## 3 Results and Discussion
### Scalability to Higher Welding Speeds  
The scalability to higher welding speeds had been examined in the following for a better understanding of the system behavior at more industrially relevant welding speeds. The welding speed was scaled up from 1 m/min to 5 m/min for this purpose.  
Figure 16 shows the comparison of the joint gap of both welding speeds considered for the unhindered gap formation and closed-loop force control. The gap size is significantly reduced for higher welding speeds due to the reduction of dissipated heat. This was also evident in the energy per unit length required for full penetration welding, which was 24 kJ/m at 1 m/min and 12 kJ/m at 5 m/min (see Section 2.1, Table 1). The qualitative characteristics were generally comparable, i.e., the resulting gap decreased as the setpoint value of the compression force \(F_{set}\) was increased. It should be noted that the gap to be bridged also decreased with increasing welding speed due to a reduced melt pool volume as shown in Figure 16 for two welded examples at 1 m/min and 5 m/min. An additional example is a force of \(-\)30 N, where an average weld length of 280 mm at 5 m/min and of 260 mm at 1 m/min was achieved despite different gap values of 0.09 mm to 0.32 mm.  
A consideration of the time-dependent behavior is shown in Figure 17 for the force-position control at a welding speed of 5 m/min. A force \(F_{set}\) of \(-\)30 N should be kept constant until a gap width of 0.05 mm (\(gap_{switch}\), approximately 20% of the focal diameter) had been reached (\(X_{set}\) = 0.05 \(mm\)). Due to a higher welding speed and a reduced energy per unit length, a smaller melt pool size was reached resulting in reduced gap bridgeability, as mentioned. Thus, a gap smaller than for 1 m/min was selected to demonstrate the possibility of a force-position control at 5 m/min welding speed. The control was initiated at time zero and reached the setpoint value \(F_{set}\) of \(-\)30 N after 0.22 s for LC1 and 0.12 s for LC2. The different times resulted from the larger effect of the welding process at the beginning of the sheet compared to the end of the sheet. The joint gap at IP1 never exceeded 0.05 mm which is why the controller continued to keep the force at \(-\)30 N. A greater difference between the nominal and actual force occurred from approximately 1 s onwards at LC2 before a gap of 0.05 mm (\(gap_{switch}\)) was reached. The rapid increase in gap size could not be fully compensated which may be attributed to the characteristic offset of a proportional controller until the closed-loop control was switched from force to position control after approx. 1.8 s. When the switching condition was reached at IP3, a further  
Figure 16: Comparison of maximum gap width for unhindered gap formation and force-controlled process at 1 m/min and 5 m/min welding speed and examples of weld seams.  
gap opening was strongly delayed immediately while the control tried to reach the \(X_{set}\) value of 0.05 mm. However, a maximum gap size of 0.058 mm after approximately 0.35 s was obtained. The gap size at IP3 was slightly decreasing afterwards to a minimum gap size of 0.042 mm while a maximum force of \(-\)106 N at LC2 occurred. The characteristic for dropping below the setpoint gap value \(X_{set}\) was favorable in terms of avoiding weld discontinuities.  
At this point, it can be stated that a transfer to higher welding speeds was possible and has been implemented. The integrated sensors and actuators can intervene quickly enough, although further tuning of the controller certainly offers potential for reduced deviations between setpoint and actual values.