Abstract
Reliable control strategies for complex dynamic systems have to account for stability and robustness despite the presence of both parameter uncertainty and measurement errors. In addition, such control strategies have to comply with performance specifications that can be described either by the minimization of suitable cost functions or by direct specifications of desired reference trajectories. To handle bounded uncertainty and errors in a reliable way, it is possible to include the use of interval analysis in real-time control environments. Previous work has shown that approaches based on the general methodology of sliding mode and predictive control are promising options in this context. This paper presents a comparison of the properties of interval extensions of both types of control procedures for the thermal subsystem of a high-temperature solid oxide fuel cell. Representative simulation results conclude this contribution.
Similar content being viewed by others
References
Auer, E., Rauh, A., Hofer, E.P., Luther, W.: 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, Springer, pp. 1–27 (2008)
Bendsten, C., Stauning, O.: FADBAD++, Version 2.1 (2007). http://www.fadbad.com
Bove, R., Ubertini, S. (ed.): Modeling Solid Oxide Fuel Cells. Springer, Berlin (2008)
Dötschel T., Auer E., Rauh A., Aschemann H.: Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control. Soft Computing 17(8), 1329–1343 (2013)
Griewank, A., Walther, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia (2008)
Gubner, A.: Non-isothermal and dynamic sofc voltage-current behavior. In: Singhal, S. C., Mizusaki, J. (ed.) Solid Oxide Fuel Cells IX (SOFC-IX)—Cells, Stacks, and Systems, vol. 1, pp. 814–826. The Electrochemical Society, India (2005)
Jaulin L., Kieffer M., Didrit O., Walter É.: Applied Interval Analysis. Springer, London (2001)
Krämer, W.: XSC Languages (C-XSC, PASCAL-XSC)—Scientific Computing with Validation, Arithmetic Requirements, Hardware Solution and Language Support (2012). http://www.math.uni-wuppertal.de/~xsc/, C-XSC 2.5.3
Limon D., Bravo J.M., Alamo T., Camacho E.F.: Robust MPC of constrained nonlinear systems based on interval arithmetic. IEE Proc. Control Theory Appl. 152(3), 325–332 (2005)
Nedialkov, N.S.: Interval tools for ODEs and DAEs. In: CD-Proc. of the 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2006, Duisburg, Germany, (2007). IEEE Computer Society, California
Nedialkov, N.S.: Implementing a rigorous ODE solver through literate programming. In: Rauh A., Auer E., (eds.) Modeling, Design, and Simulation of Systems with Uncertainties, Mathematical Engineering. Springer, Berlin, pp. 3–19 (2011)
Pukrushpan J.T., Stefanopoulou A.G., Peng H.: Control of Fuel Cell Power Systems: Principles, Modeling, Analysis and Feedback Design, 2nd edn. Springer, Berlin (2005)
Rauh A., Kersten J., Auer E., Aschemann H.: Sensitivity-based feedforward and feedback control for uncertain systems. Computing (2–4), 357–367 (2012)
Rauh A., Minisini J., Hofer E.P.: Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties. Spec. Issue Int. J. Appl. Math. Comput. Sci. AMCS Verified Methods: Applications to Modeling, Analysis, and Design of Systems in Medicine and Engineering 19(3), 425–439 (2009)
Rauh, A., Senkel, L., Aschemann, H.: Variable structure approaches for temperature control of solid oxide fuel cell stacks. In: Proc. of 2nd Intl. Conference on Vulnerability and Risk Analysis and Management ICVRAM 2014. Liverpool, UK (2014, To appear)
Rauh, A., Senkel, L., Kersten, J., Aschemann, H.: Interval methods for sensitivity-based model-predictive control of solid oxide fuel cell systems. In: Proc. of the 15th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2012, vol. 19, pp. 361–384, Novosibirsk, Russia, 2014. Special Issue of Reliable Computing. http://interval.louisiana.edu/reliable-computing-journal/volume-19/reliable-computing-19-pp-361-384.pdf
Rauh, A., Senkel, L., Kersten, J., Aschemann, H.: Reliable control of high-temperature fuel cell systems using interval-based sliding mode techniques. IMA J. Math. Control Inf. (2014). Accepted for publication.
Senkel, L., Rauh, A., Aschemann, H.: Experimental validation of a sensitivity-based observer for solid oxide fuel cell systems. In: Proc. of IEEE Intl. Conference on Methods and Models in Automation and Robotics MMAR 2013. Miedzyzdroje, Poland (2013)
Senkel, L., Rauh, A., Aschemann, H.: Robust sliding mode techniques for control and state estimation of dynamic systems with bounded and stochastic uncertainty. In: Proc. of 2nd Intl. Conference on Vulnerability and Risk Analysis and Management ICVRAM 2014. Liverpool, UK (2014, To appear)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rauh, A., Senkel, L., Auer, E. et al. Interval Methods for Real-Time Capable Robust Control of Solid Oxide Fuel Cell Systems. Math.Comput.Sci. 8, 525–542 (2014). https://doi.org/10.1007/s11786-014-0205-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11786-014-0205-x
Keywords
- Interval analysis
- Sliding mode control
- Predictive control
- Sensitivity analysis
- Temperature control of solid oxide fuel cells