## 1 Introduction
### Understanding of Steelmaking in LD Converter  
This process is referred to as LD, BOF, BOP (i.e., basic oxygen process), or BOS (basic oxygen steelmaking) in various places, but they all denote top-blown converter steelmaking [40,41]. The BOF process involves melting liquid iron steel in a base-lined LD converter by blowing oxygen through a water-cooled lance. The oxygen converter is a pear-shaped vessel of sheet steel lined with a main brick into which molten iron from a blast furnace is poured [42]. The typical capacities of oxygen converters are in the range of 50-350 t. The converter can be rotated 360\({}^{\circ}\) on pins around the horizontal axis for scrap metal loading, melt casting, steel, and debris removal during operation. The batch melting usually takes 15 to 25 min regardless of the size of the melt. The flow of the blown oxygen to the melt through the lance is also adjusted according to the weight of the batch [43]. By blowing oxygen at supersonic speed, the oxidation of impurities in the pig iron is accelerated, and the metal surface area increases. A multi-hole copper nozzle blows oxygen into the melt at a pressure of 1.6-2.8 MPa. Scrap metal is added to the LD converter at the beginning of the melting. Iron ore is added while blowing to oxidize silicon phosphorus, manganese, and carbon, but these exothermic reactions do not cause the melt temperature to rise. In addition, lime and sometimes other slag-forming agents are added to the melt during blowing to form a slag that retains impurities in the form of complex oxides. The converter slag is formed as a waste product after smelting the pig iron. Lime is used as a slag-forming additive in the melt. Crude magnesite is used to increase the MgO content in the converter slag. The magnesite is also used to cool the steel in the converter and to treat the converter liner before the end of the melt blowing. Crystalline solid sulfur is used for alloying selected steels. The tapping of the steel is usually carried out when the temperature reaches 1620-1660 \({}^{\circ}\)C and the carbon concentration is 0.03-0.04% (i.e., in low-carbon steels). Due to the high temperatures in the converter (e.g., at the melting endpoint up to 1700 \({}^{\circ}\)C), it is problematic to measure these process variables with conventional devices (e.g., thermocouples). In practice, various approaches are used to measure melt temperature and carbon content, e.g., sublance and drop probes, bomb-method, or waste gas analysis [44]. In the literature, only a few examples of the dynamic behavior of temperature and carbon obtained during decarbonization can be found (e.g., [3,45,46]). These time behaviors are usually obtained from models or a small number of measurements during melting. The behavior of temperature and carbon during melting depends on inputs to BOS and control interventions. The example of simulated behavior of temperature and carbon during selected melting is shown in Figure 1. This dynamic behavior was simulated by a complex model for indirect measurement of temperature and carbon with feedback [4,5] developed by the authors of this paper. The model is based on the assumption that the converter gas flow and its composition of CO, CO\({}_{2}\), and O\({}_{2}\) are measured. The proposed complex model aggregates models of individual steel production processes (i.e., melting of scrap, decomposition of slag-forming additives, oxidation of elements C, Si, Fe, Mn, and P in a liquid state, and processes between slag and liquid metal). The input to the model is static data recorded at the start of melting and dynamic data recorded during melting. Submodels are based on heat balances and chemical equations.