Technical aspects of physical implementation of an active noise control system: challenges and opportunities Maja Anachkova 1 Faculty of Mechanical Engineering in Skopje Rugjer Boshkovikj nn. Simona Domazetovska 2 Faculty of Mechanical Engineering in Skopje Rugjer Boshkovikj nn. Zlatko Petreski 3 Faculty of Mechanical Engineering in Skopje Rugjer Boshkovikj nn. Viktor Gavriloski 4 Faculty of Mechanical Engineering in Skopje Rugjer Boshkovikj nn.

ABSTRACT

Active noise control systems have become a subject of intensive worldwide research that have aroused considerable interest as being a promising solution to the problem of low-frequency noise control. Advanced real-time signal processing technologies offer opportunities that have been adopted in many active noise control industry applications, as well as in the modern urban environment where noise reduction is gaining priority status. Depending on the application, the concept of active sound control can be implemented using different control strategies. The development and application of such systems requires in-depth knowledge and theoretical analysis in the field of digital signal processing, sensor technology, adaptive control, understanding in hardware solutions for acquisition and data processing, as well as software capabilities for modeling, visualization and control of signals. Also, the construction of such a system must give an overview of the choice and characteristics of its components in terms of the impact of the elements that make it up on its accomplishment. This paper provides an insight into the engineering aspects for implementation of an active noise control system in a duct, emphasizing the technical requirements that need to be analyzed and might further affect the systems overall performance.

1 maja.anachkova@mf.edu.mk 2 simona.domazetovska@mf.edu.mk 3 zlatko.petreski@mf.edu.mk 4 viktor.gavriloski@mf.edu.mk

1. INTRODUCTION

According to numerous research dedicated to the problem of noise in residential as well as work environments, the main causes for the increased level of noise are the intensive globalization, industrialization, and mechanization through frequent constructive activities, as well as the dynamic transport [1] . At the same time, noise problems have become increasingly evident with the intensive use of vehicles, aircraft, industrial machinery, turbines, compressors, transformers and ventilation or air conditioning units, which as sound sources are characterized by dominant low-frequency noise. Namely, unlike the medium and high-frequency noise, the low-frequency noise below 250 Hz whose sources are more and more frequent is characterized by light propagation through obstacles and dispersion over longer distances with less energy loss due to reduced absorption. For these reasons, conventional methods using the passive noise reduction method for noise protection have reduced efficiency for low-frequency sound suspension [2] . This disadvantage is due to the fact that at these low frequencies, the acoustic wavelengths are large compared to the thickness of typical sound absorbers, and at the same time difficult to redirect in cases where the sound barrier is not extremely robust [3] . For these reasons, these problems are often difficult to solve because technical solutions must be expensive, cumbersome, and massive.

In recent years in the world, the subject of intensive research are active sound control systems that have aroused considerable interest and represent a promising solution to the problem of low- frequency noise control [4,9] . Over the past two decades, research in academia and industry in active sound control technology has suggested that primary noise disturbances can be mixed and controlled through the generation of secondary noise disturbances [10] . Active control includes an electro- acoustic or electro-mechanical system which cancels out the primary (undesirable) sound based on the superposition method, generating an anti-sound with equal amplitude and opposite phase to the original, which combines with the primary sound resulting in a lower or of both sounds. The principle of active control uses long wavelengths associated with low frequency sound and works on the principle of destructive interference between sound fields generated by the original "primary" sound source through other "secondary" sources whose acoustic outputs can be controlled [11] . Active control technology implemented in active control systems is evolving rapidly as it provides sound control improvements, often with potential benefits for size, weight, volume, and cost arising from the use of conventional methods. To date, many active sound control applications involve real-time and simulated experiments that have been adopted in many technical industrial solutions [12] .

Today, with the rapid modernization and rapid technological development of powerful and inexpensive digital signal processing processors, the implementation of advanced adaptive algorithms is encouraged to achieve faster convergence, increased robustness, and improved performance of active sound control systems. Successful application of active noise control requires good spatial and temporal matching of the primary and secondary sources in the acoustic field in order to provide signal suspension in the temporal and spatial domains [13]. Active volume control is a broad field in which knowledge of various specialized areas such as acoustics, digital signal processing, adaptive algorithms and implementation of digital processor units is necessary [14] .

Reviewing the research in [15-27] , the subject of this paper will be the analysis of the challenges and opportunities of the physical implementation of an active noise control of one-dimensional acoustic environment. By analyzing acoustic fundamentals of the sound behavior in a duct through FEM simulations, as well as the capabilities of the corresponding hardware components, physical conditions and software capabilities, a proposal for an experimental setup of an acoustic duct to demonstrate the concept of active noise control will be described.

2. PRESSURE ACOUSTICS EQUATIONS IN DUCTS

The wave equation for time-harmonic excitations in a duct of constant circular cross section can be solved in terms of modes, which come up as a result from the wave equation on a cross section of the duct. The time-harmonic sound field “p” in a duct with constant cross section can be described

by an infinite sum of modes, that retain their shape when travelling down the duct. With given frequency ω, they can be defined with the following form

𝑝(𝑥, 𝑡) = 𝜓(𝑦, 𝑧)𝑒 𝑖𝜔𝑡−𝑖𝑘𝑥 (1) and consist of an exponential function multiplied by a shape function ψ, being an eigenfunction of a Laplace-type operator on a duct cross section. The eigenfunction ψ corresponds to an eigenvalue that on its turn relates to axial wave number “k” [28].

The acoustic power brought to the input of a circular duct in a form of a plane wave radiates from the output of the duct into free space in a form of a non-plane wave due to the diffraction when the wave leaves the duct. The energy density for ideal case of a duct made of a certain material, density fluid inside “ 𝜌 ” , “ 𝑣 ” velocity of the fluid and “c” is the velocity of sound in fluid (for air: 𝜌 =1.225 kg/m 3, c=343 m/s) at a given time is:

𝜌𝑣 2 + 𝜌 2

𝜌𝑐 2

2 (2) The first part in the above equation for energy density is the acoustic kinetic energy per unit volume, and the second part is identified as the potential energy per unit volume due to compression of the fluid. Plane waves carry the majority of the energy entering and exiting the duct. As a result, the acoustic pressures associated with the incident and transmitted acoustic waves can be used to calculate the sound energy incident and transmitted from the duct [29]. The kinetic and potential energy of a plane wave are the same. This leads to the conclusion that the energy in a sound wave moves in the same direction as the sound speed.

𝑊=

For the case when the density varies with position, a single wave equation for the acoustic part of the pressure is provided as:

𝜕 2 𝑝

1

𝜕𝑡 2 = 𝜌𝑐 2 ∇∙(

𝜌 ∇𝑝) (3)

A time-harmonic wave is a specific example in which the pressure varies with time as follows:

𝑝(𝑥, 𝑡) = 𝑝(𝑥)𝑒 𝑖𝜔𝑡 (4) where  = 2  f is the angular frequency, with “f” denoting the frequency. The equation reduces to an inhomogeneous Helmholtz equation in the time-harmonic case:

𝜔 2 𝑝

1

𝜌 ∇𝑝) (5)

−

𝜌𝑐 2 = ∇∙(

In the further analysis of the paper, which is dedicated to FEM simulations of an acoustic duct with one loudspeaker as a primary sound source and one loudspeaker a control source, would be preferable and helpful to determine the acoustic pressure produced by the speakers in order to build a correct model of the system. Therefore, the acoustic pressure radiated from a speaker placed in infinitely long space and small compared to the wavelength is calculated as:

𝑒 −𝑗𝑘𝑟

4𝜋𝑟 (6)

𝑝(𝑟) = 𝑗𝜔𝜌𝑤

The speaker response defined as a ratio between radiated pressure and supply voltage, depends on the acceleration response of the loudspeaker membrane and it is given by:

𝑒 −𝑗𝑘𝑟

𝑝(𝑟)

𝑎

4𝜋𝑟 (7) where “a” is noticed as the acceleration of the membrane.

𝑉 = 𝜌𝑆

𝑉

3. FEM MODELING OF SOUND CONTROL IN A DUCT

The physics of sound dispersion and the acoustic circumstances of sound generated in a duct can be modeled and visualized in FEM modeling software that offers acoustic modules for sound propagation modeling. In this paper, the COMSOL software was used for creating a model of an acoustic duct to further investigate the sound wave transmission aspect as the fundamentals have been described in the previous part of the paper. The described approach that follows, analyses the aspects of sound dispersion in a duct, taking into consideration the basics of active noise control. This implies investigation of the acoustic behavior in an acoustic duct with a sound source from a loudspeaker brought on one side of the duct, as well as the acoustic behavior inside the duct when a controlling speaker is activated. This shall provide an insight into the wave physics and fundamentals of active noise control concept.

The acoustic duct that was used as an input geometry in the model has a circular cross-section of 200 [mm] in diameter and a length of 1700 [mm] (Figure 1). The controlling speaker is placed 200 [mm] from the end in a 200 [mm] long duct of equal cross-section. The material of the duct is PVC, with its’ acoustics characteristics defined in the software database. The sound diffusivity is 0.5 m 2 /s for attenuation and dissipation acoustics model.

Figure 1: Geometry of the acoustic duct

In order to obtain the sound dispersion model inside the duct, the Pressure Acoustics, Frequency Domain study in COMSOL was used. The sound sources from the input loudspeaker and the controlling loudspeaker were simulated as a Plane Wave Radiation condition to simulate the pressure from the speakers’ membrane air pressure, where the value for the pressure amplitude was given as a 0.2 [Pa]. The phase for the input wave and the phase for the controlling wave is 0° and 180° as a basic term for noise cancelling principle. The predefined mesh for the whole geometry was set to be extra fine.

For the purpose of obtaining the dispersion of the sound inside the acoustic duct, The Frequency Domain study was calculated for frequencies up to 2500 Hz (Figure 2).

PPEELELELLELELEE EST

Figure 2: Sound Pressure Levels at the Input, Output and Control before (left) and after (right) using

a control source

In Figure 3 are given the results from the Frequency Domain study in COMSOL, where the dispersion of the Sound Pressure Level in [dB] is visualized using pressure amplitude as an input in the model only for the primary sound source (left column), and afterwards for the primary and control sound source (right column). The purpose was to provide visual representation of the Sound Pressure Level dispersion throughout the geometry of the duct before and after using a control loudspeaker in the system. The study was conducted for frequencies up to 2.5 kHz, and the results for 50,100,200,300,400,500 Hz were chosen as representatives to be given in Figure 3.

Latency of the system is also a significant aspect that needs to be taken into account because the system must record the reference microphone, compute the response and play it back on the ANC loudspeaker in the time it takes for sound to travel between these points. In this case, the distance between the reference microphone and the beginning of the “T” section is 130 cm. The speed of sound is 343 m/s, thus our maximum latency is 3.7 ms.

50 Hz

100 Hz

200 Hz

300 Hz

`400 Hz

500 Hz

Figure 3: Sound Pressure Level dispersion before (left column) and after (right column) using a

control source

In the FEM analysis of the duct, the simulation model has the attenuation effect of excitation simple harmonic sound waves at different frequencies (50–500 Hz), as shown in simulation of the sound wave transmission aspect of the duct. This is preferable to take into account before beginning of designing the active noise control system, in terms of parameters (length of the duct, the diameter, as well as the distance of the control speaker from the primary speaker) influence in order to determine the technical expectations of the system, with possibility of its’ optimization. From Figure 3 can be noticed that the high-frequency sound generated by the primary speaker is quickly attenuated in the duct. Therefore, low-frequency sound can reduce the acquisition bandwidth of analog to digital conversion of the signal processing unit, reduce the number of iterations of the ANC system, and improve the overall noise control effect. 4. TECHNICAL ASPECTS OF ACTIVE SOUND CONTROL

As discussed in the previous section, a good knowledge of the physics and characteristics of sound waves behavior is essential to predict the sound dispersion in order to obtain an active sound control system with solid performance.

On the other hand, significant for achieving precise and stable active sound control system is the good choice of technical specifications of its’ components (sound source, sound sensor, as well as the processing unit for acquisition and signal processing). The sound sources should provide an appropriate dynamic range to be able to capture the frequencies of interest required for active sound control, the sensors should provide good sensitivity at certain frequencies, and the signal processor units should be able to reach the acquisition and response speed, as well as fast convergence. Also, the choice of controller should be such that it should be able to add a larger number of channels by adding modules for acquisition of analog signals, as well as modules for generating analog signals. Besides the technical requirements, another important aspect is the choice of the adaptive digital filter and adaptive algorithm, which leads to a proposal of more detailed analysis and directly affects the characteristics of the system.

Figure 4: Feedforward (left) and feedback (right) active sound control principles

Active sound control systems can be divided into two basic types: feedforward and feedback. These types can be divided into adaptive and non-adaptive, analog and digital, as well as frequency and time domain controllers. There are also hybrid systems that incorporate both types. Each type has its advantages and disadvantages, depending on the application for which they are intended to satisfy.

The simplest application to illustrate the principles of feedforward and feedback is to control plane wave sound propagation in a duct. A single-channel adaptive feedforward active noise control system consists of a reference sensor, a control source, an error sensor, a control algorithm and an electronic controller, as given in Figure 4. The reference sensor samples the input signal from the primary sound source which is transmitted to the controller and processed to produce the desired cancelling signal to drive the control loudspeaker. An adaptive digital filter and an adaptive algorithm that adjusts the weights of the adaptive digital filter are included in the controller. The error sensor detects the remaining signal after control and feeds it into the control algorithm, which updates the control filter weights to reduce the signal. For broadband noise control, the controller's signal processing time must be less than the time it takes for the acoustic signal to travel from the reference sensor to the control source, but there is no maximum processing time for tonal noise control because the signal is repeating. The electroacoustic circuit from the primary loudspeaker to the error microphone output is known as the primary path. When a reference signal that is correlated with the error signal is available, feedforward controllers are preferable to feedback controllers due to their inherent stability. The common problem of feedback of the control source output to the reference sensor through the feedback path is one disadvantage of feedforward controllers that is not shared by feedback controllers. Instability will almost certainly arise unless this is addressed in the controller adaption algorithm and control filter. The only component that differs between a time domain and a frequency domain system is the electronic controller section (as shown in Figure 4).

Referring to the Figure 4, can be seen that the error microphone picks up the incoming signal which is processed to derive a suitable control signal for the control source such that the error signal is minimised. Thus it is clear that the feedback type of controller will function best when the predictability of the incoming signal is good. Thus resonances in structural and acoustical systems can be controlled, and noise which has a high normalised autocorrelation for any time delay greater than the delay through the control system (which includes the control source and error sensor) is also controllable. Tonal noise is characterised by a high autocorrelation and thus is well suited to feedback control. A disadvantage of feedback controllers is their inherent instability at higher frequencies where the phase response is not easily controlled. This can cause serious acoustic noise problems in the presence of high frequency noise or if the physical system being controlled changes too much from the design condition (for non-adaptive feedback control) or too rapidly between states (for adaptive feedback control). To maximise robustness (or minimise instability problems) it is essential that the microphone be placed as close as possible to the control source which will have the effect of minimising system delays and thus maximising the autocorrelation of the noise at time delays greater than the control system time delay. The disadvantage of placing the error sensor close to the control source is that because of near field effects, the sound pressure at large distances from the error microphone may not be significantly reduced.

The propagation path from the anti-noise speaker to the error microphone is called the “secondary path” and it must be included an estimate of that secondary path in the system. The final path to consider is the feedback path from the anti-noise speaker to the noise reference microphone. The anti- noise signal from our reference microphone should be subtracted or else we have a continuous feedback loop which will lead to incorrect results.

This analysis of the active sound control background is helpful to proceed to a design of an active sound control experimental setup duct.

Figure 5: Proposed experimental acoustic duct

As described in the previous chapter, FEM software was used to examine the behavioral characteristics of sound waves in a duct with a uniform circular cross section and a PVC material (Figure 5). The same pipe geometry and material of the duct will be used for experimental modeling of active sound control using feedforward active noise control. Two Visaton W 200-8 HiFi woofers will be used for this purpose, one of which (the primary) will be used to simulate the primary harmonic excitation, and the other as a secondary sound source to generate a sound wave with the opposite phase of the primary. Two PCB Piezotronics 130F20 microphones will be used to measure the output signals from the sound sources, one as a reference microphone and the other as an error microphone which is placed at the end of the PVC duct on the location where is expected the noise cancellation to occur. The FPGA Real-time controller cRIO 9022 from National Instruments will be used to process the signals and determine the coefficients of the adaptive filter. The acquisition modules used are NI 9234 for analog input signals from the microphone and NI 9263 for the analog output signals to the speakers. The adaptive filtering and the adaptive algorithm will be manipulated using the LabView software package.

5. CONCLUSIONS AND FUTURE WORK

In this paper, the aspects of FEM modeling and developing an active noise control system in a duct are presented, taking into consideration the physics of sound dispersion in such system, as well as the technical requirements that need to be satisfied in order to successfully control the acoustic conditions inside a chosen duct geometry. The experimental modeling through the construction of a system for active control of the acoustic environment is a new emerging technique and great potential

for application in many modern applications. With the help of software modeling, the performance of adaptive algorithms in such an application is determined, as well as the necessary technical issues in order to provide appropriate conditions for effective implementation of the system.

As a future work proposal, the physical conditions and the parameters that affect the performance of the active control system will be considered through optimizing the construction of an experimental physical model of an acoustic duct, as well as the challenges in acquisition of signals and their processing. A conducted theoretical analysis of adaptive control as a key part of the active sound control system should provide insight into the impact of adaptive algorithms and their parameters on the experimental modeling of the system. Theoretical analyzes of adaptive control by using adaptive algorithms will be confirmed in order to verify the applied methodology and approach. The active acoustic sound control system will find its application for further scientific research and practical purposes to progress and develop in the field of acoustics. 6. REFERENCES

1. Hansen, C.N., 1999. Understanding active noise cancellation . CRC Press.

2. Berglund B, Hassmén P, Job RF. Sources and effects of low-frequency noise. J Acoust Soc Am. 1996 May;99(5):2985-3002. doi: 10.1121/1.414863. PMID: 8642114.

3. Hansen, C.H. and Bies, D.A., 1995. Engineering noise control . London: Spon.

4. Elliot, S.J. and Nelson, P.A., 1995. Active Noise Control: Low-frequency techniques for suppressing acoustic noise leap forward with signal processing.

5. C. H. Hansen and B. I. F. Goelzer, “Engineering Noise Control,” p. 52, 2009

6. Ardekani, I.T. and Abdulla, W.H., 2011. On the convergence of real-time active noise control systems. Signal Processing , 91 (5), pp.1262-1274.

7. Kajikawa, Y., Gan, W.S. and Kuo, S.M., 2012. Recent advances on active noise control: open issues and innovative applications. APSIPA Transactions on Signal and Information Processing , 1 .

8. Lam, B., Gan, W.S., Shi, D., Nishimura, M. and Elliott, S., 2021. Ten questions concerning active noise control in the built environment. Building and Environment , 200 , p.107928.

9. Wise, S. and Leventhall, G., 2011. Active noise control as a solution to low frequency noise problems. noise notes , 10 (1), pp.29-37.

10. C. H. Hansen and B. I. F. Goelzer, “Engineering Noise Control,” p. 52, 2009

11. Ardekani, I.T. and Abdulla, W.H., 2011. On the convergence of real-time active noise control systems. Signal Processing , 91 (5), pp.1262-1274.

12. Kajikawa, Y., Gan, W.S. and Kuo, S.M., 2012. Recent advances on active noise control: open issues and innovative applications. APSIPA Transactions on Signal and Information Processing , 1 .

13. Chang, C.Y., Kuo, S.M. and Huang, C.W., 2018. Secondary path modeling for narrowband active noise control systems. Applied Acoustics , 131 , pp.154-164.

14. Meléndez, R., 2019. Active noise control in the presence of uncertain and time-varying disturbances (Doctoral dissertation, Communauté Université Grenoble Alpes).

15. Moazzam, M. and Rabbani, M.S., 2014. Performance evaluation of different active noise control (ANC) algorithms for attenuating noise in a duct.

16. Zimmer, B.J., Lipshitz, S.P., Morris, K.A., Vanderkooy, J. and Obasi, E.E., 2003. An improved acoustic model for active noise control in a duct. J. Dyn. Sys., Meas., Control , 125 (3), pp.382-395.

17. Suman, T. and Venkatanarayana, M., 2021. Active Noise Control for PVC Duct Using Robust Feedback Neutralization F× LMS Approach. Journal of Control, Automation and Electrical Systems , 32 (5), pp.1189-1203.

18. Kim, H.W., Park, H.S., Lee, S.K. and Shin, K., 2011. Modified-filtered-u LMS algorithm for active noise control and its application to a short acoustic duct. Mechanical Systems and Signal Processing , 25 (1), pp.475-484.

19. Chen, K.C., Chang, C.Y. and Kuo, S.M., 2017, September. Active noise control in a duct to cancel broadband noise. In IOP Conference Series: Materials Science and Engineering (Vol. 237, No. 1, p. 012015). IOP Publishing.

20. Ratham, V., Ramaiah, S., 2013. Development of Active Noise Control (ANC) System for an acoustic duct.

21. Landau, Ioan & Melendez, Raul & Dugard, Luc & Buche, Gabriel, 2017. Robust and Adaptive Feedback Noise Attenuation in Ducts. IEEE Transactions on Control Systems Technology. PP. 1-8. 10.1109/TCST.2017.2779111.

22. M. Larsson, S. Johansson, L. H˚akansson and I. Claesson, 2008, October. Performance Evaluation of a Module Configured Active Silencer for Robust Active Noise Control of Low Frequency Noise in Ducts, Research Report No 2008:06, Blekinge Institute of Technology, ISSN:1103-1581.

23. Toochinda, V., Hollot, C.V. and Chait, Y., 2001, December. On selecting sensor and actuator locations for anc in ducts. In Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No. 01CH37228) (Vol. 3, pp. 2593-2598). IEEE.

24. Sawada, Y. and Ohsumi, A., 2000, June. Active noise control of sound wave in a one-dimensional duct. In Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No. 00CH36334) (Vol. 5, pp. 3013-3017). IEEE.

25. Burián, L. and Fuchs, P., 2005, September. A simple active noise control in acoustic duct. In Proceedings of the 2005 European Conference on Circuit Theory and Design, 2005. (Vol. 3, pp. III-265). IEEE.

26. Burgess, J.C., 1981. Active adaptive sound control in a duct: A computer simulation. The Journal of the Acoustical Society of America , 70 (3), pp.715-726.

27. Dumitrescu, C., Moise, I.M., Soare, B., & Dumitru, N, 2013. Adaptive noise cancellation using LabVIEW. IEEE 19th International Symposium for Design and Technology in Electronic Packaging (SIITME) , 139-143.

28. Strek, T., 2020. Modeling of sound power transmission within duct systems. Vibrations in Physical Systems , 31 (3).

29. Rienstra, S.W., 2015. Fundamentals of duct acoustics. Von Karman Institute Lecture Notes .