# A Feasibility Study of the Use of PZT Actuators for Active Control to Enrich Engine Sound
## 4 Experiment Results and Discussions
### Performance Analysis after ASE  
Figure 13 shows the comparison of the A-weighted SPLs of the three orders (C3, C5, and C6) before (dotted lines) and after (solid lines) ASE with the target sounds (dashed lines) against engine speed. The SPLs of the orders are plotted in Figure 13. In addition, the target error \(L_{\text{TE}}(f)\) is defined to assess the control performance of the proposed ASE system, which is given as:  
\[L_{\text{TE}}(f)=L(f)-L_{\text{target}}(f), \tag{11}\]  
where \(L(f)\) and \(L_{\text{target}}(f)\) are the SPLs of the measured engine sound and the target sound, respectively, at the corresponding frequency \(f\) in RPM. \(L_{\text{TE}}(f)\) can be expressed as the root mean square (RMS) over the engine speed range of 1000-3900 RPM as \(L_{\text{TE,RMS}}\). The \(L_{\text{TE,RMS}}\) of the three controlled orders are summarized in Table 1.  
Figure 13: Comparisons of the SPLs of the measured engine sound before (dotted lines) and after (solid lines) ASE with the target sounds (dashed lines). (**a**) C3 order. (**b**) C5 order. (**c**) C6 order.  
As shown in Figure 13a, the SPL of the C3 order before ASE was about 10-30 dBA less than that of the target sound. After ASE, this insufficient SPL was greatly increased to close to the target level and its \(L_{\text{TE}}(f)\) was \(-5\) to 1 dBA. Thus, \(L_{\text{TE,RMS}}\) after ASE achieved 0.9 dBA which was 19.1 dBA less than that before ASE, as shown in Table 1.  
In the case of the C5 order, as shown in Figure 13b, the SPL before ASE was enhanced by 5-25 dBA, thus reaching a level near to its target sound. Thus, \(L_{\text{TE,RMS}}\) of the C5 order was improved from 17.4 dBA to 1.5 dBA, as shown in Table 1.  
As plotted in Figure 13c, the result of the C6 order was similar to that of the C3 and C5 orders. It was found that \(L_{\text{TE,RMS}}\) after ASE was 1.1 dBA, whereas that before ASE was 19.1 dBA.  
However, it is noteworthy that there were large target errors at some engine speeds, such as at around 3800 RPM for the C3 order, at 2300 and 2800 RPM for the C5 order and at 1900 and 2300 RPM for the C6 order. These engine speeds correspond to 190 or 230 Hz, which are the anti-resonance frequencies of the secondary path. The reason for the large target errors is that \(A(z)\) was designed to not generate a high level of \(u(n)\) at these frequencies to maintain robust control stability, as can be seen from Figure 11. This degradation in performance was fundamentally due to the properties of the secondary path of the PZT-plate actuator. The component plate used in this study was only a reasonable choice to investigate the feasibility of the use of a PZT-plate actuator for the ASE system, not the perfect or optimized one. For a more practical implementation, it is therefore, very important to design a dedicated plate with vibro-acoustic characteristics suitable for ASE.  
Although some target errors were observed, the control experiment results show that \(A(z)\), which was implemented in Section 4.2, adequately compensated for the magnitude of the actual secondary path of the PZT-plate actuator so that the error signal \(e(n)\) followed the target sound \(c(n)\). Furthermore, the results indicate the PZT-plate actuator worked properly as a secondary actuator with the ASE algorithm, producing a supplemented engine sound to enrich the poor original sound in the cabin.