Previous work has demonstrated how active control may be applied to the control of random noise in ducts. These implementations, however, have been restricted to frequencies where only plane waves are propagating in the duct. In spite of this, the need for this technology at low frequencies has progressed to the point where commercial products that apply these concepts are currently available. Extending the frequency range of this technology requires the extension of current single channel controllers to multi-variate control systems as well as addressing the problems inherent in controlling higher order modes. The application of active control in the multi-dimensional propagation of random noise in waveguides is examined. An adaptive system is implemented using measured system frequency response functions. Experimental results are presented illustrating attained suppressions of 15 to 30 dB for random noise propagating in multiple modes

Elliott, S. J.

Silcox, R. J.

English

NASA Technical Reports Server

NASA Technical Memorandum 1 0 2 6 5 3
ACTIVE CONTROL OF MULTI-DIMENSIONAL RANDOM
SOUND IN DUCTS
R. J. SILCOX
S. J. ELLIOTT
MAY 1990
National Aeronautics and
Space Administration
Lanoley R_,_mr¢h C_at_r
Hampton, Virginia 23665-5225
Ur]C I , %
https://ntrs.nasa.gov/search.jsp?R=19900012287 2020-03-19T23:25:19+00:00Z

INTRODUCTION
Previous work has demonstrated how active control may be applied to the control of
random noise in ducts. 1,2 These implementations however have been restricted to frequencies
where only plane waves are propagating in the duct. In spite of this, this technology has
progressed to the point where commercial products that apply these concepts are currently
available. 3 Extending the frequency range of this technology for a fixed duct geometry requires
the development of multi-variate rather than single channel control systems and solutions to the
problems inherent in controlling higher order modes. Eriksson et al 4 used two independently
operating controllers for higher order mode control and obtained reasonable results for singular
modes. Tichy 5 suggests independent control of each mode in a multi-variate system.
This paper examines the application of active control to the multi-dimensional propagation
of random noise in waveguides. The problem of designing a realizable controller using a finite
impulse response filter and controlling the acoustic feedback path of the control source-detector
microphone path are addressed using an acoustically lined section. An adaptive system is
implemented using measured system frequency response functions. Experimental results are
presented ilhstrating suppressions of 15 to 30 dB for random noise propagating in multiple
modes.
tector V d
_ic
4.72m
I-----1.83m ---"1
coustic I//
//J liner _'_
V/l/Ill l /
t V lgilt_ Ms2
Filter 1 ]
_----'.b-_peaker
I
v
Figure 1. Schematic of duct and control system.
Error
mic 2
Frrror
mic 1
V
01
CONTROLLER DESIGN
The design of the control system parallels that of reference 1. The combination of acoustical
and control systems, shown in figure 1, is defined as a single input, multiple output system. A
block diagram incorporating the various elements of the duct and control system is shown in
figure 2. Some excitation voltage, Vp, is assumed to cause an undesired acoustic response in the
duct such that only the plane wave (mode 0) and the first cross mode (mode 1) are excited. The
output of a single detector microphone, Vd, is used as an input to a feed forward control system.
Two control voltages, Vsi, excite two loudspeakers on opposite sides of the duct. Finally, the
acoustic response downstream of the loudspeakers is represented as the error microphone
outputs, Vej.
V
P
A
1
B
(
C..
JJ
Figure 2. Block diagram of control system.
( O
J
Transfer functions between the applicable excitation voltages and the sensor output voltages
are defined as the following:
2
= Aj(a))
VP[V,,=vs2=0 Vsi Vp=0= Cji(°))
V_z=V_2=0 Vp=0
Designatingthetransferfunctionsof filter 1andfilter 2of figure 1asthevectorTi, thesensor
outputvectorrelativeto theexcitationvoltage,Vp, isgivenas
Vej CjiTiB
--=Aj+Vp i-i k
Setting this to zero and substituting Ej for the ratio Aj/B yields the expression for the controller
functions Ti that force the transmitted wave field to zero.
T i = [EjF i - Cji] -1 Ej
The function Ej is the transfer function measured between the error sensors and the detector
sensor. This makes the design of the controller independent of Vp. For previous work
involving only plane waves, this ideal controller was correct for any changing source condition
so long as the controller parameters remained constant. Since only plane wave propagation was
permitted, this arrangement could predict everything about the source in terms of it structure and
content. However, in this case, not only the frequency content but the source structure or modal
content is subject to change. The single detector microphone cannot adequately define the
magitude and phase of the spatial modes excited by the source. However, this information is
contained in the transfer function measurements between the two error microphones and the
detector microphone. Since this information is integrated into the controller only when it is
initialized, any changes in this structure will result in degraded performance of the controller even
under ideal conditions. To overcome this problem, additional detector microphones would be
necessary in order to define the source structure in the feedforward section rather than the
feedbacksection.Thisapproachhoweverimposesadditionalproblemsbeyondthescopeof this
paperaswell asadditionalhardwarecomplications.
Adaptivetechniquesmaybeappliedto overcomethis limitation for aslowlyvaryingsource
structure.Consideranadditionalvoltagevector,AVsi, is input at point 2 of figure 2, with the
controller functions having been previously set to nonzero values, Ti. The additional voltage
appearing at the inputs to the loudspeakers are
AVsi 4- Vsi ] Vp=0-- m ws i + Ti
1- Tk)
The single detector microphone output, Vd, will be modified by the above voltages multiplied by
Fi and summed. Adding an additional controller function, ATi in parallel with Ti (with inputs Vd
,and outputs summed to the outputs of Ti) a new expression may be written for the error sensor
outputs.
Vej [(1 - F'k Tk)CjiAT i + CjkTkFiAi]
Vd =E_+ 1- FkTk - FkATk
In this equation, E_is the transfer function between the jth error sensor and V d after the controller
function Ti is implemented. Setting Vej again to zero, ATi may be determined and a general
update equation determined.
Tim+l= Tm + (1-FkT_n)[E]n+lFi-(1- FkT_n)Cji-CjkT_nFi]-I n_ n+l
Here, E_n+l refers to the transfer function measured after the implementation of controller Tim .
Note that for Tim--O, the update algorithm reduces to the original controller definition.
One final comment note on the controller design. For low frequencies where only the plane
wave propagates, the controller equation was found to be nearly singular. For true plane waves
with no measurement error, this would be the case. This is due to the fact that the 2 channel
controller is redundant since only one channel is necessary. This may be used to advantage in an
arrangement where a single woofer is used to control low frequency plane waves but a pair of
midrange speakers is used to control higher frequency multimodal propagation. For the
4
implementationhere,thecontrollerfor eachsource/errormicrophonepairwastreatedasaplane
wavesystemandtheresultingscalar controller equation was solved. This applied for
frequencies up to 250 I/z, beyond which the above matrix equation was applied.
EXPERIMENTAL CONFIGURATION
In order to provide a reasonable amount of damping, a section of the duct between the
detector sensor and controller sources was lined with acoustic treatment. This provided
attenuation of the waves propagating in both directions. Thus the reflected wave field at the
detector sensor is attenuated relative to the incident acoustic wave field at the detector sensor.
This has the effect of eliminating the singularity in the controller implementation, shortening the
reverberation time of the feedback path and consequently the required controller filter length.
When the treated section is coupled to the hardwall sections at either end, any residual cut-off
modes scattered by the junction of the lined and unlined sections are attenuated so that the
necessary controller inputs are not affected.
The schematic of the duct and associated sources and sensors in shown is figure 1. The
duct cross section is 0.535m by 0.229m with the acoustic liner spanning the larger dimension.
The loudspeakers were oval and their fiat cone made up the narrower wall dimension at their
mounting location. This design yielded a first cross mode cut-on frequency of 325 Hz and a
second cross mode frequency of 650 Hz. Both of these modes have their spatial variation in the
wider dimension (0.535m) and the focus of this work is to control the plane wave and the first
cross mode in a frequency range from 50 Hz to 600 Hz. The source excitation consisted of two
speakers mounted in a similar arrangement to the controller sources. This provided control over
the input source structure. These were driven using a common random excitation but with the
speakers out of phase and at different levels in order to drive a combination of modes.
The above control algorithm was implemented using standard digital signal processing
(DSP) techniques to determine the necessary frequency response functions. The two controller
functions were implemented as finite impulse response digital filters on a TMS320C25 DSP chip
5
using256coefficientseach.All datawassampledandoutputat2048samples/second.The
frequencyresponsefunctionof eachcontrollerwasFouriertransformedto an impulseresponse
for implementationin thetimedomain.
70 _
._J
n
6O
50
.40
3O
20
0
0 /.
- __. o Cor_oo,,.,,¢',.'" "_
__. 1 c.,,.,po..,-,," ,_
\ I \ _1 v • ,..,...
I I I I I I ".' I
100 200 :500 400 500 600 700
Frequency, Hz
Figure 3. SPL and source modal distribution at error microphone location.
EXPERIMENTAL RESULTS
Figure 3 shows the spectra of the sound pressure level at error microphone 1 and the
contributions due to both the plane wave and mode 1. These were obtained by summing and
differencing the two error microphones and are valid only below the 2nd mode cut-on frequency
of 650 Hz. The overall SPLs at error microphones 1 and 2 were 102.6 and 102.7 dB. The
plane wave dominates the pressure spectrum by more than 30 dB below the cut-on of the first
mode at 325 Hz. Above mode cut-on, the higher order mode dominates the response by 10 to 20
dB.
6
_.J
t-i
7O
60
5O
40
30
20
:, ,.,,"....
0 100 200 300 400 500 600 700
Frequency, Hz
Figure 4. Effect of controller operation on SPL at error microphone 1.
30
10
O
--_ I I I I I I
O 100 200 300 400 500 600 700
Frequency, Hz
Figure 5. Attenuation at error microphones.
The effect of optimizing the controller on the SPL at error microphone 1 is shown in figure 4.
The controller is seen to provide significant attenuation across the spectrum, converging to a
minimum level in 3 iterations and remaining stable through nine iterations. The levels at iteration
0, 1, 3, and 9 are shown with most of the suppression attained in the first two iterations. The
overall reductions in SPL obtained at these iteration steps were 10.3 dB, 16.4 dB, 19.9 dB and
20.7 dB respectively. The attenuation spectra at both error microphones are shown in figure 5.
This showsthefrequencydependenceof the attenuation. In the frequency range where the plane
wave dominates (<325 Hz), the attenuation ranges from 15 to 25 dB. At higher frequencies, the
attenuation is 10 dB greater. At the mode cut-on, the resonant behavior of the duct and the
limited frequency resolution of the controller implementation limits the attenuation to about 15
dB.
m
11)
q)
o
-.,j;
70
60
50
40
30
20
B
No Control
/_ _ ..... Iteration 0
/ _ /" - \^ -- • Iteration 1
[ .'. _/ v \ ---- Iteration 3
_ • .', -; \." "..
0 1 O0 200 300 400 500 600 700
Frequency, Hz
Figure 6. Effect of controller operation on plane wave.
Figure 6 shows the level of the plane wave at similar iterations of the controller. An overall
attenuation of 19.1 dB has been obtained across the spectra from 50 to 600 Hz. It is expected
that noise floor limits were obtained over the higher frequency range. Figure 7 shows a similar
result for mode 1 where an overall reduction of 22.6 dB was attained. Both modes are quite
controllable using this configuration with better results obtained in the frequency region where
both modes are freely propagating. Above the resonance of the (1,0) mode, both modes are
controlled to a common noise floor level.
8
g,
.-.I
O
--,j:
7O
60
5O
40
3O
20
No Control
.... Iteration O
- -- Iteration 1 / ..
-- ---- Iteration 3 / :'\ %
-- - Iterati
O 1 O0 200 300 400 500 600 700
Frequency, Hz
Figure 7. Effect of controller operation on mode 1.
CONCLUDING REMARKS
These results indicate that multi-mode propagation may be controlled effectively using
active control techniques. Overall attenuations of 20 dB in SPL were obtained over a frequency
range where two duct modes were shown to be propagating. An adaptive technique was used to
mimimize the sound pressure at two error sensors with no discernible instabilities. This
controller used two independent control sources and three sensor elements to provide effective
control. This arrangernent is believed to require the minimum transducers for this source
problem and is adaptable to other control methodologies. It is noted that this technique is
sensitive to changes in the source modal content and must be adaptive in order to be able to
handle any changes in the source structure.
[1]
REFERENCES
S J ELLIOTI" & P A NELSON, "Models for Describing Active Noise Control in Ducts,"
ISVR Technical Report 127, April 1984.
9
[2] A. ROURE,"Self-AdaptiveBroadbandActive SoundControlSystem,"J.Soundand
Vibration, Vol. 101,No. 3, August8, 1985,pp. 429-441.
[3] L J ERIKSSON& M C ALLIE, "A PracticalSystemfor ActiveAttenuationin Ducts,"
SoundandVibration, February1988,pp.30-34.
[4] L J ERIKSSON,M C ALLIE, R H HOOPS& J V WARNER, "HigherOrderMode
Cancellationin DuctsusingActive NoiseControl,"Proc.of InterNoise89,Newport
Beach,CA, December4-6 1989,pp.495-500.
[5] J TICHY, "Active Systems for Sound Attenuation in Ducts," IEEE Proc. of ICASSP
1988, pp. 2602-2605.
[6] I C SHEPHERD, R F LAFONTAINE & A CABELLI, "Active Noise Control in Ducts,"
Bulletin Acoustics Australia, Vol. 13, No. 1, April 1985, pp. 17-21.
Report Documentation Page
1. Report No.
NASA TM- 102653
2. Government Accession No.
4. Title and Subtitle
Active Control of Multi-Dimensional Random Sound
in Ducts
7. Author(s)
R. J. Silcox
S. J. Elliott
9. Performing Organization Name and Addres:_
NASA Langley Research Center
Hampton, Virginia 23665-5225
12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, DC 20546-000t
3. Recipient's Catalog No.
5. Repo_ Date
May 1990
6. Performing Organization Code
8. Performing Organization Report No.
10. Work Unit No.
505-63-51-09
11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Memorandum
14. Sponsoring Agency Code
15. Supplementary Notes
Presented at Acoustics 90, Southampton, England, March 28-30, 1990.
R. J. Silcox" Langley Research Center, Hampton, Virginia.
S. J. Elliott: ISVR, Southampton, England.
16. Abstract
Previous work has demonstrated how active control may be applied to the control of
random noise in ducts. These implementations, however, have been restricted to
frequencies where only plane waves are propagating in the duct. In spite of this,
the need for this technology at low frequencies has progressed to the point where
commercial products that apply these concepts are currently available. Extending
the frequency range of this technology requires the extension of current single
channel controllers to multi-variate control systems as well as addressing the
problems inherent in controlling higher order modes.
This paper examines the application of active control in the multi-dimensional
propagation of random noise in waveguides. An adaptive system is implemented
using measured system frequency response functions. Experimental results are
presented illustrating attained suppressions of 15 to 30 dB for random noise
propagating in multiple modes.
17. Key Words (Sugge_ed by Author(s))
Active Control
Ducts
Multi-modal
Random
19. Security Classif. (of this report)
Unclassified
NASA FORM 1626 OCT
18. Distribut,on Statement
Unclassified - Unlimited
Subject Category - 71
--] 2-O. Security Classif. (of this page)I Unclassified 21. No. of pages I _" Price11 A03



Active control of multi-dimensional random sound in ducts

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