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The mesoscopic dendrite growth model in the solidification process of molten steel is established, based on the cellular automata model. To accurately describe the TiN nucleation process, a heterogeneous nucleation model was used to describe the TiN nucleation process. The accuracy of the dendrite growth model is verified by comparing the CA model and Lipton-Glicksman-Kurz (LGK) analytical model. The growth process of TiN precipitates was simulated by dynamic mesh generation. Meanwhile, the influence of grid anisotropy on dendrite growth is greatly weakened by introducing the decentered square algorithm, and the growth of the equiaxed crystal in all directions is simulated. The results show that the calculated results of the model are in good agreement with the volume and morphology of TiN observed in the experiment. Meanwhile, it is found that the smaller TiN will dissolve at the end of solidification, and there will be a re-precipitation. The precipitation time of High-N and High-Ti alloy systems with the same concentration product is basically the same, but the final precipitation solid fraction of TiN inclusions in High-N (small Ti/N) alloy is larger. N element is the decisive factor of TiN precipitation.

Currently, PID controllers have been widely used in industrial control. And computer control systems are widely used in the field environment. How to design a discrete PID controller which has a good control performance is very important for existing control objects. In this paper, particle swarm optimization and quadratic performance index are used to optimize the control parameters of the discrete PID controller. The optimized results are given at last. By simulation studies and analysis, the optimal parameters of the PID controller are found by particle swarm optimization algorithm, and the quadratic performance index has a good effect on optimal control.