Fractional order control model of steel casting process

Abstract

A control model of the steel casting process will be proposed using fractional order differential equations (FDE) and the orthogonal distance fitting (ODF). These two mathematical approaches will be used for creating a relationship between the speed of steel casting and the measured temperature of the steel strand in a critical place of the continuous steel casting machine. To obtain the required physical properties of the slab of individual sort of casted steel, a given interval of temperature should be reached in concrete parts of the steel strand. The proposed control model uses the speed of steel casting as the primary parameter (control parameter) influencing the temperature of steel in a critical place of the continuous steel casting machine (controlled parameter). This way we neglect the influence of other parameters, which are dependent on the steel casting speed anyway. A system of two fractional order differential equations is considered to describe the relation between the steel casting speed and the measured temperature. Experimental data containing information about the casting speed and the temperature of the strand are taken and an approximation (defined by optimal parameters) is sought. To find parameters of the proposed control model, the orthogonal distance fitting is used in the formulation of the fitting criterion. With the help of the created control model, it is possible to set the value of the steel casting speed based on the casted sort of the steel, to keep the measured temperature in the corresponding interval.