# Combining the Advantages of Different Processing Solutions Using a Novel Motion Processing Approach
## 5 Combining Processes with Differing Solution Principles
### Further Applications for Increasing the Operating Speed  
Above, it is shown that when processing operation-speed-dependent motion profiles, different process solutions can be executed together. There is another aspect that should be addressed at this point. It was described and validated in the authors' preliminary works [7; 16; 18]. The idea is illustrated in Figure 9. By connecting more than two motion profiles, the process window can be further increased. In the lower speed range, the motion profile for the conventional process is used up to \(f_{\text{s1}}\). There is only one motion profile in this range, which is used unchanged for all operating speeds. When the operating speed exceeds \(f_{\text{s1}}\), the motion processing approach switches discretely to the new process solution, which is more suitable for higher operating speeds [7]. For our example, two motion profiles for the new process solution are shown. They are optimized for \(f_{2}\) and \(f_{3}\) (Figure 9, blue and green). If the operating speed is increased further, the processing approach again switches discretely to the third motion profile \(f_{3}\) at operating speed \(f_{\text{s2}}\). The operating speed is limited upwards at \(f_{\text{3,ucr}}\) where the positioning error of \(f_{3}\) exceeds the tolerable error. Combining three motion profiles extends the process window significantly compared to using individual motion profiles. The black dashed line in Figure 9 shows the expected motion error as measured in previous work [7; 16; 18].  
Figure 8: Comparison of the motion principles of the conventional approach (dark gray) and the new approach (light gray). (**a**) Motion set-point in horizontal direction and (**b**) resulting 2D motion path.  
Figure 10 shows another method for increasing the operating speed even further. The idea is still based on discretely combining the different process solutions at \(f_{\rm s}\). In contrast to the approach discussed above (Figure 9), continuous processing and its advantages are used in the speed range above \(f_{\rm s}\).  
Below \(f_{\rm s}\), discrete processing of the conventional process is done. In the range between \(f_{\rm s}\) and \(f_{2}\), processing can be either discrete or continuous, since both methods implement identical behavior. Between \(f_{2}\) and \(f_{3}\), continuous processing using 1D linear interpolation is performed. With continuous processing, the optimized motion profiles \(f_{1}\) and \(f_{2}\) can be further spaced than is possible with discrete processing [7; 20]. This is because the motion error is reduced during the continuous processing compared to the discrete processing [16]. With enlarging the distance between \(f_{2}\) and \(f_{3}\), the error in between also increases. However, if the error remains below the tolerable error, the combination of those motion profiles for controlling the process is allowed. An algorithm that enables the identification of reasonable operating speeds \(f_{2}\) and \(f_{3}\) was presented in [20]. Although a different process example was used here, the algorithm can also be applied to the process considered here.  
The black dashed line again shows the product's positioning error. The validity of the procedure and the appearance of the resulting error was evaluated in [7; 16]. The operating speed can thus be increased up to the speed \(f_{\rm 3,ucr}\).  
By combining different process solutions with overlapping process windows, it is possible to enlarge the process window of the entire process. This means that the central requirement of being able to run a technological task from standstill to the highest possible operating speeds can be better met than with conventional control approaches. In the following chapter, guidance for deciding whether the approach is transferable to other processes is given.