## 2 Traditional Structure for Hybrid Active Sound Quality Control System  
Figure 1 shows a schematic diagram of the traditional structure for a hybrid active sound quality control system proposed by Reference [10]. It combines the traditional hybrid structure in Reference [15] and active line-spectrum noise control of sound quality. It also introduces the gain factor \(\beta\) and line-spectrum noise cancellation control structure. This traditional structure includes three parts, the feedforward control structure, the feedback control structure, and the line-spectrum noise cancellation control structure, which correspond to the green rectangle solid-line box, the red rectangle dotted-line box, and the blue rectangle dotted/dashed-line box, respectively, in Figure 1.  
In the feedforward control structure, the reference signal \(x(n)\) can be obtained by a reference sensor. The feedforward controller generates the secondary signal \(y_{f}(n)\) to cancel the desired signal \(d(n)\) via the gain adjustment and the secondary path \(S(z)\). The desired signal \(d(n)\) is the reference signal \(x(n)\) via the primary path \(P(z)\). The pseudo-error signal \(e^{\prime}(n)\) is the summation of the residual error signal \(e(n)\) and the \(\beta\) times secondary signal filtered by the estimated model of the secondary path \(\hat{S}(z)\); it can be used to participate in the iteration process of the weight coefficient for the control filter \(W_{f}(z)\) that is expressed as a weight coefficient vector of length \(M\), i.e., \(\mathbf{w}_{f}(n)=[w_{f}(n),w_{f}(n-1),w_{f}(n-2),\cdots,w_{f}(n-M+1)]^{T}\). In addition, the residual error signal \(e(n)\) contains the Gaussian random signal \(v(n)\). The feedback control structure has the reference signal \(x_{b}(n)\) and the control filter \(W_{b}(z)\), which is regarded as a weight coefficient vector of length \(N\). In the feedback control structure, the reference signal is the consolidation of the output signal \(y_{c}(n)\) in the line-spectrum noise cancellation control structure, the residual error signal \(e(n)\) and the total output signal \(y(n)\) of the hybrid structure filtered by the estimated model of the secondary path \(\hat{S}(z)\). The secondary signal \(y_{b}(n)\) is applied to alleviate the Gaussian random disturbance at the error sensor. The line-spectrum noise cancellation control structure uses the LMS algorithm, but the FxLMS algorithm is applied to the feedforward control structure and feedback control structure. In the line-spectrum noise cancellation control structure, the reference input signal \(x_{b}(n)\) is utilized to  
Figure 1: Schematic diagram of the traditional structure for hybrid active sound quality control system. participate in the iteration process of the weight coefficient for control filter \(W_{c}(z)\), which is considered as a weight coefficient vector of length \(L\). The output signal \(y_{c}(n)\) generated by control filter \(W_{c}(z)\) is used to eliminate the line-spectrum noise that exists in residual error signal \(e(n)\). The acquirement of the reference signal \(x(n)\) in the line-spectrum noise cancellation control structure is the same as that in the feedforward control structure. To analyze the coupling effects of the three control structures, some formulas are derived below. By utilizing the \(Z\)-transforms, in the feedforward control structure, the residual error signal is described as  
\[E(z)=D(z)+V(z)-Y(z)S(z), \tag{1}\]  
where \(Y(z)\) is the total output signal of hybrid structure. \[Y(z)=(1-\beta)Y_{f}(z)+Y_{b}(z), \tag{2}\]  
where \(\beta\) is the gain factor which can be selected on the basis of the control target of sound quality, \(Y_{f}(z)\) is the output signal of the feedforward control structure, and \(Y_{b}(z)\) is the output signal of the feedback control structure.