Bentsman-led team solves longstanding problem in steel casting control

While much glamour of the last several decades has been focused on technological innovations from Silicon Valley, the Midwest's own “Steel Prairie” – stretching from Crawfordsville to Gary (both in Indiana) – has developed innovations of a different kind.

In 1989 Nucor Crawfordsville revolutionized steel production by pioneering thin slab continuous casting, allowing steel to be made cheaper and faster. Both industries – Czochralski semiconductor crystal growth and spray-cooling-induced steel solidification – rely on material phase-change and moving boundary control to ensure safety and maximize the product quality.

The latter problem, where both the internal spatially varying temperature profile and the internally moving solidifying steel front in the steel slab must be controlled, is especially challenging, since only the solid boundary sensing and actuation are available.

MechSE Professor Joseph Bentsman and Research Professor Brian Thomas began working on steel casting control in 2005, and in 2014, extending Thomas’ one-dimensional model to 2D along the caster, they earned a patent on a system currently used in a number of industry-leading steel-making plants. The latter system, however, focused on controlling the surface temperature, while the original problem remained fundamentally unaddressed, and solving it was thought impossible.

The first breakthrough came in 2012, when Bryan Petrus, a PhD student of Bentsman and Thomas at that time, and currently at Nucor, suggested looking at the enthalpy – the full internal energy of the solidifying material, expressed through both the internal temperature and the solidifying front position described by the coupled PDE/ODE model, referred to as the Stefan Problem.

This produced the first enthalpy controller, which performed superbly, but required unmeasurable internal variables for its implementation. To alleviate this problem, Petrus suggested a sensor (state estimator), which reconstructed internal variables based on the process model and the boundary temperature measurement, giving output feedback working in simulation, but with no convergence guarantees. The latter work produced a large follow-up literature and a book (S. Koga and M. Krstic “Materials Phase Change PDE Control & Estimation,” 2020). However, the original problem remained unaddressed.

The second breakthrough came while taking a deeper look into the closed-loop system properties, resulting in the rigorous convergence proof of the entire output feedback system. Zhelin Chen, formerly a PhD student of Bentsman and Thomas, and now an adjunct research assistant professor in MechSE, proved the observer and the output feedback temperature profile convergence, while Bentsman and Hamza El-Kebir (a PhD student under Bentsman and Ornik) proved the solidification front convergence.

These results have been presented in a new paper, “Solid Boundary Output Feedback Control of The Stefan Problem: The Enthalpy Approach,” published in IEEE Transactions on Automatic Control.

The paper is part of a comprehensive effort towards control system upgrades to meet the increasing demands on the steel industry. It also provides guidance for the control-oriented continuous caster equipment upgrades, showing what is fundamentally achievable if the corresponding sensors and actuators are put into place.