Study of spray-cooling control for maintaining metallurgical length or surface temperature during speed drop for steel continuous casting

Continuous casting is an important engineering process through which nearly all of the steel is currently produced worldwide. Steel strand surface temperature and metallurgical length are two key processing variables requiring a proper real-time control to meet product quality and operational safety demands. The main focus of the control methods currently used in the steel industry is maintaining steel surface temperature. Most of these control methods are open-loop. The main reason is that the spray cooling droplets impinging on the high temperature surface induce steam clouds, which make temperature measurement unreliable. However, for operations limited by the casting speed, or for steel grades sensitive more to centerline rather than surface defects, the control of metallurgical length is more important. Operations designed to reduce centerline defects, like soft reduction, depend greatly on the metallurgical length profile. This work explores the potential of using open-loop control methods for the task of minimizing the metallurgical length deviations from the desired value during casting speed changes under temperature constraints. This objective essentially reduces to motion planning, i.e. apriori generation of spray flow rate commands that when applied to the process make the latter execute the motion that carries out the above task in the shortest time possible. In the first part of this thesis, a simple but comprehensive heat transfer and solidification model - CON1D, and a real-time dynamic version of this model - CONOFFLINE (offline version of CONONLINE) are described. CONOFFLINE uses multiple 1-D models (CON1D) interpolated to give a 2-D prediction of transient evolution of steel temperature and shell thickness in the caster, in an Eulerian frame of reference. The accuracy of CON1D is further verified by validation through a simple test problem with an analytical solution. The phenomenon of hysteresis was introduced in this work into the CONOFFLINE model as a new feature and its effects were investigated. In the second part, CONOFFLINE was applied to study the thermal behavior (surface temperature and shell thickness) of a thick-slab caster under different speed drop scenarios with constant secondary spray cooling. Analytical solutions are presented to estimate the surface temperature settling time, i.e. the time needed for the surface temperature to reach the neighborhood within 10 degree Celsius of steady state after the speed change, and the metallurgical length settling time, i.e. the time needed for the metallurgical length to reach steady state after the speed change, during sudden speed changes. In the third part, the potential of maintaining surface temperature during speed drops was studied by investigating the following four control methods: 1), constant spray cooling (no control) 2), spray table control 3), time-constant control and 4), PI control. The results show that the time-constant control method has good performance when a good spray table, which is a set of spray patterns that produce the same surface temperature profiles at steady state under different casting conditions (mainly different casting speeds in this thesis), is available. The PI controller's performance depends on the choice of the gains. In the last part, the potential of maintaining the metallurgical length during small speed drops for thick-slab caster was studied by investigating four different control methods: 1), constant spray cooling (no control) 2), spray table control 3), time-constant control and 4), bang-bang control. The performance of the above control methods is evaluated in terms of the metallurgical length deviation (the maximum metallurgical length increase/decrease after the speed drop). Based on spray patterns that produce the same metallurgical length under steady state at different casting speeds, the spray table control method decreased the metallurgical length deviation by 66.1% compared with the constant spray cooling case. The time-constant control method reduced the deviation by 41.2%. Bang-bang control method has the best performance on minimizing the metallurgical length deviation. Both the two-step bang-bang control method and the three-step one reduce the metallurgical length deviation by 70.6%