## 4 Control Strategy for Multi-Nozzle Oxygen Lances  
In the process of oxygen top-blown converter steelmaking, when the lance height is changed, the optimal NIA and NTA will also change. How to realize adaptive adjustment of the multi-nozzle oxygen lances' parameters depending on the different working conditions is unclear. Adaptive algorithms generally require training and adjustment based on a certain scale of data, which imposes higher requirements for production [31]. Numerical calculation can effectively fill this demand, and it can provide information about the flow field of the molten bath, such as the velocity and pressure, which cannot be determined experimentally [32]. Therefore, a coordinated numerical simulation and experiment is needed, where unavailable experiment data are provided by the numerical method to support training data for an adaptive control [33; 34; 35]. Based on the fuzzy control method, this paper attempts the optimal parameter adjustment control strategy between the lance height, nozzle inclination angle, and nozzle twist angle. The proposed control method firstly discretizes the three variables. Referred to actual working situation and above research, the lance height is discrete as 1200, 1600 and 2000 mm. In the present work, we propose an optimal parameter adjustment control strategy based on a fuzzy control method to control the lance height, NIA, and NTA. The proposed control method first discretizes the three variables. According to actual working situations and the aforementioned research, the lance height is discrete as 1200, 1600, and 2000 mm, the NTA is 0\({}^{\circ}\), 5\({}^{\circ}\), 8\({}^{\circ}\), and 13\({}^{\circ}\), and the NIA is 5.5\({}^{\circ}\), 8.5\({}^{\circ}\), and 13.5\({}^{\circ}\). There are 36 different working conditions in total. Through the simulation of various working conditions, the advantages, and disadvantages of the stirring effect under each situation were obtained. The membership functions of the three variables and fuzzy rules were formulated; finally, the fuzzy control system for multi-nozzle oxygen lances was established. Normalizing the vorticity of each height of molten steel can be regarded as the swirling performance under 36 working conditions. The domain of lance height is 1000-2200 mm and is divided into three fuzzy subsets: low height, middle height, and high height, respectively. The three subsets show a general bell-shaped distribution. The NTA and NIA domains are both 0\({}^{\circ}\)-15\({}^{\circ}\) and are divided into four and three fuzzy subsets, respectively. The three variable membership functions and Mamdani fuzzy system are shown in Figure 14a. Figure 12: Spray of molten bath in the preliminary stage of top-blowing with a 0\({}^{\circ}\) nozzle twist angle (NTA) nozzle. (**a**) Flow time = 0.1 s, (**b**) flow time = 0.3 s, (**c**) flow time = 0.8 s, (**d**) flow time = 1.0 s.  
Figure 13: Spray of molten bath in the preliminary stage of top-blowing with an 8\({}^{\circ}\) NTA nozzle. (**a**) Flow time = 0.1 s, (**b**) flow time = 0.3 s, (**c**) flow time = 0.8 s, (**d**) flow time = 1.0 s.  
Fuzzy rules are an important basis for fuzzy reasoning [36; 37; 38]. In this study, the fuzzy rules with different weights were formulated according to the optimal, sub-optimal, and the worst conditions under each lance height. Because of the small amount of data in the model, 13 fuzzy rules were established in this paper, as shown in Figure 14b. The fuzzy rules can be added, modified and deleted according to the actual situation in the industry field, and the inference curve based on the fuzzy control algorithm is shown in Figure 15. The parameter adaptive method based on the fuzzy control algorithm supplements the NTA and NIA well under different lance heights. The algorithm also indicates that the optimal NTA of the oxygen lance is within the range from 7.2\({}^{\circ}\) to 7.8\({}^{\circ}\), which is similar to the results of [PERSON] et al. [6].