An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems

Andreas Rauh; Luise Senkel; Harald Aschemann; Vasily V. Saurin; Georgy V. Kostin

International Journal of Applied Mathematics and Computer Science (2016)

  • Volume: 26, Issue: 1, page 15-30
  • ISSN: 1641-876X

Abstract

top
In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finitedimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are-with good accuracy-homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.

How to cite

top

Andreas Rauh, et al. "An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems." International Journal of Applied Mathematics and Computer Science 26.1 (2016): 15-30. <http://eudml.org/doc/276662>.

@article{AndreasRauh2016,
abstract = {In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finitedimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are-with good accuracy-homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.},
author = {Andreas Rauh, Luise Senkel, Harald Aschemann, Vasily V. Saurin, Georgy V. Kostin},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {heat transfer; predictive control; optimal control; state and disturbance estimation; distributed parameter systems; sensitivity analysis},
language = {eng},
number = {1},
pages = {15-30},
title = {An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems},
url = {http://eudml.org/doc/276662},
volume = {26},
year = {2016},
}

TY - JOUR
AU - Andreas Rauh
AU - Luise Senkel
AU - Harald Aschemann
AU - Vasily V. Saurin
AU - Georgy V. Kostin
TI - An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 1
SP - 15
EP - 30
AB - In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finitedimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are-with good accuracy-homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.
LA - eng
KW - heat transfer; predictive control; optimal control; state and disturbance estimation; distributed parameter systems; sensitivity analysis
UR - http://eudml.org/doc/276662
ER -

References

top
  1. Aschemann, H., Kostin, G.V., Rauh, A. and Saurin, V.V. (2010). Approaches to control design and optimization in heat transfer problems, Journal of Computer and Systems Sciences International 49(3): 380-391. Zbl1267.93043
  2. Åström, K. (1970). Introduction to Stochastic Control Theory, Mathematics in Science and Engineering, Academic Press, New York, NY/London. Zbl0226.93027
  3. Bachmayer, M., Ulbrich, H. and Rudolph, J. (2011). Flatness-based control of a horizontally moving erected beam with a point mass, Mathematical and Computer Modelling of Dynamical Systems 17(1): 49-69. Zbl05920019
  4. Bendsten, C. and Stauning, O. (2007). FADBAD++, Version 2.1, http://www.fadbad.com. 
  5. Deutscher, J. and Harkort, C. (2008). Vollständige Modale Synthese eines Wärmeleiters, Automatisierungstechnik 56(10): 539-548. 
  6. Deutscher, J. and Harkort, C. (2010). Entwurf endlich-dimensionaler Regler für lineare verteilt parametrische Systeme durch Ausgangsbeobachtung, Automatisierungstechnik 58(8): 435-446. 
  7. Gehring, N., Knüppel, T., Rudolph, J. and Woittennek, F. (2012). Parameter identification for a heavy rope with internal damping, Proceedings in Applied Mathematics and Mechanics 12(1): 725-726. 
  8. Griewank, A. and Walther, A. (2008). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, PA. Zbl1159.65026
  9. Janiszowski, K.B. (2014). Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error, International Journal of Applied Mathematics and Computer Science 24(1): 99-109, DOI: 10.2478/amcs-2014-0008. Zbl1292.93085
  10. Kersten, J., Rauh, A. and Aschemann, H. (2014). Finite element modeling for heat transfer processes using the method of integro-differential relations with applications in control engineering, IEEE International Conference on Methods and Models in Automation and Robotics MMAR 2014, Międzyzdroje, Poland, pp. 606-611. 
  11. Kharitonov, A. and Sawodny, O. (2006). Flatness-based disturbance decoupling for heat and mass transfer processes with distributed control, IEEE International Conference on Control Applications CCA, Munich, Germany, pp. 674-679. 
  12. Kostin, G. and Saurin, V. (2012). Integrodifferential Relations in Linear Elasticity, De Gruyter, Berlin. Zbl1259.74001
  13. Kostin, G.V. and Saurin, V.V. (2006). Modeling of controlled motions of an elastic rod by the method of integro-differential relations, Journal of Computer and Systems Sciences International 45(1): 56-63. Zbl1260.93010
  14. Krstic, M. and Smyshlyaev, A. (2010). Adaptive Control of Parabolic PDEs, Princeton University Press, Princeton, NJ. Zbl1225.93005
  15. Lions, J.L. (1971). Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, NY. Zbl0203.09001
  16. Malchow, F. and Sawodny, O. (2011). Feedforward control of inhomogeneous linear first order distributed parameter systems, American Control Conference on ACC 2011, San Francisco, CA, USA, pp. 3597-3602. 
  17. Meurer, T. and Kugi, A. (2009). Tracking control for boundary controlled parabolic PDEs with varying parameters: Combining backstepping and differential flatness, Automatica 45(5): 1182-1194. Zbl1162.93016
  18. Meurer, T. and Zeitz, M. (2003). A novel design of flatness-based feedback boundary control of nonlinear reaction-diffusion systems with distributed parameters, in W. Kang, M. Xiao and C. Borges (Eds.), New Trends in Nonlinear Dynamics and Control, Lecture Notes in Control and Information Science, Vol. 295, Springer, Berlin/Heidelberg, pp. 221-236. Zbl1203.93081
  19. Prodan, I., Olaru, S., Stoica, C. and Niculescu, S.-I. (2013). Predictive control for trajectory tracking and decentralized navigation of multi-agent formations, International Journal of Applied Mathematics and Computer Science 23(1): 91-102, DOI: 10.2478/amcs-2013-0008. Zbl1293.93055
  20. Rauh, A. and Aschemann, H. (2012). Parameter identification and observer-based control for distributed heating systems-the basis for temperature control of solid oxide fuel cell stacks, Mathematical and Computer Modelling of Dynamical Systems 18(4): 329-353. Zbl1272.93044
  21. Rauh, A., Butt, S.S. and Aschemann, H. (2013a). Nonlinear state observers and extended Kalman filters for battery systems, International Journal of Applied Mathematics and Computer Science 23(3): 539-556, DOI: 10.2478/amcs-2013-0041. Zbl1279.93101
  22. Rauh, A., Dittrich, C. and Aschemann, H. (2013b). The method of integro-differential relations for control of spatially two-dimensional heat transfer processes, European Control Conference ECC'13, Zurich, Switzerland, pp. 572-577. 
  23. Rauh, A., Kostin, G.V., Aschemann, H., Saurin, V.V. and Naumov, V. (2010). Verification and experimental validation of flatness-based control for distributed heating systems, International Review of Mechanical Engineering 4(2): 188-200. 
  24. Rauh, A., Senkel, L. and Aschemann, H. (2012a). Sensitivity-based state and parameter estimation for fuel cell systems, 7th IFAC Symposium on Robust Control Design, Aalborg, Denmark, pp. 57-62. 
  25. Rauh, A., Senkel, L., Aschemann, H., Kostin, G.V. and Saurin, V.V. (2012b). Reliable finite-dimensional control procedures for distributed parameter systems with guaranteed approximation quality, IEEE Multi-Conference on Systems and Control, Dubrovnik, Croatia, pp. 214-219. 
  26. Rauh, A., Senkel, L., Dittrich, C. and Aschemann, H. (2012c). Observer-based predictive temperature control for distributed heating systems based on the method of integrodifferential relations, IEEE International Conference on Methods and Models in Automation and Robotics MMAR 2012, Międzyzdroje, Poland, pp. 528-533. 
  27. Rauh, A., Warncke, J., Kostin, G.V., Saurin, V.V. and Aschemann, H. (2015). Numerical validation of order reduction techniques for finite element modeling of a flexible rack feeder system, European Control Conference ECC'15, Linz, Austria, pp. 1094-1099. 
  28. Röbenack, K. (2002). On the efficient computation of higher order maps adkf g(x) using Taylor arithmetic and the Campbell-Baker-Hausdorff formula, in A. Zinober and D. Owens (Eds.), Nonlinear and Adaptive Control, Lecture Notes in Control and Information Science, Vol. 281, Springer, Berlin/Heidelberg, pp. 327-336. Zbl1157.93378
  29. Saurin, V.V., Kostin, G.V., Rauh, A. and Aschemann, H. (2011a). Adaptive control strategies in heat transfer problems with parameter uncertainties based on a projective approach, in A. Rauh and E. Auer (Eds.), Modeling, Design, and Simulation of Systems with Uncertainties, Mathematical Engineering, Springer, Berlin/Heidelberg, pp. 309-332. 
  30. Saurin, V.V., Kostin, G.V., Rauh, A. and Aschemann, H. (2011b). Variational approach to adaptive control design for distributed heating systems under disturbances, International Review of Mechanical Engineering 5(2): 244-256. 
  31. Saurin, V.V., Kostin, G.V., Rauh, A., Senkel, L. and Aschemann, H. (2012). An integrodifferential approach to adaptive control design for heat transfer systems with uncertainties, 7th Vienna International Conference on Mathematical Modelling MATHMOD 2012, Vienna, Austria, pp. 520-525. 
  32. Stengel, R. (1994). Optimal Control and Estimation, Dover Publications, Inc., Mineola, NY. Zbl0854.93001
  33. Tao, G. (2003). Adaptive Control Design and Analysis, Wiley & Sons, Inc., Hoboken, NJ. Zbl1061.93004
  34. Thull, D., Kugi, A. and Schlacher, K. (2010). Tracking Control of Mechanical Distributed Parameter Systems with Applications, Shaker-Verlag, Aachen. 
  35. Touré, Y. and Rudolph, J. (2002). Controller design for distributed parameter systems, Encyclopedia of Life Support Systems (EOLSS), http://www.eolss.net/sample-chapters/c18/E6-43-19-02.pdf. 
  36. Utz, T., Meurer, T. and Kugi, A. (2011). Trajectory planning for a two-dimensional quasi-linear parabolic PDE based on finite difference semi-discretizations, 18th IFAC World Congress, Milano, Italy, pp. 12632-12637. 
  37. Winkler, F.J. and Lohmann, B. (2009). Flatness-based control of a continuous furnace, 3rd IEEE Multi-Conference on Systems and Control (MSC), Saint Petersburg, Russia, pp. 719-724. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.