### Abstract

An optimal control approach for minimizing metallurgical length deviation during casting speed increase under constraints on the secondary cooling flow rates for continuous steel casting process is proposed. The process is described as a single-phase Stefan problem. The temperature and the shell growth are controlled by the steel surface heat flux generated by the cooling sprays. A cost function reflecting the error in tracking of a reference shell thickness is chosen, and the control objective is formulated as the minimization of this cost function under the spray rate constraints. Finding the control law satisfying this objective is formulated as a two-step procedure. First, an analytical setting for the cost function minimization is established through deriving the corresponding direct, adjoint, and sensitivity systems. Then, a computational procedure for solving this analytical setting, which finds the actual control law, is given. A numerical example presents the application of the method proposed. The results are then extended to a 2D model, with the corresponding numerical example provided.

Original language | English (US) |
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Title of host publication | 2019 American Control Conference, ACC 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 3206-3211 |

Number of pages | 6 |

ISBN (Electronic) | 9781538679265 |

State | Published - Jul 2019 |

Event | 2019 American Control Conference, ACC 2019 - Philadelphia, United States Duration: Jul 10 2019 → Jul 12 2019 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2019-July |

ISSN (Print) | 0743-1619 |

### Conference

Conference | 2019 American Control Conference, ACC 2019 |
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Country | United States |

City | Philadelphia |

Period | 7/10/19 → 7/12/19 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*2019 American Control Conference, ACC 2019*(pp. 3206-3211). [8815355] (Proceedings of the American Control Conference; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc..

**Optimal control of free boundary of a stefan problem for metallurgical length maintenance in continuous steel casting.** / Chen, Zhelin; Bentsman, Joseph; Thomas, Brian G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2019 American Control Conference, ACC 2019.*, 8815355, Proceedings of the American Control Conference, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 3206-3211, 2019 American Control Conference, ACC 2019, Philadelphia, United States, 7/10/19.

}

TY - GEN

T1 - Optimal control of free boundary of a stefan problem for metallurgical length maintenance in continuous steel casting

AU - Chen, Zhelin

AU - Bentsman, Joseph

AU - Thomas, Brian G.

PY - 2019/7

Y1 - 2019/7

N2 - An optimal control approach for minimizing metallurgical length deviation during casting speed increase under constraints on the secondary cooling flow rates for continuous steel casting process is proposed. The process is described as a single-phase Stefan problem. The temperature and the shell growth are controlled by the steel surface heat flux generated by the cooling sprays. A cost function reflecting the error in tracking of a reference shell thickness is chosen, and the control objective is formulated as the minimization of this cost function under the spray rate constraints. Finding the control law satisfying this objective is formulated as a two-step procedure. First, an analytical setting for the cost function minimization is established through deriving the corresponding direct, adjoint, and sensitivity systems. Then, a computational procedure for solving this analytical setting, which finds the actual control law, is given. A numerical example presents the application of the method proposed. The results are then extended to a 2D model, with the corresponding numerical example provided.

AB - An optimal control approach for minimizing metallurgical length deviation during casting speed increase under constraints on the secondary cooling flow rates for continuous steel casting process is proposed. The process is described as a single-phase Stefan problem. The temperature and the shell growth are controlled by the steel surface heat flux generated by the cooling sprays. A cost function reflecting the error in tracking of a reference shell thickness is chosen, and the control objective is formulated as the minimization of this cost function under the spray rate constraints. Finding the control law satisfying this objective is formulated as a two-step procedure. First, an analytical setting for the cost function minimization is established through deriving the corresponding direct, adjoint, and sensitivity systems. Then, a computational procedure for solving this analytical setting, which finds the actual control law, is given. A numerical example presents the application of the method proposed. The results are then extended to a 2D model, with the corresponding numerical example provided.

UR - http://www.scopus.com/inward/record.url?scp=85072277608&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072277608&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85072277608

T3 - Proceedings of the American Control Conference

SP - 3206

EP - 3211

BT - 2019 American Control Conference, ACC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

ER -