Actuators positioning for multichannel active control system in circular ducts

Actuators positioning for multichannel activecontrol system in circular ducts

Alex Boudreau a,*, AndreÂ L'EspeÂ rance a, Martin Bouchard b,Bruno Paillard a

aG.A.U.S. University of Sherbrooke, Sherbrooke, QueÂbec J1K 2R1, CanadabSchool of InformationTechnologyandEngineering,UniversityofOttawa,Ottawa,Ontario,K1N6N5,Canada

Received 8 February 1999; accepted 21 June 1999

Abstract

In the particular case of multichannel control, the acoustic power limit of loudspeakers maybe an important restriction for active control application when the noise levels are very high.The goal of this paper is to present the di�erent parameters that allow to minimize the power

used by the control sources for a multichannel active control system in a circular duct. Anexperimental study of the longitudinal distribution pressure ®eld for the particular case ofhigher order modes, as well as some experimentations with active control for di�erent geo-

metric conditions have been done to analyze this problem. The results of these experimenta-tions have allowed us to understand that the most in¯uential phenomenon that determines thecontrol sources optimum position are the re¯ection from ducts closed end. With this result in

mind, a simple and e�cient methodology of positioning has been developed. The e�ciency ofthis positioning method has been proved from experimental tests. # 2000 Elsevier ScienceLtd. All rights reserved.

1. Introduction

The positioning of the error sensors for a multichannel control system in a circularduct is currently an important subject of research [1±4]. Indeed, the sensors posi-tioning plays a decisive role on the noise reduction obtained. However, the controlsources positioning is still a problem, and it is almost absent of the literature. Even

Applied Acoustics 59 (2000) 323±335

www.elsevier.com/locate/apacoust

0003-682X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.

PI I : S0003-682X(99 )00034 -1

* Corresponding author.

E-mail address: [email protected] (A. Boudreau).

so, the use of several speakers for a multichannel control system presents animportant problem regarding the necessary acoustic power needed for each speaker.In fact, the necessary power for the control sources can occasionally become greaterthan the one generated by the primary source, depending on the transfer functioncombination between di�erent speakers and error microphones. The required powerfor the control sources is, sometimes, an important limitation for industrial appli-cations, mostly when the primary acoustic ®eld is very high. Thus it seems that theoptimization of the control sources positioning is an important factor, in order tominimize the power used.One of the objectives of this paper is to quantify the importance of the limited

power for various parameters: frequency, ducts length, control sources positioningand error sensors plane. The ®rst section will present an experimental analysis of thedistribution pressure ®eld in a semi-open duct. The e�ect of the source position and ofthe duct length on the interference pattern will be analyzed from an active controlpoint of view. The second section will study an analysis of the acoustic power used byactuators in a multichannel system case. The e�ects of closed-end re¯ections, actua-tors position and error sensors position on the power used for the control sources willbe analyzed. With this in mind, a positioning method has been developed and eval-uated by experimental tests to minimize the power used by control actuators.

2. Longitudinal distribution of acoustic pressure ®eld

In the case of the inside duct sound propagation, it is common knowledge that thestationary waves are established to form an interference pattern, following there¯ection coe�cients and radiation impedance at the duct end [4±7]. Understandingthis phenomenon of propagation is relatively simple for low frequencies when theplane mode (0,0) is the only one to be propagated in the duct. However, when sev-eral propagation modes occur, the inside duct pressure ®eld distribution becomesmore complex because of the modes combination. In those cases, the pressure ®eld isnot uniform, not only following the duct axis, but also in each duct section. Beforeanalyzing the power actuators problem for the multichannel active control, itappears important to review the inside duct pressure ®eld longitudinal distributionfor the higher order modes.

2.1. Experimental assembly

To study the inside duct pressure ®eld longitudinal distribution, an experimentalstudy has been realized with the assembly shown in Fig. 1. The pressure ®eld isgenerated in a PVC duct of 30 cm diameter and 2.05 m in length, with a closed andopen end. A ®xed speaker on the duct wall is used to generate a pressure ®eld in theduct. The measurements were taken with the help of an acquisition system whichuses a ®ve rotary microphones probe. A rod following the duct length axis is used torotate the ®ve microphones, which are placed on a support in the duct radius axis.These ®ve microphones are distributed in uniform way, along the radius. A variable

324 A. Boudreau et al. / Applied Acoustics 59 (2000) 323±335

step electric motor is used to rotate the rod and to move the ®ve microphones, atevery 10�. A multiplexer is installed to make the transition from one microphone toanother. This assembly allows to choose the measurement plane according to theduct longitudinal axis. A white noise between 100 Hz and 2 kHz is generated by thespeaker installed on the duct wall. The noise level recordings have been done using aprogram on a PC. This program records 801 lines of an autospectrum, with theHPIB port of an analyzer (BK2034).For the studied frequency range (100 Hz to 2 kHz), some higher order propaga-

tion modes are found. The cut-o� frequency of the ®rst mode for the dimensions ofthe duct is 675 Hz. For the case of the frequencies higher than 675 Hz, the pressure®eld in a section of the duct is not uniform. The measurements for each microphoneallow to draw the noise level distribution of one frequency for a given duct section.For instance, Fig. 2a and b gives, respectively, the pressure ®eld distribution for asection at 800 and 1300 Hz. In Fig. 2a, it is easy to recognize the creation of a nodalline following the duct diameter, since the mode (0,0) and (0,1) are the only ones tobe propagated. The combination of modes (0,0), (0,1) and (0,2) at 1300 Hz generates

Fig. 1. Measurement of acoustic pressure ®eld in a section: experimental assembly.

Fig. 2. (a) Distribution of noise levels in a section at 800 Hz, and (b) 1300 Hz.

A. Boudreau et al. / Applied Acoustics 59 (2000) 323±335 325

a complex pressure ®eld distribution that makes it di�cult to identify the nodallines. Since it is di�cult to study the longitudinal distribution of the noise levelsfrom a section to another, it seems preferable to use the measured mean level, in onesection, as an indicator.

2.2. Measurements results

2.2.1. OverviewFig. 3a±d present examples of mean noise level distribution following the duct axis

at 800, 1000, 1200 and 1400 Hz, respectively. The global mean level inside the ductvaries signi®cantly with the frequency. These results show the interference patternfollowing the duct axis. However, these patterns become lower for high frequencies.Indeed, the di�erence between maximum and minimum mean level goes from 14 to4 dB between 800 and 1400 Hz.

2.2.2. E�ect of the actuator position on the interference pattern

The source position following the duct axis has an e�ect on the interference pat-tern identi®ed before. To illustrate this phenomenon, two positioning con®gurationsfor the noise source are presented (see Fig. 4).Because the interference patterns are well de®ned at low frequencies, a frequency

of 800 Hz will be used to describe the e�ect of the source position. Fig. 5 shows theresults of the two positions from Fig. 4. The noise source position following the ductaxis has no e�ect on the interference pattern position and shape. On the other hand,the mean pressure level for the ®rst con®guration is approximately 5 dB higher thanthe one from the second con®guration.On primary analysis, we understand that this general diminution of the pressure

®eld results from the phase between the direct and re¯ected waves for the ®rst modeon the duct closed end (see Fig. 6). For a phase of approximately 180�, the pro-gressive wave pressure is minimized, even though a phase of 0� or 360� increases thatpressure. For higher frequencies, upper modes appear and the relative e�ect of thesevariations (associated to the plane mode) are reduced. Thus, at low frequencies,when a small number of modes are propagated, and the predominance of the planemode continues to be important, we see that the source position plays a signi®cantrole on the global mean level inside the duct.For the ®rst con®guration, the phase between emitted and re¯ected wave isÿ14.5�. The second con®guration shows a phase of 140.5�. Thus, we can concludethat the con®guration #1 is a more e�cient source position.

2.2.3. E�ect of the duct length on the interference pattern

The e�ect of the duct length on the interference pattern position and its shape hasbeen evaluated with the help of a third con®guration shown on Fig. 7. The length ofthe duct has been reduced from 2.05 to 1.85 m in comparison to the one from con-®gurations #1 and #2. The measurements of the mean levels are taken at the sameplace than the ones for the ®rst and the second con®guration. The closed end of theduct is used as a reference.


Fig. 3. (a) Interference pattern versus duct axis at 800 Hz; (b) 1000 Hz; (c) 1200 Hz; and (d) 1400 Hz.

A.Boudrea

uet

al./

Applied

Acoustics

59(2000)323±335

327

Fig. 7. Con®guration #3.

Fig. 4. Con®gurations used for the primary source.

Fig. 5. Mean levels for case #1 and #2 used for primary source.

Fig. 6. Schematic explanation of the re¯ex wave's e�ect on the global noise level inside the duct.


Fig. 8 shows the mean levels for the three con®gurations, for di�erent measure-ment locations.From the results of the previous three subsections, the following conclusions have

been made:

a. The re¯ection of the plane mode from the duct closed end has a signi®cante�ect on the pressure ®eld mean level inside the duct.

b. The interference pattern position is not in¯uenced by the source position butonly by the duct length.

c. Finally, the amplitude of the interference pattern pressure ®eld inside the ductdecreases at high frequencies.

2.3. Theoretical simulation

The same kind of results have been obtained for the last three con®gurations with atheoretical model of pressure ®eld in a circular duct [4]. Fig. 9 shows results from thesimulations for three con®gurations. Although the relation between the theoreticaland experimental results are not perfect,1 the general tendencies are well respected.

3. Active control experimentation

The results from the previous sections have shown that the noise source positiongoverns the interference pattern amplitude, particularly at low frequencies This sec-tion will consider that problem, in the case of the multichannel active control. In thebeginning, the plane mode re¯ection problems will be studied, with the help of con-trol experimentation. The e�ect of the error sensors and the control sources planeposition will be considered later.

Fig. 8. Mean levels for cases #1, #2 and #3 used for primary source.

1 The di�erences between the theoretical and experimental results can be due, in part, to the interaction

between the ¯uid and the assembly structure. Indeed, in comparison to the theoretical model with the

rigid and perfect re¯ective wall assumptions, the assembly vibrates and transmits noise.


3.1. Control problems in presence of re¯ections

When the position of the control sources produces a phase of 180� between theemitted wave and re¯ected wave from the duct closed end, the power used by thecontrol sources becomes more important. In order to explain this phenomenon,some control experimentations with and without re¯ections have been realized usingthe assembly shown in Fig. 10.To make these control experimentations, a feed-forward multichannel system has

been used. This control algorithm running on aDSPC31 is linked to a PC board [8]. Allthe control speakers have the same position following the duct axis and are distributedin uniform way around the duct circumference. The active control experimentation willcover a frequency range from 1000 to 1350 Hz. For that interval, ®ve microphones and®ve speakers are used. The number of channels used and themicrophones disposition inthe control plane are based on the methodology described in Ref. [4]. The controlexperimentations have beenmade using a pure tone with a frequency step of 10Hz. Thepower used by the control sources has been estimated for each frequency.To study the e�ect of the re¯ections, two cases have been considered: the ®rst case

with and the second one without absorbent material covering the duct closed end.For these control experimentations, the error microphones plane A has been used(see Fig. 10). The normalized electric power used by the control sources is calculated

Fig. 10. Assembly used for control experimentation.

Fig. 9. Mean levels for cases #1, #2 and #3 used for primary source (model).


from rms voltage measures. These measurements are taken from each control sourceand are normalized by the primary source voltage:

P � �2rms�sc��2rms�sb�

where:

sb=noise source used to generate the primary ®eldsc=control sources.

Fig. 11a and b give the normalized electric power used by each control source forthe cases with and without absorbent material.For the normalized power higher than unity, the control sources require more

acoustic energy than the primary source. Then, we have an overconsumption prob-lem. These results show that the re¯ections from the duct closed end have animportant e�ect on the power used by the control sources. Furthermore, the graphon Fig. 11 shows that the overconsumption problem is more important at low fre-quencies, and that it becomes blurred for higher frequencies because the plane modeinterference becomes less and less important.

3.2. E�ect of the sensor plane position

Due to the interference pattern following the duct axis, the microphone plane canbe on a maximum or a minimum of pressure (see Section 2.2). To check how themicrophone plane's position on the interference pattern in¯uences the control sour-ces consumption, a second microphone plane position (B) has been considered (seeFig. 10). The control experimentation has been done at 800 Hz. The graph on Fig.12 shows the normalized power for the two microphone planes' positioning.The last graph does not show a lot of variations for the control sources used

power between the two error sensors positioning. The mean noise reduction mea-surements at the open end with and without control show that the e�ciency issmaller when the control is applied on a low noise level zone (noise reductions: 31.1versus 39.3 dB). This problem is related to the dynamic range of the input signalacquisition system. In a minimum pressure location, the microphones become morerapidly in measurement noise and, in this way, the control is less e�cient. Theseresults bring to the conclusion that the control sources used power reduction withthe help of the error sensor plane positioning seem to be impossible.

3.3. E�ect of the control sources' position

The phase between the direct and re¯ected wave from the duct closed end seems tobe the most in¯uential parameter for the control sources e�ciency. If the positioningof the control sources is in such a way that the phase is close to 0�, it seems possibleto minimize the used power.


However, it is not practical, on the experimental assembly, to change the primaryand control sources position. The method used for this paper consists in doing astudy of the phase between the emitted and re¯ected wave from the duct closed endversus the frequencies for the con®guration showed in Fig. 10. Fig. 13 shows thephase versus the frequencies for two speakers planes and for the geometric condi-tions of Fig 10.To make easier the analysis of the frequencies range for which the sources positions

are optimum, the graph of Fig. 14 has been built.

Fig. 11. (a) Electrical power used versus frequency for a ®ve channel active control system in presence of

re¯ections from the closed end. (b) Electrical power used versus frequency for a ®ve channel active control

system without the presence of re¯ections from the closed end.


Fig. 13. Phase between the primary source and the control sources versus frequency.

Fig. 14. Di�erence of phase versus frequency.

Fig. 12. Electrical power used by each sources for sensor plane's position A and B.


This last graph shows the di�erence between the absolute value of the plane modephase for the noise source and the control sources. It is easy to judge which kind ofsource is more e�cient. The positive zones show the frequencies where the controlsources e�ciency is predominant, and the negative zones indicate that the noisesource is more e�ciency. At 920 Hz, the control sources used power is smallercompared to 800 Hz. In fact, Fig. 14 shows a better e�ciency for the noise source at800 Hz.To con®rm that the control sources used power is lower at 920 Hz, a control

experimentation has been done. The used geometric con®guration is showed inSection 3.2. The results of the control experimentation are showed in Fig. 15. Thisgraph shows the normalized power for 920 and 800 Hz (for microphone plane A, seeFig. 10). The noise reduction is practically the same at 920 and 800 Hz but, at 920Hz, the control sources used power is lower. The maximum normalized power at 920Hz is less than 0.20. For these two frequencies, two modes are being propagated andthe pressure ®eld complexity is similar.

4. Conclusion

For a multichannel control system, the control sources used power may become areal limitation problem. To analyze this problem, an assembly has been realized inlaboratory. This assembly allows to analyze the pressure ®eld longitudinal distribu-tion inside the duct. Many multichannel control experimentations for various fre-quencies, control sources positions and error sensors plane positions have beenrealized. The results of these experimentations show that the mean pressure ®eldlongitudinal distribution has an important variation, and that the interference pat-tern position depends on the duct length and not on the noise source position. Thesevariations are generated by the plane mode interference. This phenomenon becomes

Fig. 15. Electrical power used by the control sources at 800 and 920 Hz.


less important at high frequencies because the plane mode importance becomessmaller in comparison to the higher order propagation modes.The e�ciency of a noise source can be modulated by its position following the

duct axis. It seems to be possible to optimize the control sources e�ciency if theplane mode phase between direct and re¯ected wave at the duct closed end is takeninto consideration. This control sources optimization method has been checked inlaboratory with a multichannel control system, and the obtained results havedemonstrated the validity of this approach. Thus, this work allows to install a mul-tichannel active control where the control sources acoustic power is an importantconstraint.

References

[1] Baumann DC, Grenier RA. Modal identi®cation approach to multi-modal cancellation. Proc. of

Inter-noise 92. p. 341±8.

[2] Erikson L. Higher order mode cancellation in ducts using active noise control. Proc. of Inter-noise

89.

[3] L'EspeÂ rance A, Bouchard M, Paillard B, Guigou C. US patent No. 5, 748, 750±May 5, 1998:

Method and apparatus for active noise control of high order modes in ducts.

[4] L'EspeÂ rance A, Bouchard M, Paillard B, Guigou C, Boudreau A. Active noise control in large

circular duct using an error sensors plane. Applied Acoustics 1999;57:357±74.

[5] Levine H, Schwinger J. On the radiation of sound from an un¯anged circular pipe. Physical Review

1948;73(4):383±496.

[6] Houiel F. ModeÂ lisation du champ de pression et simulation de controÃ le actif multicanal dans un

conduit circulaire. MaõÃ trise es sciences appliqueÂ es, speÂ cialiteÂ : geÂ nie meÂ canique; Groupe d'Acoustique

et Vibrations de l'UniversiteÂ de Sherbrooke, 1995.

[7] Homicz GF, Lordi JA. A note on the radiative patterns of duct acoustics modes. J Sound Vib

1975;41(3):283±90.

[8] Bouchard M. EÂ tude d'algorithmes d'adaptation rapide pour controÃ leurs actifs multi-variables.

MaõÃ trise es sciences appliqueÂ es, speÂ cialiteÂ : geÂ nie eÂ lectrique; Groupe d'Acoustique et Vibrations de

l'UniversiteÂ de Sherbrooke, 1995.


Documents

Actuators positioning for multichannel active control system in circular ducts