## 4 Experiment Results and Analysis
### Tracking Performance of the Proposed Additive ASP Algorithm  
Figure 12 plots the results of the proposed additive ASP control experiment (thick solid lines) along with the results displayed in Figure 8, which shows the comparisons of the tracking performance of the pure and additive ASP algorithms for the C3, C6, and C9 orders. Figure 11: Magnitude responses of \(S_{0}(z)\) (a dashed line), \(A(z)\) (a dotted line), and \(S_{0}(z)A(z)\) (a solid line). Figure 10: Impulse response of \(S_{0,\Delta}^{-1}(z)\). In the case of the C3 order, as can be seen from Figure 12a,b, there was no notable difference between the tracking errors \(L_{TE}(f)\) after the two ASP controls in the engine speed range where the leakage value was 1. On the other hand, at the vicinity of 4300 r/min (215 Hz) where the leakage value was 0.98, a little betterment in tracking performance when the additive ASP control was applied was observed with \(-7\) to 2 dBA of \(L_{TE}(f)\). Figure 12: Comparisons of the measured SPL of each order after the pure and additive ASP controls, and the tracking errors between the measured SPLs and the target profiles. (**a**) SPL of the C3 order. (**b**) Tracking error of the C3 order. (**c**) SPL of the C6 order. (**d**) Tracking error of the C6 order. (**e**) SPL of the C9 order. (**f**) Tracking error of the C9 order. compared with \(-10\) to 0 dBA after the pure ASP control. Such insufficient improvement appeared to be due to the fractional change \(B(z)\) at around 215 Hz included in the actual secondary path \(S(z)\). The reason is that, during the control experiment, \(S(z)\) had a high possibility of having a large \(B(z)\) when considering the fact that there were the large \(B(z)\) at around 215 Hz in the perturbed frequency responses of the secondary path as shown in Figure 5. However, due to this improvement by the feedforward enhancement of the additive ASP algorithm, 1.8 dBA of \(L_{TE,\text{RMS}}\) was obtained. This value is 1.1 dBA less than that of the pure ASP control experiment result as displayed in Table 3.  
In the case of the C6 order, as shown in Figure 12c,d, there was no meaningful difference between the SPLs after the two ASP controls because the feedforward enhancement was not activated at the nearly entire engine speed range with the exception of about 2150 r/min (215 Hz). However, even at this engine speed, there was nothing notable since the SPL of the target profile was almost the same as that before control. Thus, \(L_{TE,\text{RMS}}\) after the additive ASP control was 1.3 dBA, which was almost equal to that after the pure ASP control with just 0.1 dBA of difference as shown in Table 3.  
In the case of the C9 order, as plotted in Figure 12e,f, the poor tracking performances of the pure ASP control were significantly improved when the additive ASP control was applied. The discontinuity of the SPL at 4000 r/min (600 Hz) existed in the pure ASP control experiment result was removed by achieving almost 0 dBA of \(L_{TE}(f)\) through the feedforward enhancement. This feedforward enhancement also made the SPLs above 4600 r/min (690 Hz) track the target profile with about \(-5\) to 5 dBA of \(L_{TE}(f)\). However, the range of this target error was broader than that under 4600 r/min, which was about \(-3\) to 3 dBA; this was because of the increased \(B(z)\) included in the actual secondary path \(S(z)\) at the higher frequencies, as shown in Figure 5. Thus, \(L_{TE,\text{RMS}}\) after the additive ASP control was 1.7 dBA, which was about 5.8 dBA less than that after the pure ASP control as displayed in Table 3.  
These results showed that the proposed additive ASP algorithm can provide the tracking control to enhance order sound continuously at higher frequencies where the pure ASP control is limited due to high uncertainties in the secondary path. However, it was found that the tracking performance of the proposed algorithm could be degraded at some frequencies where \(B(z)\) was large. The degradation may be more distinctly observed as \(B(z)\) is more increased.