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e & i Elektrotechnik und Informationstechnik

, Volume 129, Issue 1, pp 3–10 | Cite as

Nichtlineare modellprädiktive Regelung eines Brammenwärmofens basierend auf einem zeitkontinuierlichen Zustandsraummodell

  • A. Steinböck
  • A. Kugi
Originalarbeiten

Zusammenfassung

Es wird ein nichtlinearer modellprädiktiver Regler als Teil einer kaskadierten Temperaturregelung eines kontinuierlichen Ofens zur Erwärmung von Stahlbrammen entwickelt. Dazu wird aufbauend auf einem physikalisch motivierten, zeitkontinuierlichen Zustandsraummodell ein beschränktes dynamisches Optimierungsproblem formuliert und mittels einer Transformation von Eingangsgrößen sowie zusätzlichen Straftermen im Kostenfunktional in eine unbeschränkte Optimierungsaufgabe übergeführt. Das Optimierungsproblem wird mit dem Quasi-Newton-Verfahren wiederkehrend für finite Zeithorizonte gelöst. Als Rückkopplung werden neben gemessenen Ofentemperaturen die mit einem erweiterten Kalman-Filter geschätzten Brammentemperaturen verwendet. Ergebnisse aus der Anwendung des Regelungssystems bei einem Brammenwärmofen eines Walzwerks belegen die hohe Genauigkeit der Brammenerwärmung und eine erhebliche Energieeinsparung.

Schlüsselwörter

Nichtlineare modellprädiktive Regelung Geschaltetes nichtlineares System Beschränkte dynamische Optimierung Brammenwärmofen 

Nonlinear model predictive control of a pusher-type slab reheating furnace based on a continuous-time state-space model

Summary

A nonlinear model predictive controller is developed as part of a cascade temperature control system for a continuous furnace that reheats steel slabs. Using a continuous-time state-space model based on first principles, a constrained dynamic optimization problem is formulated. It is converted into an unconstrained optimization problem by means of an input transformation and additional penalty terms in the cost functional. With the help of the quasi-Newton method, the optimization problem is recurrently solved for finite time horizons. The measured furnace temperatures as well as the slab temperatures, which are estimated by an extended Kalman filter, are used as feedback. Results from the application of the control system in a slab furnace of a rolling mill demonstrate the high accuracy of the slab reheating process and significant energy savings.

Keywords

Nonlinear model predictive control Switched nonlinear system Constrained dynamic optimization Slab reheating furnace 

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Literatur

  1. Azhmyakov, V. (2007): Consistent Approximations of Constrained Optimal Control Problems. Logos, BerlinGoogle Scholar
  2. Baehr, H., Stephan, K. (2006): Heat and Mass Transfer. Springer, Berlin Heidelberg, 2nd editionGoogle Scholar
  3. Balbis, L., Balderud, J., Grimble, M. (2008): Nonlinear predictive control of steel slab reheating furnace. Proceedings of the American Control Conference, Seattle, Washington, USA, S. 1679–1684Google Scholar
  4. Barr, P. (1995): The development, verification, and application of a steady-state thermal model for the pusher-type reheat furnace. Metallurgical and Materials Transactions B, 26B: 851–869Google Scholar
  5. Barr, P. (2003): Examining reheating furnace thermal response to mill delays. Proceedings of Materials Science & Technology 2003, Chicago, Illinois, USA, S. 126–135Google Scholar
  6. Betts, J. (2001): Practical Methods for Optimal Control Using Nonlinear Programming. Advances in Design and Control. Siam, PhiladelphiaGoogle Scholar
  7. Bryson, A. (1999): Dynamic Optimization. Addison-Wesley, Menlo Park, California, USAGoogle Scholar
  8. Camacho, E., Bordons, C. (2004): Model Predictive Control. Advanced Textbooks in Control and Signal Processing. Springer, 2nd editionGoogle Scholar
  9. Carpenter, D., Proctor, C. (1987): Temperature control and optimization of a reheat furnace using a distributed control system. Iron and Steel Engineer, 64(8): 44–49Google Scholar
  10. Chen, S. (2009): Flat-Rolled Steel Processes: Advanced Technologies, chapter Modeling for Reheat Furnace Practices, S. 99–114. CRC Press, Boca RatonGoogle Scholar
  11. Chen, S., Abraham, S., Poshard, D. (2008): Modification of reheat furnace practices through comprehensive process modeling. Iron & Steel Technology, 5(8): 66–79Google Scholar
  12. Dahm, B., Klima, R. (2002): Feedback control of stock temperature and oxygen content in reheating furnaces. Proceedings of the IOM Conference on Challenges in Reheating Furnaces, London, UK, S. 287–296Google Scholar
  13. Ditzhuijzen, G., Staalman, D., Koorn, A. (2002): Identification and model predictive control of a slab reheating furnace. Proceedings of the 2002 IEEE International Conference on Control Applications, Glasgow, UK, S. 361–366Google Scholar
  14. Doss, B., Chu, E., Mason, H., Ruiz, R., Chan, I., Kleppe, J., Jensen, J. (1992): Steel process furnace burner control using acoustic pyrometry. Proceedings of the International Gas Research Conference, Orlando, USA, S. 2231–2240Google Scholar
  15. Ezure, H., Seki, Y., Yamaguchi, N., Shinonaga, H. (1997): Development of a simulator to calculate an optimal slab heating pattern for reheat furnaces. Electrical Engineering in Japan, 120 (3): 42–53CrossRefGoogle Scholar
  16. Facco, G., Petersen, M., Schurko, R., Ferguson, N. (1990): State of the art slab reheating furnaces at Dofasco. Iron and Steel Engineer, 67 (1): 27–36Google Scholar
  17. Ferrand, L., Reynes, P., Le Duigou, F. (2006): Simulation tools make new furnace technology. La Revue de Métallurgie, 103 (2): 67–75CrossRefGoogle Scholar
  18. Fiacco, A., McCormick, G. (1990): Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Number 4 in Classics in Applied Mathematics. Siam, Philadelphia, PennsylvaniaGoogle Scholar
  19. Findeisen, R., Biegler, L., Allgöwer, F., editors (2008): Assessment and Future Directions of Nonlinear Model Predictive Control, volume 26 of Lecture Notes in Control and Information Sciences. Springer, BerlinGoogle Scholar
  20. Fontana, P., Boggiano, A., Furinghetti, A., Cabras, G., Simoncini, C. (1983): An advanced computer control system for reheat furnaces. Iron and Steel Engineer, 60 (8): 55–62Google Scholar
  21. Graichen, K., Kugi, A. (2010): Stability of incremental model predictive control without terminal constraints. IEEE Transactions on Automatic Control, 55 (11): 2576–2580MathSciNetCrossRefGoogle Scholar
  22. Graichen, K., Petit, N. (2009): Incorporating a class of constraints into the dynamics of optimal control problems. Optimal Control Applications and Methods, 30 (6): 537–561MathSciNetCrossRefGoogle Scholar
  23. Hollander, F., Zuurbier, S. (1982): Design, development and performance of online computer control in a 3-zone reheating furnace. Iron and Steel Engineer, 59 (1): 44–52Google Scholar
  24. Hollander, F., Zuurbier, S. (1985): Accurate temperature control of the reheating process at mixed cold and hot charging. Proceedings of the International Conference on Process Control and Energy Savings in Reheating Furnaces, Scanheating, Luleå, Sweden, S. 6:1–6:36Google Scholar
  25. Icev, Z., Zhao, J., Stankovski, M., Kolemisevska-Gugulovska, T., Dimirovski, G. (2004): Supervisory-plus-regulatory control design for efficient operation of industrial furnaces. Journal of Electrical & Electronics Engineering, 4 (2): 1199–1218Google Scholar
  26. Incropera, F., DeWitt, D., Bergman, T., Lavine, A. (2007): Fundamentals of Heat and Mass Transfer. John Wiley & Sons, Hoboken, New Jersey, 6th editionGoogle Scholar
  27. Kang, D.-H., Lorente, S., Bejan, A. (2010): Constructal architecture for heating a stream by convection. International Journal of Heat and Mass Transfer, 53: 2248–2255zbMATHCrossRefGoogle Scholar
  28. Knoop, P., van Nerom, L. (2003): Scheduling requirements for hot charge optimization in an integrated steel plant. Proceedings of the 2003 IEEE Industry Applications Conference, 38th IAS Annual Meeting, Salt Lake City, Utah, USA, 1: 74–78Google Scholar
  29. Ko, H., Kim, J., Yoon, T., Lim, M., Yang, D., Jun, I. (2000): Modeling and predictive control of a reheating furnace. Proceedings of the American Control Conference, Chicago, Illinois, USA, 4: 2725–2729Google Scholar
  30. Leden, B. (1986): A control system for fuel optimization of reheating furnaces. Scandinavian Journal of Metallurgy, 15: 16–24Google Scholar
  31. Lee, E., Markus, L. (1967): Foundations of optimal control theory. The SIAM Series in Applied Mathematics. John Wiley & Sons, New YorkGoogle Scholar
  32. Leifgen, U., Ganesaratnam, S., Croce, L. (2011): A new concept for the control of reheating furnaces for slabs. Proceedings of the 1st International Conference on Energy Efficiency and CO2 Reduction in the Steel Industry, EECR STEEL, Düsseldorf, GermanyGoogle Scholar
  33. Modest, M. (2003): Radiative Heat Transfer. Academic Press, New York, 2nd editionGoogle Scholar
  34. Nederkoorn, E., Wilgen, P., Schuurmans, J. (2011): Nonlinear model predictive control of walking beam furnaces. Proceedings of the 1st International Conference on Energy Efficiency and CO2 Reduction in the Steel Industry, EECR STEEL, Düsseldorf, GermanyGoogle Scholar
  35. Nocedal, J., Wright, S. (2006): Numerical Optimization. Springer Series in Operations Research. Springer, New York, 2nd editionGoogle Scholar
  36. Pedersen, L., Wittenmark, B. (1998): On the reheat furnace control problem. Proceedings of the American Control Conference, Philadelphia, Pennsylvania, USA, S. 3811–3815Google Scholar
  37. Rawlings, J., Mayne, D. (2009): Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison, WisconsinGoogle Scholar
  38. Rixin, L., Baolin, N. (1992): Mathematical model for dynamic operation and optimum control of pusher type slab reheating furnace. Industrial Heating, 59 (3): 60–62Google Scholar
  39. Sibarani, H., Samyudia, Y. (2004): Robust nonlinear slab temperature control design for an industrial reheating furnace. Computer Aided Chemical Engineering, 18: 811–816CrossRefGoogle Scholar
  40. Speyer, J., Jacobson, D. (2010): Primer on Optimal Control Theory. Advances in Design and Control. Siam, PhiladelphiaGoogle Scholar
  41. Staalman, D. (2004): The funnel model for accurate slab temperature in reheating furnaces. La Revue de Métallurgie, 101 (7): 453–459CrossRefGoogle Scholar
  42. Steinboeck, A., Graichen, K., Kugi, A. (2011a): Dynamic optimization of a slab reheating furnace with consistent approximation of control variables. IEEE Transactions on Control Systems Technology, 16 (6): 1444–1456CrossRefGoogle Scholar
  43. Steinboeck, A., Graichen, K., Wild, D., Kiefer, T., Kugi, A. (2011b): Model-based trajectory planning, optimization, and open-loop control of a continuous slab reheating furnace. Journal of Process Control, 21 (2): 279–292CrossRefGoogle Scholar
  44. Steinboeck, A., Wild, D., Kiefer, T., Kugi, A. (2010): A mathematical model of a slab reheating furnace with radiative heat transfer and non-participating gaseous media. International Journal of Heat and Mass Transfer, 53: 5933–5946zbMATHCrossRefGoogle Scholar
  45. Steinboeck, A., Wild, D., Kiefer, T., Kugi, A. (2011c). A fast simulation method for 1D heat conduction. Mathematics and Computers in Simulation, 82 (3): 392–403CrossRefGoogle Scholar
  46. Steinboeck, A., Wild, D., Kugi, A. (2011d). Feedback tracking control of continuous reheating furnaces. Proceedings of the 18th World Congress of the International Federation of Automatic Control (IFAC), Milan, Italy, S. 11744–11749Google Scholar
  47. Stengel, R. (1994): Optimal Control and Estimation. Dover Publications, New YorkGoogle Scholar
  48. Stoer, J., Bulirsch, R. (2002): Introduction to numerical analysis. Number 12 in Texts in Applied Mathematics. Springer, New York, Berlin, 3rd editionGoogle Scholar
  49. Vode, F., Jaklič, A., Kokalj, T., Matko, D. (2008): A furnace control system for tracing reference reheating curves. Steel Research International, Metal Forming, 79 (5): 364–370Google Scholar
  50. Wang, P. (1993): Optimierung der Brennstoffverteilung in Durchlauföfen. PhD thesis, Technische Universität Clausthal, Clausthal, GermanyGoogle Scholar
  51. Wang, Z., Chai, T., Guan, S., Shao, C. (1999): Hybrid optimization setpoint strategy for slab reheating furance temperature. Proceedings of the American Control Conference, San Diego, California, USA, S. 4082–4086Google Scholar
  52. Wang, Z., Wu, Q., Chai, T. (2004): Optimal-setting control for complicated industrial processes and its application study. Control Engineering Practice, 12: 65–74CrossRefGoogle Scholar
  53. Wild, D. (2010): Modellierung und Beobachterentwurf für einen Stoßofen. PhD thesis, Vienna University of Technology, Austria, Shaker Verlag, Aachen, GermanyGoogle Scholar
  54. Wild, D., Meurer, T., Kugi, A. (2009a): Modelling and experimental model validation for a pusher-type reheating furnace. Mathematical and Computer Modelling of Dynamical Systems, 15 (3): 209–232zbMATHCrossRefGoogle Scholar
  55. Wild, D., Meurer, T., Kugi, A., Eberwein, K., Bödefeld, B., Bott, M. (2009b): Entwurf eines nichtlinearen Zustandsschätzers für einen Stoßofen. Stahl und Eisen, 129 (1): 45–50Google Scholar
  56. Wild, D., Meurer, T., Kugi, A., Fichet, O., Eberwein, K. (2007): Nonlinear observer design for pusher-type reheating furnaces. Proceedings of the 3rd International Steel Conference on New Developments in Metallurgical Process Technologies, Düsseldorf, Germany, S. 790–797Google Scholar
  57. Wills, A., Heath, W. (2003): An exterior/interior-point approach to infeasibility in model predictive control. Proceedings of the 42th IEEE Conference on Decision and Control, Maui, Hawaii, USA, S. 3701–3705Google Scholar
  58. Yang, Y., Lu, Y. (1988): Dynamic model based optimization control for reheating furnaces. Computers in Industry, 10: 11–20zbMATHCrossRefGoogle Scholar
  59. Yoshitani, N., Ueyama, T., Usui, M. (1994): Optimal slab heating control with temperature trajectory optimization. Proceedings of the 20th International Conference on Industrial Electronics, Control and Instrumentation, IECON'94, Bologna, Italy, 3: 1567–1572Google Scholar
  60. Zhang, B., Chen, Z., Xu, L., Wang, J., Zhang, J., Shao, H. (2002): The modeling and control of a reheating furnace. Proceedings of the American Control Conference, Anchorage, Alaska, USA, S. 3823–3828Google Scholar
  61. Zhang, B., Xu, L., Wang, J., Shao, H. (2001): Optimization of combustion control based on fuzzy logic. Proceedings of the 10th IEEE International Conference on Fuzzy Systems, Melbourne, Australia, S. 1080–1083Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • A. Steinböck
    • 1
  • A. Kugi
    • 1
  1. 1.Institut für Automatisierungs- und RegelungstechnikTechnische Universität WienWienAustria

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