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Active control of sound

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

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Active control of sound

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  1. ACTIVE CONTROL OF SOUNDProfessor Mike BrennanInstitute of Sound and Vibration ResearchUniversity 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 shortcompared 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 longcompared with typical dimensions Lower frequency solution.

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

  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 where U+is the velocity of the right-hand piston and U-is the velocity of the left-hand piston. For x > 0 the complex pressure and particle velocity fluctuations can be written as:

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

  11. Cancellation of downstream radiation which leads to Secondary source Primary source This requirement is that is the secondary source is a delayedinverted 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 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 -1 0 1 -1 0 1 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 -1 0 1 -1 0 1 Note that when L=nλ/2 the pressure upstream of the primary source =0

  14. Time domain interpretation Secondary source Primary source

  15. Cancellation of downstream radiation using a pair of 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 Primary source Secondary sources

  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 3 3 2 2 1 1 0 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 3 3 2 2 1 1 0 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5

  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 Secondary sources Primary source

  20. Sound absorption by real sources Acoustical impedance Mechanical impedance Electrical impedance Electrical power supplied 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 To set the pressure downstream of the secondary source to zero Absorbing surface having a complex reflection coefficient R Secondary source Primary source

  22. The influence of reflections from the primary 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 Secondary source Primary source

  23. LOUDSPEAKER MICROPHONE TRANSFORMER SOUND LEVEL METER PHASE ANGLE AMPLI-TUDE HARMONIC SOURCE SOUND ANALYZER AMPLIFIER Adaptation in Feedforward Control Active Control of Transformer Noise, Conover 1956 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 Primary contribution Reference signal Error signal Electronic controller Electroacoustic system Periodic Primary source Error sensor Secondary source Electrical reference signal Electronic controller (Unaffected by secondary source)

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

  26. Control of random noise in a duct Sound from Primary source Error sensor Secondary source 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 Since the system is linear and time-invariant, we can transpose the signal paths to give Filtered reference signal Error signal Error path Controller and feedback path Filtered reference signal disturbance and measurement noise The block diagram becomes Primary and measurement noise Error signal Controller and feedback path Error path

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

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

  31. Optimal controller 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 To find minimum error substitute into

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

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

  34. Digital implementation of the controller The controller must have a delay of seconds The overall frequency response of the controller is Sampling time Frequency response of filters and data converters Digital filter Causality condition 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. Side view Plan view Active control of sound in a duct – experimental work (Roure 1985)

  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. 1130-1136, 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 www.bombardier.com Periodic excitation generates intense harmonic soundfield inside cabin

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

  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 SYSTEM OFF SYSTEM ON Typical Performance of an Active Aircraft System 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 www.Bose.com

  50. Active headrest

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