Mathematical modeling and system analysis for preventing unsteady bulging in continuous slab casting machines

In the continuous casting of steel slabs, the ferrostatic pressure in the liquid core of the strand leads to bending, i.e., bulging, of the strand shell between the guiding rolls. Unsteady bulging means that this bending process is time-varying. During the continuous casting process, the emergence of unsteady bulging can be observed, leading to unwanted mold level fluctuations and lowering the quality of the cast strand. This work presents a detailed nonlinear beam model, an approximated nonlinear beam model, and a control-oriented linear model to gain new insights into the mechanism of unsteady bulging. Simulation results show that the linear model allows real-time computation, making it feasible to design advanced model-based control and state estimation strategies. The developed models are validated using measurements from the literature and an industrial continuous casting plant. More specifically, these models permit, for the first time, a detailed stability analysis of the overall mold level control loop, which gives a system-theoretic explanation for the root cause of unsteady bulging and why it is tied to particular frequencies of mold level fluctuations. This analysis shows that the emergence of unsteady bulging is related to an unstable closed-loop system and opens up different strategies to eliminate the observed instability.