Abstract
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.
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References
Butkovskii, A.G.,Malyi, S.A., Andreev, Ju.N.: Optimal control of heating metals. Metallurgia, Moscow (1972).
Butkovskii, A.G.: Structural theory of distributed systems. Nauka, Moscow (1997).
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)
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)
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)
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)
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)
Kantorovich, L.V., Akilov, G.P.: Functional analysis. Nauka, Moscow (1984)
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)
Milyutin, A.A., Osmolovskii, N.P.: Calculus of Variations and Optimal Control, Translations ofMathematical Monographs, volume 180, American Mathematical Society, Providence (1998)
Milyutin, A.A., Dmitruk, A.V., Osmolovskii, N.P.: Maximum Principle in Optimal Control. Moscow State University, Moscow (2004)
Okman, O., Dursunkaya, Z., Tekkaya, A.E.: Generalized transient temperature behavior in induction heated workpieces. Journal of Materials Processing Technology 209, 5932–5939 (2009)
Padhi, R., Ali, S.F.: An account of chronological developments in control of distributed parameter systems. Annual Reviews in Control 33, 59–68 (2009).
Rapoport, E.: Alternance method in applied tasks of optimization. Nauka, Moscow (2000)
Rapoport, E., Pleshivtseva, Yu.: Optimal Control of Induction Heating Processes, CRC Pr I Llc, Boston (2006)
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)
Tslaf, A.: Combined properties of conductors and calculation of thermal processes in electrical and heat engineering. Elsevier, Boston (1981)
Zimin, L.S.: Heating peculiarities of rectangle bodies. Mashynostroyenie, Leningrad (1973)
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Filatova, D., Grzywaczewski, M. (2011). Optimal Control of Induction Heating: Theory and Application. In: Rauh, A., Auer, E. (eds) Modeling, Design, and Simulation of Systems with Uncertainties. Mathematical Engineering, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15956-5_8
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DOI: https://doi.org/10.1007/978-3-642-15956-5_8
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