# Measurement and Model-Based Control of Solidification in Continuous Casting of Steel Billets
## 3 Results
### Dynamic Control of Crater End Position
#### Dynamic Adaptation of Casting Speed and Spray Water Flow Rates
Figure 18 shows good agreement of the crater end positions calculated from the regression Formula (7) for this casting sequence with the related values derived from the online model simulation extrapolated to a range of casting speeds between 1.5 and 3.4 m/min. This agreement of the derived crater end positions confirms the possibility to use the simple regression Formula (7) instead of the more complex 3D simulation model to determine appropriate spray water flows and casting speeds for adjustments of given target crater end positions. Such an approach is also suitable for online applications with cyclic recalculations each 5-10 s. The implemented dynamic control procedure to be carried out within each cyclic calculation of the strand state is summarised in Appendix A. The real ESF casting sequence from Figures 16-18 has been simulated and investigated with respect to the calculated set-points for different targets of the crater end position. For  
Figure 17: Crater end position vs. casting speed for sequence casted at ESF and simulated with full 3D online temperature and solidification model. Figure 18: Crater end position from regression Formula (7) vs. crater end position from online model simulation for sequence casted at ESF. each of the defined targets, the simulation has been performed in a first scenario without and in a second scenario with using the calculated set-points for casting speed and spray water flows in the further casting process. Figures 19-23 show the resulting evolutions of actual and target casting speed, spray water flow and crater end position for defined target crater ends of 15 m, 16.5 m, 17.5 m, 18.5 m and 20 m, respectively. The spray water flows are displayed for the first cooling loop, the flows of the other loops have an analogue evolution on the scale of the respective reference flow rate. After an initial start of casting phase of about 20 min, the strand achieves a first stationary state. After about 45 min, there is a change to another steel grade with some transient behaviour, which about 10 min later results in a new stationary phase with a new crater end position in the actual casting process and the same target position in the dynamically controlled process. Figure 19: Evolution of actual and target casting speed, spray water flow and crater end position without (**top**) and with (**bottom**) application of target casting parameters for target crater end of 15 m at ESF billelect caster. The adjustment of a target crater end position of 15 m leads to maximum set-points for the spray water flows (50% higher than reference flow rates) and casting speed set-points below the values of the actual process (cf., Figure 19). For the adjustment of a target crater end position of 16.5 m, the control procedure suggests similar set-points for spray water flows and casting speed as applied in the actual process for the first steel grade. After the grade change, the actual process operates with slightly increased casting speed and decreased spray water flows, whereas the controlled process suggests the same set-points for the second stationary phase as for the first grade to keep the casting position at the target value. Here, the reference casting speed can be chosen for the whole process (cf., Figure 20). With target crater end positions of 17.5 m and 18.5 m, the set-points for spray water flows are decreased further on below the flow rates applied in the actual process (cf., Figures 21 and 22). Figure 20: Evolution of actual and target casting speed, spray water flow and crater end position without (**top**) and with (**bottom**) application of target casting parameters for target crater end of 16.5 m at ESF billet caster. Finally, the adjustment of a target crater end position of 20 m results in minimum set-points for the spray water flows (50% lower than reference flow rates) and casting speed set-points above the values of the actual process (cf., Figure 23).