# Performance Evaluation of Active Noise Control for a Real Device Casing
## 3 Experimental Verification  
### Plant  
The experiments were performed on a washing machine presented in Figure 2. The washing machine casing has different features, such as bends, embossing and internal mountings, which are not present in dedicated noise-cancelling casings. It makes the task of mathematical modelling of casing walls significantly more difficult, but such a model has to be developed in order to find appropriate locations for the actuators (if the actuators would be attached to the casing walls surface without such analysis, e.g., at random locations, it could result in inefficient control or even complete lack of controllability for certain modes of the structure, decreasing the overall performance of the control system). Therefore, a simplified model of the casing based on Mindlin-Reissner plate theory was used. Each wall of the casing was modeled independently and interactions between plates were neglected. As with the study performed for previously used, dedicated, light-weight casing shows, such a simplification can be justified for the purpose of actuators' arrangement optimization, providing satisfactory results [23]. On the other hand, even in a simpler case, when a rigid frame was assumed, acoustic coupling between plates of the casing makes the model much more complex [24]. The parameters of the plate models were identified (fitted) by a memetic algorithm. Electrodynamic actuators NXT EX-1 were modeled as additional point masses. The models were solved utilizing the Rayleigh-Ritz assumed mode-shape method. Due to real (and hence imperfect)mountings of each of the casing walls, boundary conditions elastically restrained against both rotation and translation were employed. For a more detailed derivation of the model, the reader is referred to [25]. The resulting model was employed for the process of actuators' arrangement optimization on the washing machine casing. The adopted aim of the optimization was to maximize the controllability of the least controllable mode in the frequency range up to 300 Hz. Such an objective focuses on avoiding a lack of controllability for modes of the structure in the frequency range considered. The memetic algorithm was used in the optimization process. The optimization variables were the coordinates of actuators on the plate surface. What complicates the process is the fact that the mathematical model has to be recalculated each time a different arrangement of actuators is evaluated (as the actuators' mass is taken into account in the plate model). Diagonal elements \(\lambda_{c,i}\) of the controllability Gramian matrix were used in the optimization index \(J\) as controllability measures of corresponding modes:  
\[J=\min_{i}\lambda_{c,i}\, \tag{7}\]  
where \(\lambda_{c,i}\) is the \(i\)th diagonal element of the controllability Gramian matrix, corresponding to the \(i\)th eigenmode [23]. Depending on the number of eigenmodes included in the given frequency range, a different number of eigenmodes was considered for each wall of the casing. A more detailed description of the optimization process is given in [23]. Thirteen 5 Watt electrodynamic actuators were considered in total to be placed on the casing (four on top wall and three on each other controlled wall). The bottom and back walls were not actively controlled. The arrangement of actuators is presented in Figure 3. As the pair of walls was symmetrical (left and right), a symmetrical configuration was employed for the pair. The washing machine noise significantly depends on the phase of the washing process. The loudest phase is the final spinning phase. The final spinning speed is configurable, from 400 rpm up to 1200 rpm. In this paper we focus only on final spinning, with spinning speed configured at 1000 rpm or 1200 rpm. Figure 4 shows the spectrogram of the spinning cycle for configured final spinning speed 1200 rpm. The final spinning phase takes about 200 seconds and the noise is clearly louder than in other phases.