## 3 Modified Structures for Hybrid Active Sound Quality Control System  
The Simplified Structure for a Hybrid Active Sound Quality Control System with a New Leaky FxLMS Algorithm  
A modified structure, later called the simplified structure, is proposed on the basis of the traditional structure for hybrid active sound quality control. This simplified structure can reduce the coupling effect of the control filters and decrease the computational complexity of the control structure. Figure 2 shows a schematic diagram of the simplified structure for a hybrid active sound quality control system. It can be seen from Figure 2 that the simplified structure has a simplification in the feedback control structure compared to the traditional structure. The reference input signal \(x_{b}(n)\) in the feedback control structure is now superseded by the synthesis of the residual error signal \(e(n)\) and the output signal \(y_{c}(n)\) of the line-spectrum noise cancellation control filter, i.e.,  
\[X_{b}(z)=E(z)-Y_{c}(z). \tag{13}\]From Equation (13), the merit can be seen that the term \(\hat{S}(z)Y(z)\) is removed in the reference input signal of the feedback control structure. Therefore, the computational complexity of the control structure is decreased. Supposing \(S(z)=\hat{S}(z)\) and \(D(z)=X(z)P(z)\), one can derive the residual error signal by imitating the deduction of Equation (11) and substituting Equation (13) into Equation (5). \[E(z)=\frac{1}{1+S(z)W_{b}(z)}V(z)+\frac{P(z)-[(1-\beta)W_{f}(z)-W_{c}(z)W_{b}(z )]S(z)}{1+S(z)W_{b}(z)}X(z). \tag{14}\]  
Because the residual error signal changes with the sound quality control goals, the coupling is discussed based on the residual error signal in Equation (14). From Equation (14), it can be seen that there is less coupled correlation between the feedforward and feedback control structure because of the use of the reference signal in Equation (13) when the simplified structure is compared with the traditional structure for the hybrid active sound quality control system. When the control system turns into an ANC system, i.e., the gain factor \(\beta\) is set to zero and \(W_{c}(z)\) approaches zero, it can be shown that the update of the weight coefficient for the feedforward control filter has nothing to do with the feedback control filter. The line-spectrum noise cancellation controller also does not influence the iteration of the feedforward controller. In order to attenuate the broadband disturbance \(v(n)\) and the primary signal \(x(n)\), the feedback control filter is updated to make the expression \(1+S(z)W_{b}(z)\) as large as possible. The feedback control filter is also close to \(P(z)/S(z)\). Furthermore, when the gain factor is non-zero, the coupling effect between the feedback control structure and feedforward control structure is degraded in comparison with the traditional structure, even if the iterations of control filters \(W_{c}(z)\) and \(W_{b}(z)\) still affect the convergence of \(W_{f}(z)\). The feedback control structure in Figure 2 is identical to the feedback control structure of an ANC system in Reference [10]. Although the total control system is simplified by removing the term \(\hat{S}(z)Y(z)\), several drawbacks exist in the feedback control structure because of the use of the reference signal, as presented in Equation (13). The control filter \(W_{b}(z)\) may produce a large value in some iterations such that the feedback control structure becomes instable. Accordingly, the leaky FxLMS algorithm was applied to the feedback control structure to limit the excessive weight value of the filter \(W_{b}(z)\)[24; 25]. The cost function of the abovementioned algorithm is not the minimization of the squared residual error signal, and this cost function can deteriorate the capability of noise reduction. The filter output is not constrained, and the noise attenuation performance is deteriorated owing to the utilization of the leaky FxLMS algorithm in the feedback control structure [26].