DVA MATEMATICKÉ PŘÍSTUPY PRO OPTIMÁLNÍ ŘÍZENÍ PLYNULÉHO ODLÉVÁNÍ BRAM

TWO MATHEMATICAL APPROACHES FOR OPTIMAL CONTROL OF THE CONTINUOUS SLAB CASTING PROCESS

článek ve sborníku ve WoS nebo Scopus

en

This paper deals with two suitable mathematical approaches to optimization of a continuous casting process control. The first approach is based on a nonlinear mathematical programming model, while the second one represents a black-box type solution. The aim of optimization and control of the steel slabs production is to achieve both the maximum possible savings and product quality. The continuous casting process is described by a two-dimensional mathematical model, containing a Fourier-Kirchhoff equation together with boundary conditions. From a material perspective, presence of phase and structural changes is modeled by an enthalpy approach, where the relationship between enthalpy and temperature is fitted by a suitable curve. The sought-for control parameters represent the output of the optimization models. Software implementation for mathematical programming approach was executed as a link between MATLAB and modeling language GAMS. For the black-box solution, a callable C library was created which simulates the casting process, and which is called by the black-box solver NOMAD. Final results from both approaches are compared and discussed.

Tento článek se zabývá dvěma použitelnými matematickými přístupy pro optimalizaci řízení plynulého odlévání oceli. První přístup je založen na nelineárním matematickém programování, zatím co druhý na přístupu black-box. Optimalizačním kritériem je maximalizování produktivity a finální kvality. Hlavní zaměření je na řízení vodních ostřiků v sekundární chladící zóny. Proces je popsán 2D Fourier-Kirchhoffovou rovnicí včetně okrajových podmínek. Softwarová implementace prvního přístupu je řešena pomocí propojení programu Matlab a modelovacího jazyka GAMS. Pro black-box přístup byl vytvořen model v programovacím jazyku C, kde byl použit řešič NOMAD. Výsledky obou přístupů jsou v článku porovnány.

This paper deals with two suitable mathematical approaches to optimization of a continuous casting process control. The first approach is based on a nonlinear mathematical programming model, while the second one represents a black-box type solution. The aim of optimization and control of the steel slabs production is to achieve both the maximum possible savings and product quality. The continuous casting process is described by a two-dimensional mathematical model, containing a Fourier-Kirchhoff equation together with boundary conditions. From a material perspective, presence of phase and structural changes is modeled by an enthalpy approach, where the relationship between enthalpy and temperature is fitted by a suitable curve. The sought-for control parameters represent the output of the optimization models. Software implementation for mathematical programming approach was executed as a link between MATLAB and modeling language GAMS. For the black-box solution, a callable C library was created which simulates the casting process, and which is called by the black-box solver NOMAD. Final results from both approaches are compared and discussed.

Nonlinear optimization, mathematical programming, black-box, temperature field

2010

23.06.2010

Brno University of Technology

Brno

978-80-214-4120-0

Mendel 2010 - 16th International Conference on Soft Computing

395–400

6