# Directional Active Noise Control with a Local Minimax Error Criterion
## 5 Experimental Results and Discussion  
In this section, an experimental evaluation of the ANC system based on the two criteria is presented. A panoramic view of the experimental environment is shown in Figure 5.  
The board was positioned obliquely on the wire mesh to reduce the friction with the wire mesh when excited by the actuator in the anechoic chamber. The frequency of the original harmonic signal generated from the DSP board was 100 Hz. We conducted seven experiments as mentioned in Section 4, respectively in two different directional areas. The mean and standard deviation values were calculated to generate the error bar diagrams. The results of the experiments are presented in Figure 6.  
An uncontrollable directivity was formed at Point No. 8 in Figure 5(a) and in Figure 5(b) when the MSE method was adopted. The directional reductions of Area 1 and Area 2 were achieved with the local minimax method, where Points No. 2, No. 4, and No. 6 and No. 6, No. 8, and No. 10 were the desired points of Area 1 and Area 2, respectively. Points No. 3, No. 5, No. 7, and No. 9 were the monitor points of the two areas. Similar to the global minimax method, the proposed method also led to a uniform residual sound at the desired points. The comparison with the MSE criterion method showed that an increase in the reduction in the directional area was accompanied by a reduction in the orthogonal direction, which was due to the choice of desired error points and the optimization algorithm. The local minimax criterion method aims to achieve the reductions at local points rather than all error microphones. Moreover, the local criterion optimization based on the Nelder-Mead algorithm with a known initial point can balance reductions between the local and global area, avoiding no reduction in orthogonal directions. It is worth noting that the standard deviations of the residual sound curves of the proposed method were larger than those of the two other curves in both figures. Figure 5: Panoramic view of the experimental environment. The effect of \(\mathbf{P}\left({{jw}}\right)\), \(X({jw})\), and \(\mathbf{G}\left({{jw}}\right)\) can be ignored, according to Equation (1). It is very likely that this effect was caused by the floating variation of \(\mathbf{W}_{opt}\left({{jw}}\right)\). A comparison of two optimal filter coefficients with two directional areas is presented in Figure 7.  
Similarly, the amplitude and phase curves of the local minimax method also had larger standard deviations. In Section 3, we mentioned that \(\mathbf{W}_{2}\) was obtained by a local optimization using \(\mathbf{W}_{1}\) as the initial value. The Nelder-Mead algorithm is a heuristic search method that will likely converge to non-stationary points. This means that the algorithm has the same problem, and different initial conditions could produce different results in each run. Therefore, a slight change resulting from the measurement error and calculation error in the calculation of \(\mathbf{W}_{1}\) may cause \(\mathbf{W}_{2}\) to change greatly. Fortunately, larger fluctuations in \(\mathbf{W}_{1}\) do not adversely affect the results of the algorithm. The overall reductions of the two methods are shown in Figure 8, where the floating change of the reductions was already explained. Figure 6: Noise control performance of the two methods with two directional areas. (**a**) Active noise control (ANC) performance of the two methods with Directional Area 1; (**b**) ANC performance of the two methods with Directional Area 2; (**c**) Geometric configuration of the experiments with Directional Area 1. The points in green, red, and blue are the desired, monitor, and the rest of the error microphones points, respectively; (**d**) Geometric configuration of the experiments with Directional Area 2. The points in green, red, and blue are the desired, monitor, and the rest of the error microphones points, respectively.