OPTIMAL CONTROL OF THE CYLINDRICAL HEATING PROCESS BASED ON A 1-D ELECTROMAGNETIC–THERMAL MODEL
Keywords
DOI:
https://doi.org/10.34238/tnu-jst.14040Abstract
This paper proposes and implements an optimal control method for the inductor frequency to achieve rapid and uniform heating of a cylindrical workpiece. Based on a 1-D radial electromagnetic–thermal model, the optimization problem is formulated as pointwise computations and solved using fmincon with constraints that ensure the surface temperature precisely reaches the prescribed value within the allotted time, while maintaining the thermal gradient between core and surface below the allowable limit. The results show that the initial frequency increases with the target temperature and then decreases over time to prevent overheating; the uniform distribution of confirms the effectiveness of the optimal solution, and the smooth trajectory of demonstrates practical feasibility. This study lays the groundwork for extending the model to 2-D (r–z) to account for axial heat conduction and end-boundary conditions, as well as for developing multi-parameter control laws for applications in additive manufacturing, semiconductor heat treatment, and composite materials.Downloads
References
S. Midson and K. Brissing, “Semi-solid casting of aluminum alloys: a status report,” Mod. Cast., vol. 87, pp. 41–43, 1997.
S. Midson,V. Rudnev, and R. Gallik, “Semi-solid processing of aluminumalloys,” Ind. Heat., vol. 1, pp. 37–41, 1999.
H. K. Jung and C. G. Kang, “Induction heating process of an Al–Si aluminum alloy for semi-solid die casting and its resulting microstructure,” J. Mater. Process. Technol., vol. 120, pp. 355–364, 2002.
Y. Ono, C. Q. Zheng, F.G. Hamel, R. Charron, and C. A. Loong, “Experimental investigation on monitoring and control of induction heating process for semi-solid alloys using the heating coil as sensor,” Meas. Sci. Technol., vol.13, pp. 1359–1365, 2002.
D.-C. Ko, G.-S. Min, B.-M. Kim, and J.-C. Choi, “Finite element analysis for the semi-solid state forming of aluminum alloy considering induction heating,” J. Mater. Process. Technol., vol. 100, pp. 95–104, 2000.
M. C. Flemings, “Behavior of metal alloys in the semi-solid state,” Metall. Trans. A, vol. 22, pp. 957–981, 1991.
K.T. Nguyen and A. Bendada, “An inverse approach for the prediction of the temperature evolution during induction heating of a semi-solid casting billet,” Modell. Simul. Mater. Sci. Eng., vol. 8, pp. 857–870, 2000.
S. Midson, V. Rudnev, and R. Gallik, “The induction heating of semi-solid aluminum alloys,” in: Proceedings of the Fifth International Conference on Semi-Solid Processing of Alloys and Composites, Golden, CO, 1998, pp. 497–504.
A. Bendada, K. T. Nguyen, and C. A. Loong, “Application of infrared imaging in optimizing the induction heating of semi-solid aluminum alloys,” in Proceedings of the International Symposium on Advanced Sensors for Metals Processing, Quebec, 1999, pp. 331–342.
P. Kapranos, R.C. Gibson, D. H. Kirkwood, and C. M. Sellars, “Induction heating and partialmelting of highmelting point thixoformable alloys,” in Proceedings of the Fourth International Conference on Semi-Solid Processing of Alloys and Composites, Sheffield, 1996, pp. 148–152.
A. G. Butkovskii and A. Y. Lerner, “The optimal control systemswith distributed parameter,” Auto. Remote Control, vol. 21, pp. 472–477, 1960.
Y. Sakawa, “Solution of an optimal control problem in a distributed parameter system,” IEEE Trans. Auto. Contr., vol. 9, pp. 420–426, 1964.
Y. Sakawa, “Optimal control of a certain type of linear distributed-parameter system,” IEEE Trans. Auto. Contr., vol.11, pp. 35–41, 1966.
R. K. Cavin and S. C. Tandon, “Distributed parameter system optimum con- trol design via finite element discretization,” Automatica, vol. 13, pp. 611–614, 1977.
R. A. Meric, “Finite element analysis of optimal heating of a slab with temperature dependent thermal conductivity,” Int. J. Heat Mass Transfer, vol. 22, pp. 1347–1353, 1979.
R. A. Meric, “Finite element and conjugate gradient methods for a nonlinear optimal heat transfer control problem,” Int. J. Numer. Methods Eng., vol. 14, pp. 1851–1863, 1979.
C. T. Kelley and E. W. Sachs, “A trust region method for parabolic boundary control problems,” SIAM J. Optimization, vol. 9, pp. 1064–1081, 1999.
C. H. Huang, “A nonlinear optimal control problem in determining the strength of the optimal boundary heat fluxes,” Numer. Heat Transfer Part B, vol. 40, pp. 411–429, 2001.
C. H. Huang and C. Y. Li, “A three-dimensional optimal control problemin determining the boundary control heat fluxes,” Heat Mass Transfer, vol. 39, pp. 589–598, 2003.
C. J. Chen and M. N. Ozisik, “Optimal heating of a slabwith a plane heat source of timewise varying strength,” Numer. Heat Transfer Part A, vol. 21, pp. 351–361, 1992.
X. Cui et al., “Analysis and optimization of induction heating processes,” Applied Energy, vol. 321, pp.1-10, 2022.
P. Garois et al., “Data-Driven Inverse Problem for Optimizing Double-Frequency Induction Heating,” Metals, vol.13, pp. 1-15, 2023.
M. Zarghoon et al., “Full-state feedback LQR with integral gain for control of induction heating of steel billet,” Engineering Science and Technology, an International Journal, vol. 55, pp. 1-14, 2024.
B. Heinrich, “Efficient induction heating frequency analysis,” Master Thesis, Technische Universitat Wien, Mat.No. 11826363, 2023.
V. I. Lusgin et al., “Energy-efficient installations of multi-zone multi-frequency induction heating of steel billets for large deformation,” IOP Conf. Series: Materials Science and Engineering, vol. 950, pp.1-11, 2020.
H. Ghafoorinejad et al., “Cascade deep learning approach for design and control optimization of a dual-frequency induction heating device,” Energies, vol. 18, pp.1-19, 2025.
