Control of constrained moving-boundary process with application to steel continuous casting

continuous casting, heat transfer, Stefan problem, solidification, optimal control, boundary hysteresis

Chen, Zhelin

关键词: continuous casting, heat transfer, Stefan problem, solidification, optimal control, boundary hysteresis;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/108003/CHEN-DISSERTATION-2020.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Continuous casting is an important engineering process producing nearly all steel currently used worldwide. Regulation of the steel temperature through the water spraying during casting critically affects the final product quality as well as operational safety. Most of the cooling spray control techniques currently used in the steel industry are effectively open-loop due to the lack of reliable measurements to enable feedback. Namely, the high temperatures, the variable surface emissivity, the scale formation, and the steam from water spray make accurate measurements of the steel surface temperature impossible with current technology. Another difficulty is the inadequacy of the existing feedback control techniques for coping with the nonlinear moving boundary problem dynamics. The present work provides several key building blocks towards a comprehensive solution of the continuous steel casting feedback control problem. In the first part of this dissertation, a mathematical model of the process and a state-of-the-art industrial control system are introduced. The steel casting process can be described as a single-phase Stefan problem under some simplifying but practically justified assumptions on the unknowns. The temperature and the shell growth are controlled by the steel surface heat flux generated by the cooling sprays. In the industrial control system, a real-time computational model of the caster is used as a software sensor to estimate the temperature and the shell thickness of the strand. The model is calibrated through the steady-state measurements of the thin-slab caster from reliable pyrometer measurements outside the spray zone as well as the metallurgical length detection trials and verified by comparing model predictions with the transient measurements of the roll forces. In the second part, the control problem is studied for the simpler, but still fundamentally nonlinear PDE model of the caster. A boundary-sensing-based observer that under an additional physically valid assumption provides a stable reconstruction of the full system state is proposed. By combining a full state enthalpy-based controller with an observer, an output feedback control law is presented, and the stability of the closed-loop output feedback system is proven. This estimation framework is then extended in the current work to a more realistic sensing setting. Online calibration using a single discrete-in-time temperature measurement is introduced to remove the estimation error arising due to the mismatch of a single unknown parameter in the model. One-phase Stefan problem with hysteresis induced by the interaction of the cooling water sprays with the hot surface under Neumann boundary actuation is then considered. A hysteresis-compensating full state feedback control law and an output feedback control law are developed for this problem by introducing the hysteresis inverse. An optimal control approach for minimizing the metallurgical length deviation during casting speed increase under constraints on the secondary cooling flow rates for the continuous steel casting process is proposed. A cost function reflecting the tracking error of a reference shell thickness is chosen, and the control objective is formulated as the minimization of this cost function under the spray rate constraints. In the third part, the verified transient 2-D thermal solidification model of the process, ConOffline, is used to assess the effect of the transient thermal behavior on the product quality in the continuous casting of steel.