1. ACTIVE CONTROL OF SOUND Professor Mike Brennan Institute of Sound and Vibration Research University of Southampton, UK

2. Active control of sound
Active control of sound in ducts
Single secondary source
Two secondary sources
Where does the power go?
Control of harmonic disturbances
Control of random disturbances
Single channel feedforward control
Constraint of Causality
Active control of sound in enclosures
Cars
Aircraft
Active head sets
Vibroacoustic control

3. Passive Control of Sound
Sound source
Observer
Passive control relies on barriers, absorption and damping.
It works well when the acoustic wavelength is short compared with typical dimensions  Higher frequency solution.

4. Active Control of Sound
Sound source
Observer
Acoustic or structural actuators are driven to cancel waves:
It works well when the acoustic wavelength is long compared with typical dimensions  Lower frequency solution.

5. Patent for Active Control of sound by Paul Lueg 1936
Active Control of Duct-Borne Sound
Patent for Active Control of sound by Paul Lueg 1936

6. Loudspeaker source in a duct
If the frequency of interest is such that the acoustic wavelength is greater
than twice the dust cross-section then it can be modelled as a pair of massless pistons forced to oscillate apart with a fluctuating volume velocity q(t) between them.

7. Loudspeaker source in a duct
For x > 0 the complex pressure and particle velocity fluctuations can be written as:
For x < 0
where U+ is the velocity of the right-hand piston and U- is the velocity of the left-hand piston.

8. The plane monopole source

9. The plane monopole source
We define the source strength as So

10. Cancellation of downstream radiation using a single secondary source
Choose a secondary source strength to set pressure field downstream of secondary source to zero
Primary source
Secondary source
The fields due to the primary and secondary source are
Use the principle of superposition to calculate the net sound field

11. Cancellation of downstream radiation
Primary source
Secondary source
This requirement is
which leads to
that is the secondary source is a delayed inverted form of the primary source.

12. The net sound field in the duct
The field between the primary and secondary sources is give by
Upstream of the primary source it is given by
Downstream of the secondary source it is given by

13. The net sound field in the duct-1 1
0.5
1.5 2
2.5
Note that when L=nλ/2 the pressure upstream of the primary source =0

14. Time domain interpretation
Primary source
Secondary source

15. Cancellation of downstream radiation using a pair of sources
Primary source
Secondary sources
Downstream of the second secondary source the net pressure field can be set to zero by setting
With two sources it is possible to ensure zero radiation upstream of the
Secondary source pair by setting

16. The net sound field in the duct
The field upstream of the secondary sources is given by
Between the secondary sources it is given by
Downstream of the secondary sources it is given by

17. The net sound field in the duct
0.5 1
1.5 2
2.5 3

18. Time domain interpretation
The secondary sources are given by
To enable interpretation in the time domain let us choose a primary source strength whose Fourier transform is some function i.e.,
In the time domain this assumes
It then follows that
or in the time domain So

19. Time domain interpretation
Primary source
Secondary sources

20. Sound absorption by real sources
Electrical power supplied
Electrical
impedance
Mechanical
impedance
Acoustical
impedance
The acoustical power can be negative; in such cases less electrical
power will be required to sustain a given piston velocity u

21. The influence of reflections from the primary source
Absorbing surface having
a complex reflection
coefficient R
Primary source
Secondary source
To set the pressure downstream of the secondary source to zero

22. The influence of reflections from the primary source
Secondary source
For a primary source next to the reflecting surface (D=0)
Now, if R=1, then
Thus the secondary source strength required to cancel the sound field
becomes infinite when

23. Adaptation in Feedforward Control
Active Control of Transformer Noise, Conover 1956
TRANSFORMER
AMPLIFIER
PHASE
ANGLE
AMPLI-TUDE
HARMONIC SOURCE
SOUND ANALYZER
SOUND LEVEL METER
LOUDSPEAKER
MICROPHONE
An error microphone is introduced to monitor the performance.
Changes in the disturbance and plant response, from loudspeaker to the microphone, require adaptation of the feedforward controller.

24. Single channel feedforward control
Periodic
Primary
source
Error
sensor
Electrical
reference
signal
Secondary
source
Electronic
controller
(Unaffected by
secondary source)
Reference
signal
Electronic
controller
Electroacoustic
system
Error
Primary
contribution

25. Single channel feedforward control
Reference
signal
Electronic
controller
Electroacoustic
system
Error
Primary
contribution
At the n-th harmonic the error signal can be completely cancelled if
Reference signal is

26. Control of random noise in a duct
Sound from
Primary source
Secondary
source
Error
sensor
Detection
sensor
Electronic
controller
There are two main differences between the control of random and
harmonic disturbances
The detected signal x(t) is generally influenced by the
electroacoustics of the feedback path
2. There is a constraint of causality on the controller

27. Control of random noise in a duct
Measurement noise
at detection sensor
Primary path
Signal at
detection sensor
Signal to
secondary source
Controller
Error
signal
Error path
Signal due
to primary
source
Feedback path
Measurement noise
at detection sensor

28. Optimal controller The block diagram becomes
disturbance and
measurement
noise
The block diagram becomes
Primary and
measurement
noise
Error
signal
Controller and
feedback path
Error path
Since the system is linear and time-invariant, we can transpose
the signal paths to give
Controller and
feedback path
Error path
Error
signal
Filtered reference signal
Filtered reference signal

29. Optimal controller Power spectral density of the error signal is
where E[ ] is the expectation operator and * denote complex conjugation
Now So
This can be written in standard Hermitian quadratic form as
(dropping the explicit dependence on frequency)

30. Optimal controller
The power spectral density of the error signal can be written as
Global minimum So

31. Optimal controller To find minimum error substitute into To give
which can be written as
Now
and
Coherence between signals from
detection sensor and error sensor
prior to control So
The maximum possible attenuation in dB at each frequency is thus given by

32. Optimal controller So the optimal controller is given by Controller
Error
signal
Error path
Feedback path
So the optimal controller is given by

33. Digital implementation of the controller
Sound from
Primary source
Secondary
source
Error
sensor
Detection
sensor
Electronic
controller
Digital filter
Analogue
to digital
converter A D C
Digital to
analogue
anti alias
reconstruction
filter

34. Digital implementation of the controller
The overall frequency response of the controller is
Sampling time
Frequency response of
filters and data converters
Digital filter
Causality condition
The controller must have a delay of seconds
Approximate delay through an analogue filter is roughly due to 45°
phase lag or 1/8 cycle of delay at its cut-off frequency, fc
Total delay through two filters which have a total of n poles is n/8fc
The cut-off frequency is typically 1/3 the sampling frequency (fs=1/T), so that fc=fs/3=1/(3T)
Allowing 1 sample delay for the data converters and the digital filter
means the total delay is given by

35. Causality condition - example
Sound from
Primary source
Secondary
source
Error
sensor
Detection
sensor
Electronic
controller
Rectangular duct with largest dimension D=0.5m – single channel
control can only be achieved below about 300 Hz
Sampling frequency = 1kHz (T=1ms)
Two 4th order analogue filters (n=8)
Delay in analogue path is about 4ms

36. Active control of sound in a duct – experimental work (Roure 1985)
Side view
Plan view

37. Active control of sound in a duct – experimental work (Roure 1985)
Amplitude spectra of the fan noise at the error microphone with a mean
duct velocity of 9m/s
Active control off dB
Active control on
Frequency (Hz)

38. Active control of sound in enclosures
Electronic Sound Absorber
H.F. Olson and E.G. May, Journal of the Acoustical Society of America,
pp , 1953

39. Active Control of Sound inside Cars
Low-frequency engine noise in the car cabin can be controlled with 4 loudspeakers, also used for audio, and 8 microphones, also used for hands-free communication (Elliott et al. 1986).

40. Initial Demonstration Vehicle

41. Measured Results in a Demonstration Vehicle
A-weighted sound pressure level at engine firing frequency

42. Active Sound Control in Propeller Aircraft
System is standard fit on Dash 8 Q400 (Stothers et al. 2002)

43. Active Sound Control in Propeller Aircraft
Periodic excitation generates intense harmonic soundfield inside cabin

44. Active Sound Control in Propeller Aircraft
Spectrum of Pressure Inside Propeller Aircraft
Dash-8 Series 200: Reduction 11.3 dB(L), 8.2 dB(A)
Frequency (Hz)
dB(A) re arbitrary level

45. Active Sound Control in Propeller Aircraft
Control System for Propeller Aircraft Active Noise System
Centralised digital system made by Ultra Electronics controls 5 harmonics with 48 structural actuators at 72 acoustic sensors, distributed throughout cabin.

46. Active Sound Control in Propeller Aircraft
Typical Performance of an Active Aircraft System
SYSTEM OFF
SYSTEM ON
Single multichannel centralised digital controller used with 48 actuators and 72 sensors distributed throughout the cabin

47. Feedback control of Sound
Active Headset using Feedback Control
If no external reference signal is available, conventional feedback control can be used to control sound at low frequencies.

48. Feedback control of Sound
Active Headset using Feedback Control
Active control off dB
Active control on
Frequency (Hz)

49. Feedback control of Sound
Active Headset using Feedback Control

50. Active headrest

51. Active headrest – zones of quiet
kL=0.2
KL=0.5
10dB
20dB
KL=1
KL=2

52. Active Vibroacoustic Control

53. Objective: To minimise the transmitted sound power
The Problem
Incident
sound power
baffle
Transmitted
sound power
Simply supported panel
Objective: To minimise the transmitted sound power

54. The Active Control System
Panel
Accelerometer
Piezoceramic actuator
Analogue controller

55. Piezoceramic ActuatorsF d
plate
actuator M
plate F

56. Active Control Performance (simulations)
Feedback gain
Sound transmission ratio (dB)
Integrated from 0-1kHz
Piezoceramic Actuators
Force Actuators
Frequency (Hz)
Sound transmission ratio (dB)
Increasing gain

57. What Happens to the Panel Vibration?
Integrated from 0-1kHz
Kinetic energy (dB)
Increasing gain
Frequency (Hz)
Piezoceramic Actuators
Kinetic energy (dB)
Force Actuators
Feedback gain

58. Experimental Result (after Bianchi et al)
Pressure (dB re arbitrary units)
Gain limited by accelerometer resonance
Compensator used in feedback circuit

59. Concluding Remarks
Active sound control is being used as an alternative to passive
control in many different applications especially at low
frequencies
ducts
aircraft
automobile
Combination of acoustic and vibration control maybe seen in
the future