# A Review of Sound Field Control
## 4 Active Noise Control
### ANC Applications  
ANC facilitates the protection of instruments or human hearing from damage by controlling noise or vibration. It has been widely used in noise control and vibration elimination of industrial and mechanical equipment, such as pipeline noise, aircraft noise, car noise, magnetic resonance imaging (MRI) noise, etc. Noise-canceling headphones are a typical one-dimensional noise reduction scenario and may be the most successful application of ANC, as shown in Figure 7a. Because of low computational cost and flexibility, fixed and digital controllers are often used to implement both feedforward and feedback control [62; 86]. The feedforward controller may be designed by approximating the optimal Wiener solution regardless of stability. In feedback ANC headphones, the noise reduction performance, noise amplification, and robustness to secondary path variations should be considered for the design of the controller [15]. Most ANC feedback controller design methods have employed the ad-hoc techniques named loop shaping. [PERSON] assumed a multiplicative uncertainty model and optimized the controller with H\({}_{2}\) performance criteria and H\({}_{\infty}\) constraints of secondary path uncertainty [87]. However, these methods require some guess work and personal experience. In Figure 7a, the controller is implemented by a codec ADAU1772 with 44.1 kHz sampling rate. This codec has several biquad filters to approximate target controller response [88]. Recently, chips with higher sampling frequencies such as 768 kHz are developed and applied to commercial headphones, expecting lower latency and noise reduction bandwidth. Pipe mufflers in Figure 7b are another one-dimensional noise reduction application which involves acoustic feedback and effects of airflow and temperature. Because the primary noise is usually periodic, non-acoustic reference signals such as revolving speed, acceleration signal, and generated tonal signal are widely used to remove the secondary  
Figure 7: ANC applications. (**a**) is the ANC headphone in [88], (**b**) is the pipe muffler in [55], (**c**) is the adjustable ANC headrest for electric vehicles [77], (**d**) is the local quiet zone in [76]. path feedback effect. In the case of narrowband active noise control, frequency mismatch (FM) between estimated frequencies and true frequencies may decrease the noise reduction and even make the system unable to work properly in some extreme circumstances. Some improvements have been made in the narrow-band ANC system involving variable step-size algorithms [89] and frequency estimation algorithms [90]. In Figure 7b, a circular pipe system with an active-passive hybrid compound muffler was established. The primary source is set at the front-end of the pipe system while the secondary source at the after-end of the muffler. Signal processing is performed online by a controller with a development board Omap-L137 based on TMS320C6747. This system achieves good reduction performance of multiple tones with time-varying frequencies. For spatial noise reduction, active headtests in Figure 7c are also very promising designs. They do not need to be worn on the ears. By placing speakers around the seats or windows, a good noise reduction can be obtained near the ears. In Figure 7d, active headtests are used to control the noise around passengers' ears in cabins, improving the robustness when the head is rotated. In order to expand the noise reduction area, existing ANC systems are often improved from perspectives of combining optical sensors, virtual sensing technology, and modal domain algorithms. Cabin and aircraft noise control is interior noise control. In this regard, piezoelectric materials are utilized to actively reduce the structural sound radiation, through which enclosed sound fields are controlled [91; 92; 93; 94]. Combined with psychoacoustics, ANC systems tend to achieve a comfortable residual sound field rather than simply a quiet one.