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 Control of random disturbances Single channel feedforward control Constraint of Causality Active control of sound in enclosures Cars Aircraft Active head sets Vibroacoustic control

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.

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.

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

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.

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.

The plane monopole source

The plane monopole source We define the source strength as So

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

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.

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

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

Time domain interpretation Primary source Secondary source

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

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

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

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

Time domain interpretation Primary source Secondary sources

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

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

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

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.

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

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

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

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

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

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)

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

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

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

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

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

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

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

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)

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

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).

Initial Demonstration Vehicle

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

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

Active Sound Control in Propeller Aircraft www.bombardier.com Periodic excitation generates intense harmonic soundfield inside cabin

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

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.

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

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.

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

Feedback control of Sound Active Headset using Feedback Control www.Bose.com

Active headrest

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

Active Vibroacoustic Control

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

The Active Control System Panel Accelerometer Piezoceramic actuator Analogue controller

Piezoceramic Actuators F d plate actuator M plate F

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

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

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

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