# Review of Control Technologies for Quiet Operations of Advanced Air-Mobility
## 4 Active Noise Control (ANC) Technology
### On-Blade Actuation
For an idealized point source ejecting mass into a quiescent medium, the jet mass flow rate is given as [51]:  
\[\dot{m}_{jet}=\rho_{jet}A_{jet}V_{jet} \tag{1}\]  
With velocity of source moving with respect to the medium \(\overset{\rightarrow}{V}_{source}=\overset{\rightarrow}{\Omega}x \overset{\rightarrow}{r}_{jet}+\overset{\rightarrow}{V}_{\infty}\). Assuming \(\rho_{jet}=\rho_{0}\) then:  
\[\overset{\rightarrow}{F}_{jet}=\dot{m}_{jet}\bigg{(}\overset{\rightarrow}{ V}_{jet}+\overset{\rightarrow}{V}_{source}\bigg{)}=\dot{m}_{jet}\bigg{(} \overset{\rightarrow}{V}_{jet}+\overset{\rightarrow}{\Omega}x \overset{\rightarrow}{r}_{jet}+\overset{\rightarrow}{V}_{\infty}\bigg{)} \tag{2}\]  
Comparing with FWH equation, we get the permeable mass and momentum injection terms as:  
\[Q=\rho A(u_{n}-v_{n})\text{ and }\overset{\rightarrow}{F}=\rho A\overset{ \rightarrow}{u}(u_{n}-v_{n}) \tag{3}\]  
where \(\overset{\rightarrow}{u}=\overset{\rightarrow}{V}_{jet}+\overset{ \rightarrow}{V}_{source}\) and \(\overset{\rightarrow}{v}=\overset{\rightarrow}{V}_{source}\). The anti-noise acoustic pressure was derived to be the combination of the pressure due to the mass injection term, and that due to the momentum injection. This method resulted in a reduction in the peak negative amplitude of the test rotor's radiated noise by 5 Pa at the target microphone, but was impractical as the required mass flow rate needed required a high exit jet velocity profile (see Figure 9). [PERSON] et al. [52] explored the use of trailing edge winglets for unsteady force excitation. This method specifically looks to target the rotor thickness noise. The method involves the application of an unsteady aerodynamic force to excite a secondary or anti-sound wave. This excitation was done with the use of a trailing edge winglet near the tip of the rotor (see Figure 10). Figure 8: (**a**). Location of microphones; (**b**). Mean BVI sound pressure level for open-loop controller; (**c**). Mean Low-frequency Sound Pressure Level [48]. Reprinted with permission from [PERSON] (2016). A harmonic formulation for prescribing the motion of the trailing edge winglet actuator was devised:  
\[F=F_{n}\sin(n\psi+\psi_{o}) \tag{4}\]  
where \(F_{n}\) is amplitude, \(n\) is the harmonic, \(\psi\) and \(\psi_{o}\) are azimuthal angle and initial excitation angle. The limitations of this approach are that the formulation of the anti-noise actuation depends on the correct amplitude of the forcing function, \(F_{n}\), the harmonic number, and the phase angle (see Figure 11). There was no direct correlation to obtain the exact wave form without experimentation. Figure 11: Effect of force amplitude on noise reduction. (**a**) \(F_{n}=2\) N, (**b**) \(F_{n}=4\) N, (**c**) \(F_{n}=8\) N [52]. Figure 10: Schematic of experimental setup [52]. Figure 9: Experimental Setup for tip air blowing [50]. Reprinted with permission from [PERSON] (2014). Another approach was devised by [PERSON] et al. [53] by canceling the in-plane thickness noise with a point source loading noise formulation. They utilize a single-bladed rotor with a radius of 5.79 m, a chord of 0.381 m, and an advancing-tip Mach number of \(M_{AT}=0.8\) with a target observer 100 Radii away from the center of the rotor. From the differential form of the FWH equation, the loading noise is formulated by equating the thickness noise at an observer to the loading noise:  
\[p_{L}^{\prime}(x,t)=-p_{T}^{\prime}(x,t) \tag{5}\]  
This technique was implemented both numerically and experimentally using a flap for a single observer and a single rotor blade. They tested two actuators--an active flap and a winglet on the blades and found that the active flap resulted in about 3 dB noise reduction over an azimuth range of 150 to 210 degrees, and the winglet showed more than 6 dB reduction over an azimuthal range of 120 to 240 degrees in the rotor plane. All the discussed methods have proven to be successful in cancelling thickness noise, but the practicality of the applications is still questionable.