## 4 Experiment Results and Discussion  
### Property of the Secondary Path  
The secondary path indicates the electronic relationship between the control signal to operate the ESG and the acoustic signal measured by the error microphone.  
Figure 5 shows the magnitude response (upper) and the coherence (lower) of the secondary path in the frequency range of 50-500 Hz. The frequency range for ARNC was determined to utilize 100-250 Hz where the magnitude was large enough to suppress road noise and the coherence was sufficiently high as it reached almost 1. This indicates that the ESG-cowl pair is an effective sound radiator at that frequency range in the car cabin. It was observed that there were three dominant resonances at about 130, 175, and 220 Hz in that control frequency range and they were the three most eminent acoustic modes at the driver's ear in the cabin.  
The frequency ranges out of 100-250 Hz were excluded in the control as its magnitude response was not sufficiently large and varied over time and the coherence was not high enough. This is because changes such as ambient temperature fluctuations can affect the mechanical property of the metallic cowl panel where the ESG was installed.  
Then, the secondary path model \(\hat{S}\) was designed as an FIR filter with 250 coefficients at the sampling frequency of 3200 Hz, as shown in Figure 6 (upper). The FIR device was sufficiently long to contain the electro-acoustic characteristics of the secondary path as the decay of the impulse response was enough at that length. In addition, the computational  
Figure 5: Frequency response of the secondary path between the ESG and the error microphone. (**a**) Magnitude response. (**b**) Coherence.  
resource of the controller (dSPACE 1401), when the number of the reference channels was 12, was considered to determine the length of the FIR device, although the longer impulse response in the path model offers a smaller mean square error in this control scheme.  
It is noted that the path model length of the ESG-cowl pair was almost twice that of a typical built-in door loudspeaker by the driver's seat in a similar car, as plotted in Figure 6. The reasonable length of the impulse response of the loudspeaker was about 130 taps for the path modeling, as shown in Figure 6 (lower). This implies that the vibration of a cowl panel continues much longer than that of a loudspeaker against an impulse. The longer impulse response of the cowl panel limits the control performance of the ANC or ARNC algorithms based on the FxLMS approach. Thus, careful considerations on the design of the secondary path model and the decision on the control frequency range are necessary to adopt a structural actuator such as the ESG-cowl pair in this study.  
In addition, the equalized eigenvalue approach was applied to design the secondary path model for achieving higher control performance by allowing a larger gain while maintaining control stability [19]. The filtered reference signal vector \(\overset{\wedge}{\mathbf{x}}\) defined in Equation (7) was generated after passing through this impulse response.  
It is noteworthy that the vibration of the cowl panel excited by the ESG can be detected by the reference sensors, and this can disturb the reference sensors in detecting the pure reference signals, which are strongly correlated with the road-tire interaction. This is a feedback path to the reference sensors caused by the actuation force of the ESG. However, the effect of the feedback path was sufficiently small compared to the pure reference signals when the test car was driven at 60 kph, so the feedback path was not considered in the proposed ARNC algorithm.