A control-oriented mathematical model for the evolution of temperatures and phases in a steel strip during cooling

In the state of the art of steel production, the temperature evolution of steel strips is typically controlled to regulate the phase contents indirectly and, with this, their material properties. This paper proposes a novel computationally efficient, real-time capable dynamic model that captures both the temperature evolution and the phase transformations in the steel strip. The steel strip is processed in a cooling section after a continuous annealing furnace. The phase transformations cover the austenite decomposition which is mainly controlled by specifically decreasing the temperature during the cooling process. For this, a phenomenological state-space model is derived, which is inspired by the Johnson-Mehl-Avrami-Kolmogorov and the Koistinen-Marburger model. Phase transformations generally change the specific latent heat of the material, which is captured in the proposed distributed-parameter model of the strip temperature by an energy balance. Lumped-parameter models are used for the temperature evolution of the wall, the rolls, and the radiant tubes. Heat transfer due to convection, radiation, and conduction couple the individual thermal submodels. A comparison of simulation results and measurements from both experimental material tests and the real plant operation demonstrate the accuracy and feasibility of the proposed model. The model is computationally inexpensive and serves as a solid basis for advanced real-time control and optimization.