Active Vibration

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Indian Institute of Technology Roorkee

Noise and Vibration Control

9. ACTIVE NOISE AND VIBRATION CONTROL9. ACTIVE NOISE AND VIBRATION CONTROL

Additional References:

1. Active Noise Control Primer, Scott. D. Snyder,

Springer Verlag, 20002. Active Control of Vibrations, C.C. Fuller, S. J.

Elliott, P.A. Nelson , Academic Press, 1997


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ACTIVE VIBRATION CONTROLACTIVE VIBRATION CONTROL

Passive control of vibration:

Relatively simple & straightforward

Robust, reliable & economical

LIMITATIONS:Control force generated depends on natural dynamics

Impossible to adjust the control forces

No power supply from external source

Incomplete control- Not always possible to directly targetthe control action at particular responses (in complex &

higher order systems)

Active control:

System responses directly sensed using sensor-transducer devices

control action of specified values are applied to desired locations of

system.

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objective of active vibration control- to reduce the vibration of a mechanical system

by automatic modification of the system's

structural response. components of a system:

1. sensor (to detect the vibration),

2. electronic controller (to suitably manipulate the

signal from the detector)

3. actuator (which influences the mechanical

response of the system).

types of actuator - fully-active- semi-active

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Fully-active actuators are able to supply mechanical

power to the system. Examples : electromagnetic shakers, piezoelectric

ceramics and films, magnetostrictive and electrohydraulic

devices.

Actuators -used to generate a secondary vibrationalresponse in a linear mechanical system,

- reduce the overall response by destructive interference

with the original response of the system,

Semi-active actuators behave as passive elements

they can only store or dissipate energy.

Their passive mechanical properties can be adjusted bythe application of a control signal - called 'adaptive systems'.

Semi-active actuators can be constructed using

electrorheological fluids or shape memory alloys

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Only active vibration control systems which employ fully-

active actuators have been discussed.

Feedback control systems

control signal obtained from the sensor is affected by

both the primary source and the secondary actuator

over which we have control, and this is fed backdirectlyto the actuator.

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Fig. 1 A system for active control of vibration

Plant & Controller- 2 essential components of Control system

Plantmust be monitored ; its response measured using Sensors,

for feedback into the Controller.

Controllercompares the sensed signal with a desired response &

uses the error to generate a proper control signal- Feedback control

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Single-channel feedback control systems

Transfer function of the feedback controller, H(s):-ratio of the Laplace transform of the secondary excitation

to the system,Fs(s ),

to the Laplace transform of its response, W(s),

Fig. 2 The components of a feedback control system

[ C.C. Fuller, S. J. Elliott, P.A. Nelson ,Active Control of Vibrations]

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Fig.3 Equivalent electrical block diagram of a feedback control system

[ C.C. Fuller, S. J. Elliott, P.A. Nelson ,Active Control of Vibrations]

Laplace transform of the secondary excitation:

Fs(s ) = H(s)W(s).

Combining these equations we obtain

W(s) = G(s)[Fp(s)- H(s)W(s)].

transfer function of the mechanical system with feedback control

can be written as

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Transforming the above transfer function into a frequency

response by substituting s=j, the frequency response of

closed loop system is:

For the open loop frequency response, G(j)H(j), to have

little phase shift in the frequency range of interest but

simultaneously to have a gain of much greater than unity,

then we can write for in the working range

( ) ( ) 11 >>+ jHjGSo that

)()()(

jGjFjW

p


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Example of an idealised single-channel feedback control system

Fig. 4 Feedback controller applied to a lumped mass-spring-

damper system [ C.C. Fuller, S. J. Elliott, P.A. Nelson ,Active

Control of Vibrations]

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Prior to active control,

- the control signal driving the secondary actuator

will be zero and so the secondary force will also

be zero.

the dynamic response of the SDOF system can

be deduced from its differential equation,

which can be written in terms of the time

histories of the primary force, fp(t), and the

displacement of the mass, w(t), as

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C


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use of velocity and displacement feedback in the active

control of the vibrations of a circular saw

Fig. 5 The mechanical arrangement of the feedback control system

used for the active control of circular saw vibrations. [ C.C. Fuller, S.

J. Elliott, P.A. Nelson ,Active Control of Vibrations]

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N i d Vib ti C t l


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Fig. 6 The electrical block diagram of the feedback control system

used for the active control of circular saw vibrations. [ C.C. Fuller, S.

J. Elliott, P.A. Nelson ,Active Control of Vibrations]

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N i d Vib ti C t l


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The state variable approach

Instead of directly transforming the differential equationswhich describe a dynamic system into the Laplace domain,

an alternative approach is

to recast the time domain equations into a standard form;

in terms of the internal state variables of the system. then manipulate this state variable representation, using

well established matrix methods.

Consider the differential equation describing the SDOF system

rewriting

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Define two variables which completely define the internal

state of the system.state variablesx1(t) and x2(t).

suitable state variables : displacement and velocity of

the mass:

xl(t) = , x2(t) = )(tw&)(twstate variables are related by the first-order differential equation

)()(12 txtx

&=

rewriting the differential equation of the SDOF system in

state variable form

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From above:

where

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Fig. 7 State variable representation of a dynamic system

transient response of the SDOF system :

The unforced solution to the state variable equations for the ithstate variable can be written as

where the constants eil, ei2, etc., depend on the initial conditions

of the internal states and 1, 2, etc. are the eigenvalues of the A

matrix.

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For the SDOF system, there are:

two state variables -> two eigenvalues for the associatedA matrix, and two terms in the transient response,

the free response of a system described in state variable

form will decay to zeroprovided the real parts of all the eigenvalues of the A

matrix have negative real parts

The eigenvalues of A-solutions of the characteristic equation resulting from setting

the determinant of1- A to zero,

- can be written as

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The characteristic equation is thus

which has the solutions

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Feedforward Control

system under control is linear and the secondary actuator is fully active

superposition : secondary disturbance can be generated

which destructively interferes with that due to primary

sourceprior knowledge of excitation due to primary source can be

obtained

Two examples:

1) where the disturbance is deterministic. future behaviour can be predicted from its previous

behaviour.

For example, disturbances caused by reciprocating

machines such as internal combustion engines, atachometer signal related

to the crankshaft rotation is often used to generate a

reference signal.

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2) when the vibrational disturbance is propagatingthrough a mechanical structure, and a sensoris used

to detect this disturbance.

The frequency response of the electrical controllermay be adjusted or 'tuned' in response to the output of

this sensor in order to make the feedforward control

system adaptive.

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Single-channel feedforward control

Fig 8. Components of a feedforward control system.

The electrical controller, H, is driven by an estimate of original

excitation of mechanical system due to primary source x.signal proportional to the response of mechanical system e,

plays no direct part in the control path,

but could be used to adapt the response of the controller.

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The original excitation influences the mechanical system

via the primary force, fp, which is related to the original

excitation via the primary transmission path P.

The net excitation of the mechanical system is proportional

to the difference between the primary and secondary forces

(fp-fs), andthe response of the system is related to this excitation via

the response of the mechanical system, G.

Fig. 9. Equivalent block diagram of a feedforward control system.

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The signals are all represented by their Laplace transforms,

and responses of various components by their transferfunctions.

One potentially complicating feature of feedforward control

systems:

which is often present when the excitation is random anda detection sensor is used to obtain estimate of original

excitation,

is feedback from the secondary input back to the detection

sensor.

This feedback path is generally due to mechanical

disturbances, caused by the secondary force, finding their way

back to the detection sensor through the primary path.

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A more complete block diagram should include thisfeedback path, and

also include measurement noise signals in the outputs

from the detection and response.

The effect ofmeasurement noise

Redrawing the block diagram of the feedforwardcontroller.

The transfer functions of the controller and mechanical

systems have been replaced by their frequencyresponses, and

the spectra of the various signals are shown rather than

their Laplace transform.

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Fig. 10a Alternative block diagram of the feedforward control system.

U(j) and E(j)- electrical voltages applied to the secondary

actuator and measured at the response sensor, respectively.

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Fig. 10b Alternative block diagram of the feedforward control system.

Spectrum of the filtered excitation signal is defined as

R(j) = G(j)X(j).

block diagram of Fig. 9(b) is exactly equivalent to that

shown in Fig. 9(a), provided the controller and mechanical

system are linear and time-invariant.The spectrum of the net disturbance will be

E(j) = D(j)- H(j)R(j).

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Active noise control (ANC)

Technique which aims to cancel unwanted noise byintroducing

an additional, electronically generated, sound field.

Practically all noise control involves Passive control

techniques. Reasons for not using active noise control:

1) ANC only useful for certain type of problems

- Low frequency problems, usually tonal

2) ANC more complicated than passive NC, since it

involves the integration of electronics, transducers

(loudspeakers, microphones, etc.)

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Passive noise control:

Aims to reduce acoustic levels by altering the acoustic

environment in which the sound source operates, by addingenclosures or barriers in the case of free space radiation.

Transmission loss is inversely proportional to fraction of energytransmitted

T.L. = Noise inside noise outside

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Figure 11 Maximum possible acoustic power attenuation for two

small sound sources [Ref: Active Noise Control Primer, S.D. Snyder]

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Fig 12.The principle of active sound control was first introduced by

Lueg (1936) in a patent for the single channel feed-forward control of

tonal disturbances propagating in a one-dimensional acoustic

waveguide. [Sound and Structural Vibration, F. J. Fahy &

P.Gardonio, Elsevier Publishers, 2007]

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Feed-Forward Control

The waveform of the primary wave described by the solidline S1 is detected by a microphone Mand used to drive the

control loudspeakerL via the electronic controllerV.

The loudspeaker generates a secondary acoustic wave,

whose waveform is defined by the dotted line S2.

The control system Vis set to manipulate the detected

signal from the microphone in such a way that the

secondary waveform destructively interferes with the

primary wave.

Thus, the secondary wave is generated to have the same

frequency and amplitude but opposite phase to the primary

wave.

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Adaptive Feedforward Active Noise Control

Fig 13. Main components in a typical adaptive feedforward

active noise control system [Ref: Active Noise ControlPrimer, S.D. Snyder]

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Adaptive Feedforward Active Noise Control

Reference microphone- provides the measurement(reference signal) of the impending noise some time before it

arrives at the controller.

Control system- responsible for taking the reference signalmeasurement of the impending noise and calculating what is

required to cancel it.

Control source- used to generate the canceling sound field.

Error microphone- used to sample what noise actually

remains after cancelling operation (error signal)

Adaptive controller- able to adjust its calculation procedure

(adaptive algorithm) to suit the current environment in which it

is operating (ensures complete cancellation at the error

microphone).

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The two main mechanisms for sound cancellation, i.e.destructive interference and impedance coupling, may

occur together or separately.The difference is related to whether the acoustic wavesdecay with distance traveled:

If an actuator is close to the disturbance source,destructive interference and impedance coupling canboth occur

when the actuator is far from the disturbance, so thatany wave it creates decays completely before reachingthe disturbance, there can still be destructiveinterference near the actuator, even though the actuatorcannot affect the impedance seen by the disturbance

(example: the tiny speaker in an active controlheadphone will not affect the impedance seen by acannon firing a mile away, but it can create destructiveinterference within the headphone)

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Physical understanding of Active Noise Control

Noise control- by either reducing or redirecting acoustic

energy flow

Redirecting acoustic energy flow- how?

Consider two sound sources operating in free spaceand producing a series of sound waves

At some points in space the waves cancel (50%

shading)

At some points in space they add (Dark and lightportions)

Local areas of attenuation are provided at the expense

of other areas of increased sound level.

Implication: On an average, the sound levels have increased,

not decreased

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Fig 14. Interference pattern between two coherent sound sources

[Ref: Active Noise Control Primer, S.D. Snyder]

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How to achieve global sound attenuation using ANC

techniques?

Only possible way Reduce the total energy flow

The introduction of second loud speaker must do the

following:1. cause a reduction in the acoustic power output of both

sound sources, such that the total is less than the power

output of original source

2. One of the sound sources must absorb power (energyflow into the loudspeaker, not out of it), while the energy

flow from other source stays roughly the same or

reduces.

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Acoustic impedance = pressure/ flow

Important factors for ANC:1. Separation distance between the sound sources must be

small.

2. Sound sources must be coherent.

3. Sound sources must be roughly of same size.

Fig. 15. The sound fields of two sources quickly differ as the

separation distance moves from small (less than 1/5 wavelength) to

one full wavelength. [Ref: Active Noise Control Primer, S.D. Snyder]

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Note:

1. At 0.5 wave-length separation, no reduction in sound

power is possible.

2. The separation distance should be less than one-tenth of

wavelength to achieve 10 dB power attenuation.

Fig. 16. Maximum possible acoustic power attenuation for two small

sound sources, plotted as a function of separation distance between

them [Ref: Active Noise Control Primer, S.D. Snyder]

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Implementation difficulties

Acoustic feedback from the control source to the noise

detecting microphone may cause controller instability

Turbulent pressure fluctuations (traveling at flow speed)

contaminate the microphone signals and may cause the

controller to generate false acoustic canceling signals

(traveling at sound speed)Loudspeakers have poor frequency response at low

frequency and usually do not have uniform response at

higher frequencies either

Reflections from the loudspeakers, duct bends and ductends also complicate the control problem

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Contaminated flows cause problems to

microphones and loudspeakersThe lifespan of loudspeakers is short (1-3years) because of the large cone

excursions that are found to be necessaryDuct wall vibrations may also radiate soundand affect the error sensor output

Numerical issues related to digitalimplementation (sampling, delays, quantization,finite precision arithmetic's)

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General applications

Automotive systemsElectronic mufflers for exhaust systems, noise attenuationin passenger compartment, etc.

Household appliances

Noise attenuation in air conditioning ducts, airconditioners, refrigerators, washing machines, lawnmowers, vacuum cleaners, room isolation, etc.

Industrial equipment

Fans, air ducts, chimneys, transformers, blowers,

compressors, pumps, chain saws, wind tunnels, noisyplants, etc.

Transportation equipment

Airplanes, ships, boats, helicopters, motorcycles, diesel

locomotives, etc.Other applications

Office cubicle partitions, public phone booths, earprotectors, headphones, etc.

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THANK YOU

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Active Vibration