# Performance Evaluation of Active Noise Control for a Real Device Casing
## 2 Active Noise Control  
The goal of the proposed active noise control system is to achieve global noise reduction. It is assumed that the most significant noise transmission path is through the casing walls and that the goal can be achieved by controlling device casing vibrations. The device casing vibrations might be induced by noise inside the casing and by mechanical vibrations of elements connected to the casing. The vibrational coupling can be reduced by vibration control systems, usually passive ones. For instance, in the washing machine we used, all moving parts, i.e., the drum and the engine, are partially isolated from the casing by passive vibration isolators. However, even with ideal vibration isolation, the vibrations of isolated subsystems may still propagate through the air. The acoustic path is usually harder to control. Passive sound absorbing materials can be mounted on walls; however, the performance for low frequencies is limited. The active control system of device casing by appropriate control of casing's vibration should provide good reduction of noise propagated through both paths: sound and mechanical vibrations. The control of device casing vibrations is achieved by using actuators mounted on the casing. The control of a whole casing for wide frequency band requires a large number of actuators, a lot of output channels and high processing power. For practical implementations, distributed control using multiple simpler controllers is preferred. Thus, the control algorithm is explicitly divided into \(P\) tasks [17]. They can operate on multiple processing units (processors, cores) in a single system or even independent systems that share some signals: the reference signal, error signals and signals needed for acoustic feedback elimination, if needed. Figure 1 shows the simplified block diagram of the Active Noise Control (ANC) system. It is based on the filtered-x least mean square (FxLMS) algorithm architecture. It offers an online adaptation scheme that is necessary for the considered plant due to the non-stationarity of the primary noise (among others, due to varying washing program) and the time-varying plant itself (the primary and secondary paths may change due to, e.g., the heat produced by the operating device). On the other hand, the FxLMS algorithm, among the adaptive control algorithms, offers a satisfactory performance, while requiring affordable computational power, what enables its practical real-time implementation. Nevertheless, a number of important modifications have been proposed and applied to the original FxLMS algorithm to better fit the requirements of the active casing control system. The primary noise \(d(n)\) propagates though primary paths \(\mathbf{P}\), and after being measured, by the feed-forward control system: the reference path \(X\); set of control filters \(\mathbf{W}(z^{-1})\), one per actuator; and by secondary paths. The adaptation algorithm adapts control filter weights to achieve destructive interference. The control signals for all actuators are generated by linear adaptive filtration of a single reference signal:  
\[u_{p,c}(n+1)=\mathbf{w}_{p,c}(n)^{T}\mathbf{x}_{u}(n), \tag{1}\]  
where \(\mathbf{w}_{p,c}(n)=[w_{p,c,0}(n),w_{p,c,1}(n),\dots,w_{p,c,N_{W}-1}(n)]^{T}\) is a vector of parameters of the adaptive control filter for the \(c\)th output of the \(p\)th task; the \(N_{W}\) is the number of parameters of each control filter. The \(\mathbf{x}_{u}(n)=[x(n),x(n-1),\dots,x(n-(N_{W}-1))]^{T}\) is a vector of regressors of the reference signal \(x(n)\), the same for all outputs. Control filter weights are updated using the switched-error normalized leaky FxLMS algorithm with only one active error [18]. This algorithm adapts the weights of the control filter using multiple error signals, such multiple error FxLMS [19]; however, in each sample only one error is used. This reduces the computational complexity of the adaptation algorithm by the number of errors at cost of the convergence rate.