Numerical solution to the optimal feedback control of continuous casting process

Guo, Bao‐Zhu; Sun, Bing

doi:10.1007/s10898-006-9130-0

Cited by 14 publications

(7 citation statements)

References 19 publications

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“…A model optimization of billet continuous casting steel secondary cooling with an implicit enthalpy mathematical solidification was developed to calculate three dimensional and stationary temperature fields and to decrease center segregation [6]. An approach based on Hamilton-Jacobi-Bellman equation satisfying the value function has been used to the optimal problem of the SCZ with water spray control of a low-carbon billet caster [7]. Chakraborti et al solved the pertinent transport equations in the mold of continuous caster using a finite volume approach with genetic algorithms.…”

Section: Introductionmentioning

confidence: 99%

The optimisation of the secondary cooling water distribution with improved genetic algorithm in continuous casting of steels

Zhai

et al. 2015

Materials Research Innovations

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An improved genetic algorithm is presented for the water consumption of the secondary cooling zone based on the heat transfer model of the off-line bloom caster. This study is to control the existing cooling systems and the steel casting practises in order to produce steel with best possible quality. The fitness function of improved genetic algorithm is founded according to the metallurgical criteria. This algorithm coupled with heat transfer model and metallurgical criteria, added dynamic coding method and self-adapting mutation on the original genetic algorithm can increase water distribution adaptively and improve the process efficiency. The simulation results of T91 bloom show that the optimised distribution reduced by 2% of water consumption comparing to that of before optimisation. The maximum surface cooling rate and the rate of temperature rise reduced, and the equiaxed rate increases. The function is built for explaining the relationship between the casting speed and water distribution. Statement of noveltyIn this paper, an improved genetic algorithm is designed for the water consumption of the secondary cooling zone based on the heat transfer model of the off-line bloom caster. This algorithm coupled with heat transfer model and metallurgical criteria, added dynamic coding method and self-adapting mutation on the original genetic algorithm, can increase the simulated water distribution adaptively, improve the efficiency of the simulation process and the convergence ratio, and reduce the reheating between the zones. In the experimental, it is found that the water consumption after optimization reduced by 2%, compared to that of before optimization. The maximum surface cooling rate and the rate of temperature rise reduced, and the equiaxed rate increases. Then a function is built for explaining the relationship between casting speed and water distribution, which can be the direction to control the cooling system in manufacturing process. So far, to our knowledge, although a lot of intelligent algorithms are used to optimize the secondary cooling conditions, but there are few reports on the simulation of this process with the developed algorithms. In this study, the improved genetic algorithm to optimize the secondary cooling water distribution is concerned, and the results show that the developed algorithm can save more water consumption with lower reheating and cooling rates. AbstractAn improved genetic algorithm is presented for the water consumption of the secondary cooling zone based on the heat transfer model of the off-line bloom caster. This study is to control the existing cooling system and the steel casting practice in order to produce steel with best possible quality. The fitness function of IGA (improved genetic algorithm) is founded according to the metallurgical criteria. This algorithm coupled with heat transfer model and metallurgical criteria, added dynamic coding method and self-adapting mutation on the original genetic algorithm, can increase water distribution adaptively and...

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Section: Introductionmentioning

confidence: 99%

The optimisation of the secondary cooling water distribution with improved genetic algorithm in continuous casting of steels

Zhai

et al. 2015

Materials Research Innovations

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“…This strategy will present a bright foreground. At the same time, multi‐objective optimization 12, 13, minimization of cost function 14–18, neural networks 19, artificial intelligence 20–22, and ant colony optimization 23 etc., are used to control and optimize the secondary cooling process.…”

Section: Introductionmentioning

confidence: 99%

Compensation Control Model of Superheat and Cooling Water Temperature for Secondary Cooling of Continuous Casting

Zhang

Chen

Wang

et al. 2010

steel research int.

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In this paper, a compensation control model of secondary cooling process of billet continuous casting for quality steel has been presented. The effects on the spray control of the various parameters such as steel superheat, casting speed, cooling water temperature and chemical component of steel were considered. The parameters of control model were determined to associate with the two‐dimensional heat transfer equation and solved by finite‐difference method. Effects of steel superheat and cooling water temperature on surface temperature, solidification structure and solidifying end point were discussed. Results indicate that steel superheat significantly affects solidification structure and solidifying end point but has a little effect on slab surface temperature. Moreover, secondary cooling water temperature affects surface temperature and solidifying end point but has a little effect on solidification structure. The surface temperature and solidifying end point can be maintain stabilized through applying the compensation control model when steel superheat and cooling water temperature vary. The models have been validated by industrial measurements. The results show that the simulations are in very good agreement with the real casting situation.

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“…It makes some effective algorithms for low dimensional problems, thus initially confined to only "toy" problems, can be generalized to deal with much more complicated practical optimal control problems. The upwind finite-difference scheme is such a well-adapted algorithm and has been successfully applied to many examples ( [13,14,15]). And most of all, its convergence has been rigorously proven in [28].…”

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confidence: 99%

A feedback design for numerical solution to optimal control problems based on Hamilton-Jacobi-Bellman equation

Tao

Sun

2021

era

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In this paper, we present a feedback design for numerical solution to optimal control problems, which is based on solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. An upwind finite-difference scheme is adopted to solve the HJB equation under the framework of the dynamic programming viscosity solution (DPVS) approach. Different from the usual existing algorithms, the numerical control function is interpolated in turn to gain the approximation of optimal feedback control-trajectory pair. Five simulations are executed and both of them, without exception, output the accurate numerical results. The design can avoid solving the HJB equation repeatedly, thus efficaciously promote the computation efficiency and save memory.

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Numerical solution to the optimal feedback control of continuous casting process

Cited by 14 publications

References 19 publications

The optimisation of the secondary cooling water distribution with improved genetic algorithm in continuous casting of steels

The optimisation of the secondary cooling water distribution with improved genetic algorithm in continuous casting of steels

Compensation Control Model of Superheat and Cooling Water Temperature for Secondary Cooling of Continuous Casting

A feedback design for numerical solution to optimal control problems based on Hamilton-Jacobi-Bellman equation

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