Optimal Control of Induction Heating: Theory and Application

  • Darya Filatova
  • Marek Grzywaczewski
Part of the Mathematical Engineering book series (MATHENGIN, volume 3)


The theoretic background of an optimal control task for a precision induction heating problem is studied in this work. The basics of electro-magnetic and heat transfer theory are used to describe the dynamics of induction heating processes of rectangle workpieces. The main result of this work, presented as the first-order necessary conditions for the optimal solution of the considered control task, allows one to employ interval representations of the mathematical model’s main parameters in order to study the influence of environment uncertainties which have dominant effects on induction heating processes.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Butkovskii, A.G.,Malyi, S.A., Andreev, Ju.N.: Optimal control of heating metals. Metallurgia, Moscow (1972).Google Scholar
  2. 2.
    Butkovskii, A.G.: Structural theory of distributed systems. Nauka, Moscow (1997).Google Scholar
  3. 3.
    Dicoussar, V.V., Filatova, D.V., Grzywaczewski, M., W´ojtowicz, M.: Optimal Control Coupled Fields in the Process of Induction Heating (Control Applications of Optimization 2003). Elsevier, Amsterdam (2003)Google Scholar
  4. 4.
    Favennec, Y., Rouizi, Y., Petit, D.: On the use of reduced models obtained through identification for feedback optimal control problems in a heat convection-diffusion problem. Comput. Methods Appl. Mech. Engrg 199, 1193 – 1201 (2010)CrossRefGoogle Scholar
  5. 5.
    Huang, M.-Sh., Huang, Y.-L.: Effect of multi-layered induction coils on efficiency and uniformity of surface heating. International Jounal of Heat and Mass Transfer 53, 2414 – 2423 (2010)CrossRefGoogle Scholar
  6. 6.
    Jang, J.-Y., Chiu, Y.W.: Numerical and experimental thermal analysis for a metalic hollow cylinder subjected to step-wise electro-magnitic induction heating. Applied Thermal Engineering 27, 1883–1894 (2007)CrossRefGoogle Scholar
  7. 7.
    Jiang, H., Nguyen, T.H., Prud’homme, M.: Optimal control of induction heating for semi-solid aluminum alloy forming. Journal of Materials Processing Technology 189, 182 – 191 (2007)Google Scholar
  8. 8.
    Kantorovich, L.V., Akilov, G.P.: Functional analysis. Nauka, Moscow (1984)MATHGoogle Scholar
  9. 9.
    Kranjc, M., Zupanic, A.,Miklavic, D., Jarm, T.: Numerical analysis and thermographic investigation of induction heating. International Journal of Heat and Mass Transfer 53, 3585–3591 (2010)MATHCrossRefGoogle Scholar
  10. 10.
    Milyutin, A.A., Osmolovskii, N.P.: Calculus of Variations and Optimal Control, Translations ofMathematical Monographs, volume 180, American Mathematical Society, Providence (1998)Google Scholar
  11. 11.
    Milyutin, A.A., Dmitruk, A.V., Osmolovskii, N.P.: Maximum Principle in Optimal Control. Moscow State University, Moscow (2004)Google Scholar
  12. 12.
    Okman, O., Dursunkaya, Z., Tekkaya, A.E.: Generalized transient temperature behavior in induction heated workpieces. Journal of Materials Processing Technology 209, 5932–5939 (2009)CrossRefGoogle Scholar
  13. 13.
    Padhi, R., Ali, S.F.: An account of chronological developments in control of distributed parameter systems. Annual Reviews in Control 33, 59–68 (2009).CrossRefGoogle Scholar
  14. 14.
    Rapoport, E.: Alternance method in applied tasks of optimization. Nauka, Moscow (2000)Google Scholar
  15. 15.
    Rapoport, E., Pleshivtseva, Yu.: Optimal Control of Induction Heating Processes, CRC Pr I Llc, Boston (2006)Google Scholar
  16. 16.
    Rapoport, E., Pleshivtseva, Yu.E.: Algorithmically precise method of parametric optimization in boundary-value optimal control problems for distributed-parameter systems. Optoelectronocs, Instruments and Data Processing 45 (5), 464 – 471 (2009)CrossRefGoogle Scholar
  17. 17.
    Tslaf, A.: Combined properties of conductors and calculation of thermal processes in electrical and heat engineering. Elsevier, Boston (1981)Google Scholar
  18. 18.
    Zimin, L.S.: Heating peculiarities of rectangle bodies. Mashynostroyenie, Leningrad (1973)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.UJKKielcePoland
  2. 2.Analytical Centre of Russian Academy of SciencesMoscowRussia
  3. 3.Politechnika RadomskaRadomPoland

Personalised recommendations