# An Improved Dynamic Model of the Vanadium Extraction Process in Steelmaking Converters
## 1 Introduction  
Many researchers have studied mathematical models of the steelmaking process, aiming to predict and automatically control the complicated steelmaking process using computers. An appropriate mathematical model can help us understand the essence of the steelmaking process and improve the techniques used; this is the foundation of automatic control in the steelmaking process. China is one of the main countries which produces steel through vanadium extraction [1]. The Panzhihua Iron and Steel Group (PISG), located in the Sichuan Province, is one of the most important steel industry bases in China. The region is rich in vanadium-titanium magnetite, whose vanadium content accounts for 61% of the proven reserves in China [2]. The industrial uses of vanadium-titanium magnetite mainly includes vanadium extraction and steelmaking. At first, vanadium is extracted from the vanadium-containing molten steel in a converter, following which the resultant semi-steel is smelted to steel. Currently, the vanadium extraction process still depends on manual operation and control of the production relies on the experience of operators. Therefore, it is important to establish mathematical models to predict the changes of composition in molten steel and slag. There have been many studies focused on mathematical models of the steelmaking process. [PERSON] et al. [3] studied the converter steelmaking process from thermodynamic and kinetic standpoints, obtained the reaction trend when the process was regarded at thermodynamic equilibrium, and compared it with the actual process. [PERSON] et al. [4] proposed a mathematical model that can be applied to an automatic blowing process and gave an estimate of the content of some components in the molten steel by sampling analysis of the blowing process. [PERSON] and [PERSON] [5] established a mathematical model of the AOD (Argon Oxygen Decarburization) and VOD (Vacuum Oxygen Decarburization) refining processes. According to their model, in the case of high carbon, the decarburization rate is proportional to the oxygen supply rate; while, in the case of low carbon, the decarburization rate is related to both the carbon content and oxygen supply rate. [PERSON] et al. [6] established a non-linear model to consider the estimation of carbon content in the process of steelmaking and proved that the error is locally asymptotically stable. [PERSON] et al. [7] developed a general dynamic system simulator as a tool to analyze dynamic systems, represented by differential equations, difference equations, and algebraic equations. [PERSON] et al. [8] proposed an endpoint prediction model based on correlation vector machines to predict the carbon content and temperature of an oxygen converter. [PERSON] [9] put forward some hypotheses on the oxidation mechanisms of C and Cr under different conditions and developed a reaction model to predict the oxidation rates of C and Cr in the AOD process. [PERSON] and [PERSON] [10,11] proposed a mathematical model for stainless steel refining and validated the model with data obtained from a 45-ton converter producing 304 stainless steel. [PERSON] and [PERSON] [12,13] put forward a mathematical model of the stainless steel decarbonizing process, based on the mass and heat balance of the system. [PERSON] et al. [14] obtained a multiple linear regression model to predict the oxygen blowing quantity by analyzing the factors that affect oxygen consumption during the basic oxygen furnace steelmaking process. The Nippon steel corporation [15] has developed an expert system for converter steelmaking. [PERSON] et al. [16] established a prediction model and control model based on a neural network by analyzing BOF steelmaking characteristics. [PERSON] and [PERSON] [17,18] believed that the distribution ratio of oxygen which is blown to the molten pool across various elements is proportional to its Gibbs free energy of reaction. However, few studies have focused on mathematical models of vanadium extraction. [PERSON] et al.