## 3 Experimental Set-Up
### Property of the Secondary Path Using the ESG-Cowl Pair  
The two ASP algorithms can be operated on the same control system set-up using the ESG-cowl pair as explained in Section 3.1. The actual secondary path \(S(z)\) was defined as the electro-acoustic relationship between the input signal to the ESG and the output signal from the error microphone in the control board. The measured frequency responses below 850 Hz of \(S(z)\) at five different conditions of engine room temperature when the engine was off are plotted in Figure 5. As shown in the plot, it was observed that the change of engine room temperature affected the path to become perturbed rather easily especially at higher frequencies.  
This indicates that the secondary path using the ESG-cowl pair can be suffered from uncertainty at actual driving condition and this can restrict the control performance while maintaining proper control stability at higher frequencies.  
The nominal secondary path \(S_{0}(z)\) was obtained by averaging the responses as plotted with a thick line in Figure 5. Then \(S_{0}(z)\) was used to design the path model \(\hat{S}(z)\), which was an FIR filter with the first 500 samples of the impulse response of \(S_{0}(z)\) as shown in Figure 6. The filter length was determined to accommodate the electro-acoustic property of the impulse response sufficiently. It must be considered that the computation requirement in the real-time control board is increased with a longer secondary path model.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Dimensions & \(\mathcal{O}65\times 40\) mm \\ \hline Max. force & 5 N (at 300 Hz) \\ \hline Frequency range & 100 to 1500 Hz \\ \hline Force rate & 0.6 N/V \\ \hline Weight & 250 g \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of the ESG.  
Figure 5: Measured frequency responses of the secondary path using the ESG-cowl pair at five different temperature conditions. (**a**) Magnitude responses. (**b**) Phase responses.  
In addition, the eigenvalue equalization approach [16] was applied to the design of the secondary path model. This approach can help achieve higher control performance by allowing a large gain while maintaining control stability. Hence, the convergence coefficient \(\alpha\) in Equation (4) was set to a constant value regardless of frequency.  
By the way, the leakage term in Equation (4) was utilized to prevent the ASP control from becoming unstable at higher frequencies where \(B(z)\) were large. This term with a proper value can strongly suppress the control signal not having a huge value or not being diverged. Thus, the leakage term was scheduled with frequency, and its values from 690 Hz to 850 Hz with large \(B(z)\) were set to 0.98. This number was experimentally obtained. In addition, the leakage values at the frequencies, under 50 Hz and about 100, 215, 590 Hz, where the coherences of the nominal secondary path were less than 0.92 were also given by 0.98 for maintaining control stability. The leakage values at the other frequencies were set to 1. The scheduled leakage term was included in both the pure ASP algorithm and the additive ASP algorithm for updating their adaptive controller in the real-time control experiment and was applied to all orders to be controlled.  
Incidentally, the two frequency groups divided according to the leakage values, 0.98 and 1, were utilized for the switching condition for Equations (6a) and (6b) in the suggested additive ASP algorithm.