## 3 Results and Discussion
### Optimization of Throttle Actuation  
The throttle closure was optimized by varying the duration of the four transitions between the openings equal to 40, 30, 20, 10, and 3\({}^{\circ}\), as stated in Section 2.2 (Figure 2). The objective was to find the fastest throttle closure which did not induce the appearance of compressor surge, without the aid of the anti-surge control system. Regarding the rest of the actuations, the VVT system was configured to provide a constant valve overlap of 40 CAD during the whole tip-out, and the VGT was fully open in 2 cycles from its full load position at the same timing as the throttle (that is, no delay between the start of the 2 actuations considered). Besides, the time profile of spark timing was defined to avoid knocking and misfires for all cases. As explained in Section 2.3, the compressor outlet pressure signal and its time derivative were processed and utilized to identify the surge. Figure 2: Optimization of throttle closure. Figures 3 and 4 depict the evolution of \(\widehat{p_{2}}\) and its time derivative (\(\dot{\widehat{p_{2}}}-\dot{\overline{p_{2}}}\)) for two cases per transition, i.e., in a descending order of duration, the first case where surge was detected and the previous one (which was the optimum). Taking into account the amplitude threshold of 1 bar/s for oscillations in the time derivative, the minimum durations without surge for the four transitions were respectively: 3, 5, 5, and 3 cycles. Thus, the optimum throttle actuation had a total duration of 17 engine cycles (around 1.4 s), including the cycle between throttle positions equal to 60 and 40. Once the throttle actuation was optimized without the compressor ASV, two more tip-outs were tested: the reference case, in which the throttle was closed in two cycles using the anti-surge control system, and another tip-out with no ASV, where the throttle closure was designed to provide the closest operating path to the theoretical surge line on the compressor map. Figure 5 shows the throttle actuation (a) and compressor speed map (b) for these two tip-outs, respectively tagged as Case A and Case B, and the case with the throttle closure optimized with no ASV, labelled as Case C. In addition, the time evolution of compressor outlet pressure (a), air mass flow at filter outlet (b), turbocharger speed (c), and engine load (d) also for Case A, B, and C is presented in Figure 6.  
Figure 3: Time evolution of compressor outlet pressure and its time derivative for two cases of the transitions 40–30\({}^{\circ}\) (**a,b**) and 30–20\({}^{\circ}\) (**c,d**). In the insets, the duration of the transition is stated between pantheses. Figure 4: Time evolution of compressor outlet pressure and its time derivative for two cases of the transitions 20–10\({}^{\circ}\) (**a**,**b**) and 10–3\({}^{\circ}\) (**c**,**d**). In the insets, the duration of the transition is stated between parentheses. Figure 5: Throttle actuation (**a**) and compressor speed map (**b**) for Cases A, B, and C. The corrected compressor speed values are given in kRFM. Focusing on Cases B and C, the compressor operating path for the latter was clearly located to the left of the surge line, except for compression ratios between 1.2 and 1.4 (Figure 5b). This was reflected in the throttle actuation (Figure 5a), which was notably slower for Case B, mainly after the first second. Therefore, it was demonstrated that the surge line was not a reliable limit when the turbocharger, characterized in gas test stand, was coupled to the engine. Regarding Case A, it was observed that the throttle reached its minimum opening 1.2 s earlier than in Case B. These significant differences in throttle actuation were especially noticeable in the evolution of air mass flow and engine load (Figure 6). Hence, two remarks can be made in view of the results. After throttle closure optimization with no ASV, the compressor stable operation was ensured during the whole tip-out.