## 3 Results and Discussion  
The block diagram shown in Figure 4 is implemented in the MATLAB Simulink environment. The impact of the active control on the sound pressure in front of the lining and on the vibration of the lining is evaluated based on simulation results obtained with the implemented model. The sound pressure results are based on the acoustic residual \(\mathbf{e}_{a}\), which is calculated from the measured acoustic disturbance \(\mathbf{d}_{a}\) and from the anti-sound from the active system \(\hat{\mathbf{y}}_{a}\). The vibration results are based on  
Figure 4: Block diagram of the adaptive controller with observer filter and performance outputs. the vibratory residual \(\mathbf{e}_{s}\) that is calculated from the measured vibratory disturbance \(\mathbf{d}_{s}\) and from the actuator vibration feedback on the remote sensors \(\mathbf{\hat{y}}_{s}\) (see Figure 4). Figure 5 shows the SPL distribution in front of the lining evaluated on the two planes defined in Section 2.1. The \(y\)-axis is aligned with the longitudinal axis of the aircraft (in the laboratory it is rotated). The \(z\)-axis indicates the distance from the lining. In configuration 1, which is the uncontrolled case, the highest SPL occurs close to the lining surface at \(y\)-values from 0.4-0.7 m. In this \(y\)-range, the windows are located. The SPL decreases with increasing distances from the lining surface which is expected for an anechoic environment. In configuration 2, two virtual error microphones are placed in plane \(\alpha\). This leads to strong SPL reductions close to the two microphone locations. Increased SPL are observed at locations further away from these so-called quiet zones. The mean SPL in plane \(\alpha\) is slightly reduced, whereas the mean SPL in plane \(\beta\) is significantly increased. This behavior is expected for ANC systems with local error sensing schemes. It must be noted that configuration 2 realizes a square control system because it has two actuators and two error sensors. Therefore, the residual SPL at the two virtual microphone locations should vanish. Approximation errors in the \(t\to F\) block are responsible for the non-zero residual. These errors decrease with increasing sampling rates. In configuration 3, six virtual error microphones are placed in plane \(\alpha\). The y-locations of these six microphones coincide with the y-locations of the maximum SPL in the uncontrolled case. Compared to configuration 2, the SPL reductions are less strong but more evenly distributed. In both planes, a reduction of the average SPL is achieved. In configuration 4, six additional virtual microphones are placed in plane \(\beta\) at the same \(y\)- and \(z\)-locations as in configuration 3. This leads to a stronger SPL reduction in plane \(\beta\) without compromising the control performance in plane \(\alpha\). Finally, in configuration 5, virtual microphones are placed in all possible 60 locations. Compared to configuration 4, this leads to a further reduction of the mean SPL and a more homogeneous SPL distribution. It is concluded that a larger number of virtual microphones improves the homogeneity of the remaining sound field with regard to the SPL. This is mainly due to the higher harmonics and interaction tones of the CROR as can be seen in Figure 6. Increasing the number of error sensors is easily achieved for a remote sensing scheme because the number of physical sensors and the number of complex filter weights are not influenced. Only the row dimension of the observer \(\mathbf{O}\) and the actuator FRF matrix \(\mathbf{\hat{G}}_{a}\) increase with the number of virtual sensors, which slightly increases the numerical computation effort of the real-time control system. Figure 6 contrasts the tonal SPL reductions achieved by configurations 2, 3 and 5. For the sake of simplicity, the mean value of the SPL reductions in both planes is shown in each plot.