossel; Martin Löffler; Nils Christian Strupp; and Wilhelm Tegethoff. Distributed energy system simulation of a vehicle. In Vehicle Thermal Management Systems Conference. Institution of Mechanical Engineers; SAE International; 2011.
[21] D B Leineweber; I Bauer; A A S Schäfer; H G Bock; and J P Schlöder. An Efficient Multiple Shooting Based Reduced SQP Strategy for Large-Scale Dynamic Process Optimization (Parts I and II). Computers and Chemical Engineering; 27:157–174; 2003.
doi: 10.1016/S0098-1354(02)00158-8.
[22] MODELISAR. Function Mock-up Interface for Model Exchange; 2010. Specification; Version 1.0.
[23] K.D. Mombaur. Stability Optimization of Open-loop Controlled Walking Robots. Phd thesis; Universität Heidelberg; 2001.
[24] Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer; Berlin; Heidelberg; New York; 2nd edition; 2006.
[25] Andreas Pfeiffer. Numerische Sensitivitätsanalyse unstetiger multidisziplinärer Modelle mit Anwendungen in der gradientenbasierten Optimierung. Phd thesis; Martin-Luther-Universität Halle-Wittenberg; 2008.
[26] E. D. Tate; Michael Sasena; Jesse Gohl; and Michael Tiller. Model Embedded Control: A Method to Rapidly Synthesize Controllers in a Modeling Environment. In 6th International Modelica Conference; pages 493–502; Bielefeld; 2008.
