Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control
In this contribution, we present interval methods for mathematical modeling, for parameter identification, and for control design of dynamical systems. The corresponding approaches are applied to the thermal subsystem of a high-temperature solid oxide fuel cell (SOFC) which is available as a test ri...
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| Vydáno v: | Soft computing (Berlin, Germany) Ročník 17; číslo 8; s. 1329 - 1343 |
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| Jazyk: | angličtina |
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01.08.2013
Springer Nature B.V |
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| ISSN: | 1432-7643, 1433-7479 |
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| Abstract | In this contribution, we present interval methods for mathematical modeling, for parameter identification, and for control design of dynamical systems. The corresponding approaches are applied to the thermal subsystem of a high-temperature solid oxide fuel cell (SOFC) which is available as a test rig at the Chair of Mechatronics at the University of Rostock. In practice, most internal parameters of SOFC stack modules cannot be measured directly. Therefore, system characteristics such as heat capacities or internal thermal resistances cannot be identified exactly, but only bounded. For this reason, intervals represent a good first approach to dealing with parameter uncertainty. In the first part of the paper, we present interval methods for the parameter identification aiming at the computation of globally optimal parameterizations. In comparison with classical local optimization procedures, the approximation quality is improved by the presented identification approach. The corresponding bounds for admissible domains are used to design a robust sliding mode control law for arbitrary operating points compensating the impact of disturbances and parameter uncertainties in a reliable way. In the second part of the paper, we show a simple approach to handling non-smoothness appearing in SOFC models based on ordinary differential equations in a verified way. We use a generalized derivative definition for a certain type of non-smooth functions inside the algorithm of the verified solver
ValEncIA-IVP
to be able to compute solutions to non-smooth initial value problems. The applicability of our method is demonstrated using the designed sliding mode controller. |
|---|---|
| AbstractList | In this contribution, we present interval methods for mathematical modeling, for parameter identification, and for control design of dynamical systems. The corresponding approaches are applied to the thermal subsystem of a high-temperature solid oxide fuel cell (SOFC) which is available as a test rig at the Chair of Mechatronics at the University of Rostock. In practice, most internal parameters of SOFC stack modules cannot be measured directly. Therefore, system characteristics such as heat capacities or internal thermal resistances cannot be identified exactly, but only bounded. For this reason, intervals represent a good first approach to dealing with parameter uncertainty. In the first part of the paper, we present interval methods for the parameter identification aiming at the computation of globally optimal parameterizations. In comparison with classical local optimization procedures, the approximation quality is improved by the presented identification approach. The corresponding bounds for admissible domains are used to design a robust sliding mode control law for arbitrary operating points compensating the impact of disturbances and parameter uncertainties in a reliable way. In the second part of the paper, we show a simple approach to handling non-smoothness appearing in SOFC models based on ordinary differential equations in a verified way. We use a generalized derivative definition for a certain type of non-smooth functions inside the algorithm of the verified solver ValEncIA-IVP to be able to compute solutions to non-smooth initial value problems. The applicability of our method is demonstrated using the designed sliding mode controller. In this contribution, we present interval methods for mathematical modeling, for parameter identification, and for control design of dynamical systems. The corresponding approaches are applied to the thermal subsystem of a high-temperature solid oxide fuel cell (SOFC) which is available as a test rig at the Chair of Mechatronics at the University of Rostock. In practice, most internal parameters of SOFC stack modules cannot be measured directly. Therefore, system characteristics such as heat capacities or internal thermal resistances cannot be identified exactly, but only bounded. For this reason, intervals represent a good first approach to dealing with parameter uncertainty. In the first part of the paper, we present interval methods for the parameter identification aiming at the computation of globally optimal parameterizations. In comparison with classical local optimization procedures, the approximation quality is improved by the presented identification approach. The corresponding bounds for admissible domains are used to design a robust sliding mode control law for arbitrary operating points compensating the impact of disturbances and parameter uncertainties in a reliable way. In the second part of the paper, we show a simple approach to handling non-smoothness appearing in SOFC models based on ordinary differential equations in a verified way. We use a generalized derivative definition for a certain type of non-smooth functions inside the algorithm of the verified solver ValEncIA-IVP to be able to compute solutions to non-smooth initial value problems. The applicability of our method is demonstrated using the designed sliding mode controller. |
| Author | Auer, Ekaterina Rauh, Andreas Dötschel, Thomas Aschemann, Harald |
| Author_xml | – sequence: 1 givenname: Thomas surname: Dötschel fullname: Dötschel, Thomas organization: Chair of Mechatronics, University of Rostock – sequence: 2 givenname: Ekaterina surname: Auer fullname: Auer, Ekaterina email: auer@inf.uni-due.de organization: Faculty of Engineering, University of Duisburg-Essen – sequence: 3 givenname: Andreas surname: Rauh fullname: Rauh, Andreas organization: Chair of Mechatronics, University of Rostock – sequence: 4 givenname: Harald surname: Aschemann fullname: Aschemann, Harald organization: Chair of Mechatronics, University of Rostock |
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| CitedBy_id | crossref_primary_10_3390_cleantechnol3010012 crossref_primary_10_1016_j_cam_2019_112484 crossref_primary_10_1016_j_ijhydene_2020_01_032 crossref_primary_10_1007_s11786_014_0205_x crossref_primary_10_1515_auto_2017_0117 crossref_primary_10_1007_s00500_014_1300_2 |
| Cites_doi | 10.1023/B:REOM.0000032107.85627.45 10.1007/978-1-4020-6995-6 10.2478/v10006-009-0035-1 10.1109/MMAR.2011.6031306 10.3182/20120711-3-BE-2027.00374 10.1002/acs.1232 10.3182/20120215-3-AT-3016.00093 10.1007/978-3-642-96104-5 10.1080/13873954.2011.642384 10.1007/978-3-540-85521-7_1 10.1007/s11075-008-9180-0 10.1007/978-1-4757-2495-0 10.1007/978-3-642-15956-5_7 10.1007/978-94-015-7793-9 |
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| Keywords | Slide Mode Control Solid Oxide Fuel Cell Switching Point Initial Value Problem Subdivision Strategy |
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| References | Goldsztejn A, Ishii D (2011) A parallelotope method for the simulation of nonlinear hybrid systems, abstract of a talk at SWIM 2011 workshop in Bourges Filippov A (1988) Differential equations with discontinuous righthand sides. Kluwer Academic Publishers, Dordrecht Rauh A, Kletting M, Aschemann H, Hofer EP (2006) Interval methods for simulation of dynamical systems with state-dependent switching characteristics. In: Proceedings of the IEEE CCA 2006, pp 355–360 Dötschel T, Rauh A, Aschemann H (2012) Reliable control and disturbance rejection for the thermal behavior of solid oxide fuel cell systems. In: Proceedings of MATHMOD 2012, Vienna. http://ifac-papersonline.net Bove R, Ubertini S (eds) (2008) Modeling solid oxide fuel cells. Springer, Berlin Veres SM (ed) (2011) Special issue: bounding methods for state and parameter estimation. International Journal of Adaptive Control and Signal Processing, vol 25. Wiley, Malden Lohner R (1988) Einschließung der Lösung gewöhnlicher Anfangs- und Randwertaufgaben und Anwendungen. PhD thesis, Universität Karlsruhe Auer E, Rauh A, Hofer EP, Luther W (2008) Validated modeling of mechanical systems with SmartMOBILE: improvement of performance by ValEncIA-IVP. In: Proceedings of Dagstuhl Seminar 06021: reliable implementation of real number algorithms: theory and practice. Lecture Notes in Computer Science, pp 1–27 Rauh A, Senkel L, Aschemann H (2012b) Sensitivity-based state and parameter estimation for fuel cell systems. In: Proceedings of 7th IFAC Symposium on Robust Control Design, ROCOND'12, Aalborg Mahmoud S, Chen X (2008) A verified inexact implicit Runge-Kutta method for nonsmooth ODEs. Numer Algorithms (47):275–290 Bendsten C, Stauning O (2007) FADBAD++, Version 2.1. http://www.fadbad.com RauhAAschemannHParameter identification and observer-based control for distributed heating systems—the basis for temperature control of solid oxide fuel cellsMath Comput Model Dyn Syst2012184329353295494310.1080/13873954.2011.642384 Nedialkov N, von Mohrenschildt M (2002) Rigorous simulation of hybrid dynamic systems with symbolic and interval methods. In: Proceedings of the American Control Conference, ACC, Anchorage Eble I (2007) Über Taylor-Modelle. PhD thesis, University of Karlsruhe Rihm R (1992) Enclosing solutions with switching points in ordinary differential equations. In: Computer arithmetic and enclosure methods. Proceedings of SCAN 91. North-Holland, Amsterdam, pp 419–425 Walter W (1972) Gewöhnliche Differentialgleichungen. Springer, Berlin Rauh A, Dötschel T, Aschemann H (2011) Experimental parameter identification for a control-oriented model of the thermal behavior of high-temperature fuel cells. In: CD-Proceedings of IEEE International Conference on Methods and Models in Automation and Robotics MMAR, Miedzyzdroje Kearfott RB (1996) Rigorous global search: continuous problems. Kluwer, Boston RauhAMinisiniJHoferEPVerification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertaintiesInt J Appl Math Comput Sci2009193425439 Rauh A, Dötschel T, Auer E, Aschemann H (2012a) Interval methods for control-oriented modeling of the thermal behavior of high-temperature fuel cell stacks. In: Proceedings of 16th IFAC Symposium on System Identification SysID 2012, Brussels Nedialkov NS (2002) The design and implementation of an object-oriented validated ODE solver. Kluwer Academic Publishers, Dordrecht MunozHKearfottRBSlope intervals, generalized gradients, semigradients, slant derivatives, and CsetsReliable Comput20041016319320578741072.6509410.1023/B:REOM.0000032107.85627.45 Eggers A, Fränzle M, Herde C (2009) Application of constraint solving and ODE-enclosure methods to the analysis of hybrid systems. In: Numerical analysis and applied mathematics 2009. American Institute of Physics, vol 1168, pp 1326–1330 Stauning O (1997) Automatic validation of numerical solutions. PhD thesis, Technical University of Denmark, Lyngby Keil C (2008) Profil/BIAS, Version 2.0.8. http://www.ti3.tu-harburg.de/keil/profil Kieffer M, Csaba M, Schichl H, Walter E (2011) Verified global optimization for estimating the parameters of nonlinear models. In: Rauh A, Auer E (eds) Modeling, design and simulation of systems with uncertainties, mathematical engineering. Springer, Berlin Schnurr M (2007) Steigungen höherer Ordnung zur verifizierten globalen Optimierung. PhD thesis, Universität Karlsruhe A Rauh (1003_CR19) 2009; 19 1003_CR18 1003_CR15 1003_CR16 1003_CR13 1003_CR11 1003_CR12 1003_CR10 1003_CR4 1003_CR5 H Munoz (1003_CR14) 2004; 10 1003_CR6 1003_CR7 1003_CR8 1003_CR9 1003_CR1 1003_CR2 1003_CR26 1003_CR3 1003_CR27 1003_CR24 1003_CR25 A Rauh (1003_CR17) 2012; 18 1003_CR22 1003_CR23 1003_CR20 1003_CR21 |
| References_xml | – reference: RauhAAschemannHParameter identification and observer-based control for distributed heating systems—the basis for temperature control of solid oxide fuel cellsMath Comput Model Dyn Syst2012184329353295494310.1080/13873954.2011.642384 – reference: Goldsztejn A, Ishii D (2011) A parallelotope method for the simulation of nonlinear hybrid systems, abstract of a talk at SWIM 2011 workshop in Bourges – reference: Rauh A, Dötschel T, Aschemann H (2011) Experimental parameter identification for a control-oriented model of the thermal behavior of high-temperature fuel cells. In: CD-Proceedings of IEEE International Conference on Methods and Models in Automation and Robotics MMAR, Miedzyzdroje – reference: Rihm R (1992) Enclosing solutions with switching points in ordinary differential equations. In: Computer arithmetic and enclosure methods. Proceedings of SCAN 91. North-Holland, Amsterdam, pp 419–425 – reference: Eggers A, Fränzle M, Herde C (2009) Application of constraint solving and ODE-enclosure methods to the analysis of hybrid systems. In: Numerical analysis and applied mathematics 2009. American Institute of Physics, vol 1168, pp 1326–1330 – reference: Auer E, Rauh A, Hofer EP, Luther W (2008) Validated modeling of mechanical systems with SmartMOBILE: improvement of performance by ValEncIA-IVP. In: Proceedings of Dagstuhl Seminar 06021: reliable implementation of real number algorithms: theory and practice. Lecture Notes in Computer Science, pp 1–27 – reference: Walter W (1972) Gewöhnliche Differentialgleichungen. Springer, Berlin – reference: Bove R, Ubertini S (eds) (2008) Modeling solid oxide fuel cells. Springer, Berlin – reference: Dötschel T, Rauh A, Aschemann H (2012) Reliable control and disturbance rejection for the thermal behavior of solid oxide fuel cell systems. In: Proceedings of MATHMOD 2012, Vienna. http://ifac-papersonline.net – reference: Eble I (2007) Über Taylor-Modelle. PhD thesis, University of Karlsruhe – reference: Keil C (2008) Profil/BIAS, Version 2.0.8. http://www.ti3.tu-harburg.de/keil/profil/ – reference: Rauh A, Senkel L, Aschemann H (2012b) Sensitivity-based state and parameter estimation for fuel cell systems. In: Proceedings of 7th IFAC Symposium on Robust Control Design, ROCOND'12, Aalborg – reference: Veres SM (ed) (2011) Special issue: bounding methods for state and parameter estimation. International Journal of Adaptive Control and Signal Processing, vol 25. Wiley, Malden – reference: Bendsten C, Stauning O (2007) FADBAD++, Version 2.1. http://www.fadbad.com – reference: Filippov A (1988) Differential equations with discontinuous righthand sides. Kluwer Academic Publishers, Dordrecht – reference: Lohner R (1988) Einschließung der Lösung gewöhnlicher Anfangs- und Randwertaufgaben und Anwendungen. PhD thesis, Universität Karlsruhe – reference: Stauning O (1997) Automatic validation of numerical solutions. PhD thesis, Technical University of Denmark, Lyngby – reference: Kearfott RB (1996) Rigorous global search: continuous problems. Kluwer, Boston – reference: MunozHKearfottRBSlope intervals, generalized gradients, semigradients, slant derivatives, and CsetsReliable Comput20041016319320578741072.6509410.1023/B:REOM.0000032107.85627.45 – reference: RauhAMinisiniJHoferEPVerification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertaintiesInt J Appl Math Comput Sci2009193425439 – reference: Nedialkov N, von Mohrenschildt M (2002) Rigorous simulation of hybrid dynamic systems with symbolic and interval methods. In: Proceedings of the American Control Conference, ACC, Anchorage – reference: Nedialkov NS (2002) The design and implementation of an object-oriented validated ODE solver. Kluwer Academic Publishers, Dordrecht – reference: Rauh A, Dötschel T, Auer E, Aschemann H (2012a) Interval methods for control-oriented modeling of the thermal behavior of high-temperature fuel cell stacks. In: Proceedings of 16th IFAC Symposium on System Identification SysID 2012, Brussels – reference: Rauh A, Kletting M, Aschemann H, Hofer EP (2006) Interval methods for simulation of dynamical systems with state-dependent switching characteristics. In: Proceedings of the IEEE CCA 2006, pp 355–360 – reference: Schnurr M (2007) Steigungen höherer Ordnung zur verifizierten globalen Optimierung. PhD thesis, Universität Karlsruhe – reference: Kieffer M, Csaba M, Schichl H, Walter E (2011) Verified global optimization for estimating the parameters of nonlinear models. In: Rauh A, Auer E (eds) Modeling, design and simulation of systems with uncertainties, mathematical engineering. Springer, Berlin – reference: Mahmoud S, Chen X (2008) A verified inexact implicit Runge-Kutta method for nonsmooth ODEs. 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| SubjectTerms | Algorithms Artificial Intelligence Boundary value problems Computational Intelligence Control Control systems design Control theory Differential equations Energy Engineering Focus Fuel cells Gases Heat High temperature Hydrogen Influence Local optimization Mathematical Logic and Foundations Mathematical models Mechatronics Natural gas Optimization techniques Ordinary differential equations Parameter estimation Parameter identification Parameter uncertainty Partial differential equations Robotics Robust control Sliding mode control Smoothness Solid oxide fuel cells Subsystems Temperature Thermodynamic properties |
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| Title | Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control |
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| Volume | 17 |
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