CA2095038C

CA2095038C - Active vibration control system with multiple inputs

Info

Publication number: CA2095038C
Application number: CA002095038A
Authority: CA
Inventors: Colin Fraser Ross; Graham Paul Eatwell
Original assignee: Noise Cancellation Technologies Inc
Current assignee: Noise Cancellation Technologies Inc
Priority date: 1990-10-29
Filing date: 1991-10-22
Publication date: 1997-12-30
Anticipated expiration: 2011-10-22
Also published as: ES2116297T3; EP0555248A1; ATE166172T1; GB9023458D0; DE69129413D1; JPH06502258A; AU8734991A; CA2095038A1; WO1992008224A1; EP0555248B1; DK0555248T3; AU660291B2; DE69129413T2

Abstract

An active vibration control system having at least two input sensors generating first signals representative of a primary vibration field, a plurality of actuators driven by second signals and producing a secondary vibration field, monitoring sensors responsive to both the primary and secondary vibration fields and producing third signals, and a controller having one output waveform generator for each second signal and responsive to the first signals to generate respective second signals so that vibration is reduced in a chosen region excited by both the primary and secondary fields, the controller being adaptive to adjust the waveform generator outputs to maintain the reduced vibration in this region.

Description

'~092/08224 PCT/GB91/01850 ,,J,j, , r2ticr c~ntrcl c~--t~ ple ln~utC

F~slc Or Ir~G~tl~r The invention relates to a system for activel~ controllin~
vibration. In common with pre~ious methods it useC multiple actuators and sensors, but the improved method dri~es the ac~uators using output wave generator~ each of which is responsi~G to at least two input signals. In particuler, unlike pre~ious methods, the invention can be applied to the control o~ vibration from multiple source_ irrespective of lC the degree of correlation between the sources.

Background to the Invention In the following the use of the word vibration shall include sound and other similar linear disturbances.

There have been many publications relating to the active control of vibration in solids and in fluids. They use one -or more actuatorC to produce secondary vibration that tends 2C to cancel an unwanted vibration in some region~ Sensors in this region produce signalc representative of the residual vibration. These signals (the residual si~nals) are used in a control system together with input signals to adjust the signals sent to the actuators.
Active control systems can be broadly categorised according to the type of input signals used. The first type uses ~nput signals which are both time and amplitude related to the primary vibration or the combination of both primary 30 and Qecondary vibration. The second type ,uses input signals which are time related to the primary vibration but contain no amplitude information.

SUE3STITUTE SHE~
.

. -~ . ., ... . . .. , ~ .. . .

W092J08224 ~ v~J~ ~ PCT~GB91/018 This second type of system is usually used for controlling periodic or tonal vibrations and an example is described in UK patent 1,577,322 (Active Attenuation of Recurring Sounds, G.B.B Chaplin).

When there is more than one source of vibration it is sometimes possi~le to use one control system each source, provided that the sources are uncorrelated with each other.

Another method treats the vibration as if it were coming from a-single source and to use a fast-adapting control system ~to compensate for the modulations caused by the interactions of the sources ( UX patent 1' 2,132,053 (Warnaka L Zalas), UK patent 2,126,837 (Groves), UK patent 2,149,614 (Nelson & Elliot) ).
This will only work if the sources are correlated over the timescale of the adaption process. It could not be used, for example, for controlling aircraft 2C~ propeller noise when the synchroph~ser is switched off, since modulations are then too rapid.

There are many applications where the vibrati~n is produced by vibration sources which are at least p~rtially correlAted. one example of this is the generation of road noise inside a vehicle. There is some correlation between the vibration produced from ~~ch wh-el as a result of road uneveness and in ~ddition is not always possible to position vibration ~~ which are repsonsive to one wheel only.

Another example of this is when the vibration sources ~r- tonal in nature. If the frequencies of the sources are very close together then the cross-corre~ation of .
.

- -. -. .. . ... . . , .: ,. .. .
- . ;-. ... -. , . ~

PCT/GB 9 1 1 0 1 8 r ~ 6 Novembe~ 1992 th~ sio~nalc from the individual Sources must be c31cul~ted o~er a long ti~e before the correlation bec~me= negligible. There have been attemp~s to cepa~ate the signal~ in a reduced time bv using phase inform~ti~n from the different sources (for example PCT/GB89/00913 (Eatwell & Ross) ), but this relies upon the frequencies remaining fixed and separate over the measurement time and makes the assumption that the sources e~e uncorreleted over some specific time period.
- "
In many real applications not only do the frequencies change, but they can overlap. ~his is the case for example when two machines are connected by a clutch which~.
can slip, when they are governed to run at the same nominal speed, or when they are linked with a control system such as a synchrophaser for aircraft propellers.
In these cases it is often impossible to identify accurately which vibration is due to which source using the input signals only.

Summary of the Invention According to a first aspect of the present invention an active vibration control system comprises:
~ . ', -at least two input sensors which generate first signalsrelated to at least one characteristic of a primary vibration field or of the sources which generate the primary vibration field, : .. .
a plurality of actuators driven by second signals which produce a secondary vibration field, .~ '' ,.. . ..

- ~ ...i.., .io.~,al A,;'~.lct~tflfoCO ¦ SUBSTITU~ ~i~T

PC~ 9 l l G l ~ ~ u 6 ~ovember 1992 a ~luralitj cf monitoring censors responciv~ to the c-~;bin-tio~ of the caid pri~ary an~ secondar~ ~-ibration fields and which produce third signals, a controller including one output waveform senerator for each second signal wherein each output waveform generator is responsive to the said first signals and generates one -of the said second signals so that the combined effect of the second signals is that the vibration in a region, which is excited by the said primary and secondary vibration fields, tends to be reduced, -~
_, .
characterised in that the input sensors generate first -~
signals related to the phase and amplitude of the primary vibration field or of the sources which generate said field, and in that the controller adapts the output -waveform generators so that the vibration in the region is maintained at a reduced level.

Typically the adaption of the output waveform generators uses information from the first and third signals, and --this may be in the form of one or more matrices.

The first signals may be cross correlated to form a ' cross correlation matrix and the latter may be employed in the adaption of the output waveform generators.
. . .
The first signals and third signals may be cross correlated to form a cross correlation matrix and the latter may be employed in the adaption of the output waveform generators.
-According to another aspect of the invention, an active -vibration control system comprises: ~
, ,~ . . :
:: .
m ~ g~ca ~ ;3~
;.'..al Ap~ at~
, . :

, .

r~ U ~,, u lu~
- ~ November 1992 i~t leact two ~ut censorC which sQnerate first signals ral~ted to tha ?hace and/or the 2mF1itude of i~ prim3ry ration field or the sourees whi~h generate the primar~
~ibrstion field, a plurality of actuators driven by second signals which produce a secondary vibration field, a plurality of monitoring sencors responsi~e to the combination of the said prim2ry-and secondary vibration fields and which produce third si~nals, a controller including one outpu~ waveform generator for each second signal wherein each output waveform generator lS is responsive to the said first signals and generates one of the said second signals so that the combined effect of the second signals is that the vibration in a region, which is excited by the said primary and secondary vibration fields, tends to be reduced, characterised in that the controller adapts the output waveform generators so that the vibration in the region is ~aintained at a reduced level, said adaption of the output waveform generators taking account of the cross correlation matrix of the first signals and/or the cross correlation matrix between the first and third signals.

Some input sensors may sense vibration in the field produced by vibration sources or may be associated with or linked to the source in such a way as to produce a signal indicative of the activity of the source which produces the vibration (e.g. rotation of a turbine).
. i!~ ' ' ':

~ ~ - ' ~iY~idl~m Pc~t~t Office n;l~nal A~ ication .
. ..

" . .;. . . , . , - ; -,. . . . .,. . , -. .. . .. .. . ........ . . . .

. ~. - - ; ,: - , ; - - - , - - . .

PCT/aB 91 / 0 18 50 6 ~ovember1992 5a T~-~ically thG 2daption proceCc cmploved is an itcrative ?rocess involving an ~pdate.

Ccme or all of the adaption up~ates ~ay be scalGd ~v the reciprocal of the largest eigen~alue of the crcss correlation matrix of the first signals.

Alternatively some or all of the adaption updates may use a modified form of the inverse of the cross correlation matrix of the first signals.

Some or all of the adaption updates may use a matrix derived from the eigenvectors andjor the eigenvalues -of the cross correlation matrix of tho first signals.
Some or all of the adaption updates may use a matrix which is selected to minimise the one-step-ahead residual vibration in the region.
. '' '.
Changes in the first signals may be cross correlated - to form a cross correlation matrix of the changes in the first signals, and some or all of the adaption updates may use a matrix which is selected at least partly with reference to the said cross correlation matrix of the changes in the first signals.
~, .

Ch~nges in the third signals occurring during an ~ -lnitial measuring or calibrating step when no ~ -~econdary field is being generated may be cross ,~ 30 correlated to form a cross correlation matrix of the . .

~.. :: . .
,-. :
~;
. . ~ .
.~: , . . . - .:
"" "'.~ SUBSTIrUT~
Ç ,.
- - .
-.;' ~" . . ' .' .... . ~. . . . ' . ' ... . :. . . .

W092/08224 ; PCT/GB91/0185 ,~ J~

changes in the third signals, or the cross correlation matrix of changes in the third signals may be calculated from estimates of what the third signals would be without the secondary field, and some or all c of the adaption updates may use a matrix which is selected at least partly with reference to the said cross correlation matrix of the changes in the third signals.

The first signals and the noise (as hereinafter defined in equation 5) may be cross correlated to form a cross correlation matrix between the first signals and the noise, and some or all of the adaption updates may use a matrix which is selected at least partly with reference to the said cross correlation matrix between the first signals and the noise.
: .
Where the first signals contain components attributable to the second~ry vibration the latter is preferably subtracted from the outputs of the input sensors so that the first signals available for use by the controller do not contain any substantive components attributable to the secon~A~y vibration.
~ ;;~ . . .
The cross correlation matrix of the first signals may be stored as reguired in the controller. ~ -.
The cross correlation matrix between the first and third signal~ may be stored in the controller.
The cross correlation matr'ix of the first signals (or ~ , the first and third signals) may be formed at least in , -~
part during an initial measuring or cali,brating step or ~ay be formed during the vibration reduction mode '''~ ' 35 of operation of the controller or partly during an ''' . . , ' ~ ' r ut~092tO8224 ~U~ PCT/GB91/01850 initial step a~d partly during a vibration reduction mode of operation of the controller.

Where the primary vibration field is produced ~y two or more sources each of which has a repetitive or periodic or quasi-periodic characteristic or any combination thereof and each input sensor is linked to a seperate source and produces a first signal indicative of the repetitive or periodic or quasi-periodic activity of that source the waveformgenerator may include a sampled-data system for each first signal each of which systems is supplied with a control signal derived from one of the said first signals.
Where there are two or more sources and therefore two or more sampled-data systems and each sampled-data system has to be synchronized, the synchronization may be achieved using some or all of the control signals derived from the said first signals.
- :
Where there are two or more sources and therefore two or more sampled-data systems each sampled-data system may comprise a sampled-data filter ~eg a digital filter) the input of which is supplied with one of the first signals, and the sample data filters may be synchronized from a single synchronizing signal.

In the present invention each output wave generator~
may be a device which produces a signal waveform which is ~es~onsive to two or more input signals. Each of these input signals could be . ' .
~ - ,, .

w092/0822~ PCT/GB91/018S~
~ ' I,J tJ :" ~J '.' J

(i) a signal which is time related to one of the vibration sources or to the unwanted ~primary) field such as in Ux patent 1,577,322 (from a tachometer for example), or (ii) a signal which is time and amplitude related to the primary vibration.

~iii) a signal representative of the time or phase ;-difference between the primary vibration or one of the vibration sources and some reference signal. This -~
phase difference could, for example, be in the form of an angle difference for rotating machines or a timing difference. ~
;~-The output wave generator can be a sampled-data device and can operate (i) as a fixed (uniform) time-base filter.
~
(ii) on a the time-base of a reference signal, which ~ -could be one of the input signals, so that a specified number of output points are generated in each vibration cycle. This can be thought of as a - 25 synchronous sampled-data filter.
. ,. -(iii) on multiple time-bases, each time-base cG,L~ ~onding to a reference signal which could be one of the input signals. This would be thought of as multiple s~,.ch~nous sampled-data filters whose output is combined to produce the wavefor~ generator output.
:. .' :
The sampled-data devices could be digital devices.

,, ~ .
.'- ~ ., ' . ' ''~ ' "~'~ ' .

~092/08224 , ~ 2i PCT/GB91/018S0 The invention also lies in the method by which the output wave generators are adjusted or adapted in response to the input (flrst) signals and the signals from the residual sensors (third signals), so that their combined effect is to tend to cancel the unwanted vibration.

In one particular embodiment of the invention in which the output wave generators are filters, the unwanted vibration is generated by two vibration sources and the two input signals are derived directly from the sources, one from each. The inputs to the controller at time t are ul(t) and u2(t) and the impulse responses of the corresponding filters for the n-th actuator are Xl(n,t) and X2(n,t). The combined output (second) signal from the output waveform generator to the n-th actuator is x(n,t)=u~(t)*Xl(n,t)+ u2(t)*X2(n,t), (l) ~
where * denotes convolution. In matrix notation we can -write X(t)=Xl(l,t),X2(l,t) (2) Xl(2,t), X2(2,t) ...... ...... .
~ ...... ...... .
Xl(N,t), X2(N,t) ,, ~ . .

u(t) ~ ul(t) (3) U2 ~t) :~ -~tc., so that -- , ~ .

W092/08224 j_J I j PCT/GB91/018S~

x(t) = X(t) * u(t) (4) The third signal at the m-th sensor whe~ no control is ~ ~ -applied is y(m,t) = Ul(t)*yl(m,t) ~ u2(t)*y2(m,t) + n(m,t) (5) where the first two terms on the right hand side are the contributions from the two vibration sources and a is the noise not associated with the vibration lC sources As above this can be written in matrix notation as ~
y(t) = Y(t) * u(t) + n(t) (6) ;

15 The residual signal at the M microphones is ~ ~ -e(t) = y(t) + A(t)*x(t), (7) where A(t) is the matrix of responses describing the way in which impulses from a controller output (second signals) affect the (third) signals from the - -residual sensors . .
- In the case where Yl and Y2 can be identified separately the first filter output ~l can be used to cancel Yl since it is assumed to be well correlated with ul, and the second used for Y2 The signal p.c_~ssing approach used in Eatwell and Ross sought to ~eparate the components in the residual signals This cannot be done accurately unless the signals are ~- sufficiently noise-free or the eonstituent c~~po~nts in constant for a long time However, the ~ul~ert nv-ntion recogniSres that when separation is ' difficult, as in the case of synchrophased - 3~ propellers, it is also unnecess~y since the aim of , ~
,. ~ - . ,: .
~.~. .. . . . ..
~.~ ;. ....
,."~ . ., .. . . :, ~092/08224 ,~ J PCT/GB91/01850 an active control system is only to reduce the unwanted vibration.

The primary vibration can be thought of as a sum of independent (uncorrelated) components. These correspond to the contributions from the individual sources only when the input signals themselves are uncorrelated. The method is best expl~ined in terms of these components. -.
A measure of the degree of correlation is given by the off- diagonal elements of the cross-correlation matrix of the first signals which is defined by C(T) = <uuT> = <ul(t)ul(t+T)> <ul(t)u2(t+T)> (8) <U2(t)ul(t+T)> <U2(t)u2(t+T)> ' The angle brackets denote expectations which can be approximated by short term time averages. This !''' definition is for two input (first) signals but the . extension of this definition to more than two first signals is obvious. This can be transformed to the freguency domain, in which case it could be called the cro-s spectrum matrix howev-r the use of the term ~- cross correlation matrix should be taken to include ~~~ th- fregu-ncy domain eguivalents. In the particular ca-e when the input signals do not contain any amplitude information they can be normalised so that ' ~ the diagonal elements of the matrix are unity, giving the complex matrix ) ~ f) (9) 3S B (f) A ~, ~ . , . ' ' .

S.'~. ",.~ . .. .

,..;~ -,f W092/08224 PCT/GB91/018S~
-, U ~

where B(f) is the Fourier transform of <ul(t)u2(tlT)>, f is the frequency and the superposed * denotes complex conjugation.

In the frequency domain, when ul and u2 are suitably normalised, u2(f~ult(f) = exp( i2~ft ), (lO) 10 where t is the time between the start of a cycle of one vibration source and the start of a cycle of the other source. When the sampling is synchronised to one source , U2(nfo)ul (nfO) = exp( ine ), (ll) where fO is the fun~ -ntal freguency, n is the ~ ~
harmonic number and e - 2~fot is phase angle between il :
the sources. ~
- -The complex Hermitian matrix C can be decomposed as C(f) = dlylYl I d2Y2Y2 , (l2~ ~

25 where the eigenvectors are ~ -dl - l + R and d2 ' l - R , (13) R is the modulus of B(f). The eigenvectors are ~Yl - {exp(argB), l}T/sgrt(2) (14) ~
,: ' '' '' "
~ . and , ~ .
.. ~ ~ .... ..

, ~ , : ' .

~092/08224 ~ PCT/GB91/01850 V2 = {exp(argB), -l}T/s~rt(2~, (15) where argB is the argument of B and exp(.) is the exponential function.

A co~on way of measuring the performance of a control system is to calculate the mean s~uare error at the residual sensors. This is denoted by 10 E = trace< e(f)_(f) >. (16) This is most useful when Y and X are only changing very slowly. We look at this case first in order to illustrate the importance of the cross-correlation lS matrix.

Using equtions 4, 6 and 7 this can be written as E = trace{(Y+AX)C(Y+AX) } + < n n >, (17) 2~
or E = (Y+AX) YlYl (Y+AX)dl + (Y+AX) Y2Y2 (Y+AX)d2 + < n*n >. (18) When the two vibration sources are well correlated R
is close to unity and the first eigenvalue is much larger than the second. Hence, if Yyl and YY2 are of similar size we see that the first term on the right hand side gives a much larger contribution to the error E than does the second. This indicates that it may not be important to obtain a good estimate of this second ~~ ,on~nt.

. . - ~ . . - - - - . . : ............... .. . . ~~ .. . - . .
- ... .. . .. _: . . . - . ~- .. : .. . .. : . .

w092/08224 PCT/GB91/0185 ,~j;jt~:, jJ

However, the matrlx Y is ~ot measured directly, s~ we must use the alternative expression E = trace< (y+AXu)(y+AX_) >

= trace{<y y>+ AX<uv ~ + <vu >X A + AX<uu >X A }
(1~) . . -.
The optimal solution for X is X = -(A A) lA <vu ~C-l, (20) where lS C l = vlvl /dl + Y2V2 /d2 , (21) Thus the cross-correlation is used in the calculation of the optimal actuator drive signals.

The calculation assumes that both A and _ are known.
In practice they cannot be known exactly. The effect of these inaccuracies are largest when the matrix C is poorly conditioned, that is when d2 is small. The error is then increased by a factor which scales on the noise level and on d2/h2, where h2 is the estimate of d2 used in the calculation of C l. In addition the solution for X, even if it is accurate in the mean, is highly sensitive to the measurement noise.

This can be demonstrated by looking at the effect of errors in the eigenvalues of C. If hl and h2 are are the estimates of the eigenvalues we can write the estimate of C l as (I+c)C l where ~ , , , .. , , . ,, :

~092/08224 ~ ,,, PCT/GB91/01850 c = vlvl (dl/hl-l) + V2V2 (d2/h2 l) ' (22) and I is the identity.

From this it is clear that the error c is most likely to be large whenever h2 is small.

The resulting mean square error, when A is known exactly and can be inverted, can be shown to be l~ increased by an absolute amount <uv >cC lc<vu ~ . (23) The error relative to the primary vibration is therefore increased by an amount depending on c and on the coherence between _ and y. One factor affecting this coherence is the signal to noise ratio, s=<y*y>/<n*n>.

One aspect of the current invention is to use a modified estimate of C l such as D-l = -lVl /dl + -2-2 /g~d2) (24) where g(d2) is a function which tends to increase d2 when it is small and leave it unchanged if it is large enough. The scaling of this function can be determined by the signal to noise ratio, s, or by any other measure of the noise or the coherence. One such -~s~re which can be measured 'on-line' is <u*e><e*u~/{~n n><y u>} ~ (25) -: . :-. .: .: . - -:; - :. ... : . .: : :: . : . : - , :. : ::. : .:: , : :. ., . .. , . , ~. ., .:
-.- -:

:. - - . . .: - ~ . .
- . -.. . . .~ .. . .- ;; ... -.. . ..... .. ~. ... ~. .. . .

W092/08224 ,~ 1! j, PCT/GB91/0185 In most applications the primary vibration field is changing, this means that an adaptive control scheme must be used.

The adaptive scheme takes the form xi+l Xj - ~R<ej_j >Q (26) where ~ is a convergence parameter and R and Q are matrices to be chosen, and <_iuj*> is the cross correlation matrix of the first and third signals. The expectation denotes a combination of measurements such as an average or exponentially weighted average and includes the case where a single measurement is used.
Typical expressions for R when there is a single vibration source are R = A* or R = (A A ~ A* (27) where I~ is the identity metrice and- is a small positive number included to improve the conditioning of the matrix inversion. These expressions can be used for the multiple source case described here.

2~ The choice of the matrix Q, which constitutes one aspect of this invention, is Q YlYl ~f(dl) + Y2V2 ~g(dl,d2) . (28) Another aspect of this invention is the choice of the ~unctions f and g and the convergence parameter ~.

We shall do this by eYamini~g the performance of the algorithm. This can be done by loo~ing at the change . i . . ;

.. : . . - . :
.-. : . . ~ .
..... . . - ~ . : , . , - , , -. : - . . . , : .

~092/08224 ~iJ J~ U v~ PCT/GB91/01850 in the residual signal after one iteration of the update scheme. The error after the j-th iteration is j+l = yj+l + (AXj-~l.AR<ejuj*>Q)Uj+
= (yj~l_yj) + (Ej-~AREj<ujuj >Q)Uj - ~AR<ajUj >QUj + Axj+l(uj+l-uj) (29) where Ej = Yj + AXj (30) lQ and xj+l = Xj-~REicujui >Q-~R<njuj >Q. (31) The term cujuj >Q can be written as <ujuj*>Q =CQ = _1v1 d1f(d1) + -2V2 d2g(dl'd2) (32) <(yj+1-yj)(yj+1-vj)*> is the cross correlation matrix of the changes in the third siqnals which would occur if the secondary field were not produced.
<(uj+1-uj)(uj+1-_j)*> is the cross correlation matrix of the changes in the first signals. <Bj_j*> is the cross correlation between the noise and the first signals. Equation (29) shows that there are four contributions to the new residual vector. The first term represents the change in the primary noise field, 25 this can only be reduced by increasing the update rate. The second represents the error that would occur in a noise-free situation where the vibration sources were not changing. This term can be reduced by choosing ~ to be unity, choosing R such that AR is 30 close to the identity mat,rix, and by choosing Q to be close to C 1. The terms involving nj is additional noise introduced by the adaption algorithm. This term can be re~uced by making ~, R or Q small (which is in conflict with reducing the second term) or by 35 combining more meas~r~ ?nts (which is in conflict with .:: . - . :.. .... - . - . . ~ : . . .- . .. . ~ . .

W092/08224 PCT/GB91/0185~
"

l~i reducing the first term). The las~ term is proportional to the change in the input vect~r u this can be reduced ~y increasing the update rate, It is also proportional to X~+l which is affected by choice ; of ~ and Q. In particular, when the function g is large, xj+l as given in equation 31 contains a large noise term.

The functions f and g may be chosen so as to minimise l0 the one step ahead residual and so they depend upon the noise levels and the rate of change of the input vector u. The choice of ~ may then be made with reference to f and g. We shall now give some examples.

15 One choice for Q uses f(dl) = g(dl,d2) l, gives Q = I, the identity. Upon substituting equation 30 into equation 29 it is clear that for convergence of the algorithm 0 < ~ < 2t{dl.norm(AR)} , (33) where norm(.) denotes the matrix norm. Hence the update scales on the largest eigenvalue of the cross-correlation matrix C.
Another choice is f(dl) = l/dl and g(dl,d2) is some function which tends to a fixed value when d2 is very small and tends to l/d2 when d2 is sufficiently large.
For example g(dl,d2) = l/sqrt(dld2) which ensures that 30 the amplification of the ,noise is not too large. Q is then close to the inverse of the cross-correlation matrix C. For this case the algorithm converges provided 0 < ~ < 2/norm(AR) .

, ,, , :~

The foregoi~g analysis shows that the choice of functions f(.) and g(.) which will mini~,ize the one-step ahead residual noise will depend upon the dynamics of the vibration sources and upon the noise levels. Hence the choice of the functions f(.) and g(.) may be made, for a particular application, with reference to the dynamics of the vibration sources and/or the noise levels in such a way as tc reduce the expected value of the one-step ahead residual noise.
One way this choice may be made is calculate or estimate the terms of equation 29 and select the functions which minimize the left hand side.

The invention may be applied to control the propeller noise in an aircraft with two propellers. This example is now described with reference to the accompanying drawing, in which Figure l shows one type of output wavefrom generator. Each output waveform generator 20 (for simplicity only one is shown) receives a -tachometer pulse train, 1, from one of the propellers and generates the anti-sound (second) signal, 2, for each loudspeaker in synchronization with it (again only one loudspeaker is shown for reasons of 25 simplicity). The phase and amplitude of the loudspeaker signals are governed by output weighting coefficients, 3, which are adjusted by the adaptive algorithm.

The values of aj and bj, are the cosine and sine output weighting coefficients of the anti-sound signal for propeller 1, for each loudspeaker (at each harmonic ;), and the values of a'j and b'j, are the 35 coefficients for propeller 2. These output weighting .

-. : ... . . : ............ .. : : . , . . ~ ..

... . . . - -.
-: , . : - .

~~ J ~ I ~J

coefficients are adjusted by the adaptive algorithm once per adaptive update. Regularly the phase signal, ~ , or a timing signal from which the phase is derived, is re-measured and used to co..,bine the values of aj, a'j, bj, and b~j according to the equation:

c = a + atCp - b'Sp d = b + b'Cp + a'Sp .

(the subscript j has been dropped for clarity) 1~ where:
c is the combined coefficient for the cosine generator, d is the combined coefficient for the sine generator, Cp is the cosine of the phase angle (of propeller 2 relative to propeller 1), and Sp is the sine of the phase angle.

Each time a pulse is received from the tachometer pulse train the output to each loudspeaker is calculated according to the equation:

x(i) - cjWCj(i) + djWSj(i) where WCj(i) is a stored cosine wave of harmonic number j, and WSj(i) is a stored sine wave of harmonic number j. This represents the sum of the cosine and ... . , ~ . , . . . . . . , . -.. , . . . . - . :. :
. .
. ~
'. ' ' ~. . ~:: : ; . '- : . ,, . . ' ~ .. , : -, ~ ~ ; . : , - .
- , - . .
,: ' ~' '.... ' ; , . ' , ' ~ .

~092/08224 PCT/GB91/01850 J v IJ ~ J

sine generator outputs weighted by the coefficients Cj and dj and summed for each harmonic j. In figure l, two harmonics are being controlled.

; The adaption in the controller may be done with reference to the third signals from microphones in the cabin. These could be used to adjust the output weighting coefficients a and b (or a' and b'), which are subsequently used by the output waveform generators to create the an'i-sound signals.

Other embodiments of the invention could use more than two input signals and could have different forms of output wave generators.

; . - . . . , , , . ... :: :, - , . .. . .. . .,: . . : .. ~ , ,

Claims

Claims:

1. An active vibration control system comprising:

at least two input sensors which generate first signals related to at least one characteristic of a primary vibration field or of the sources which generate the primary vibration field, a plurality of actuators driven by second signals which produce a secondary vibration field, a plurality of monitoring sensors responsive to the combination of the said primary and secondary vibration fields and which produce third signals, a controller including one output waveform generator for each second signal wherein each output waveform generator is responsive to the said first signals and generates one of the said second signals so that the combined effect of the second signals is that the vibration in a region, which is excited by the said primary and secondary vibration fields, tends to be reduced, characterized in that the input sensors generate first signals related to the phase or amplitude of the primary vibration field or of the sources which generate said field, and in that the controller adapts the output waveform generators so that the vibration in the region is maintained at a reduced level, said adaption of the output waveform generators taking account of the cross-correlation matrix of the first signals.

2. A system as claimed in claim 1, wherein said first signals are related to both the phase and amplitude of the primary vibration field or of the sources which generate this field.

3. A system as claimed in claim 1, wherein the controller adapts the output waveform generators by means of the cross-correlation matrix between the first and third signals.

4. A system as claimed in claim 2 or 3, wherein the adaption of the output waveform generators is scaled by the reciprocal of the largest eigenvalue of the cross-correlation matrix of the first signals.

5. A system as claimed in claim 2, 3 or 4, wherein the adaption of the output waveform generators uses a modified form of the inverse of the cross-correlation matrix of the first signals.

6. A system as claimed in claim 2, 3, 4 or 5 wherein the adaption of the output waveform generators uses a matrix derived from the eigenvectors and/or the eigenvalues of the cross-correlation matrix of the first signals.

7. A system as claimed in claim 2, 3, 4, 5 or 6, wherein one of the matrices used in the adaption of the output waveform generators is chosen to minimize the one-step-ahead residual vibration in the region.

8. A system as claimed in claim 2, 3, 4, 5, 6 or 7, wherein one of the matrices used in the adaption of the output waveform generators is chosen at least partly with reference to the estimate of the cross-correlation matrix of the changes in the first signals.

9. A system as claimed in claim 2, 3, 4, 5, 6, 7 or 8, wherein one of the matrices used in the adaption of the output waveform generators is chosen at least partly with reference to the estimate of the cross-correlation matrix of the changes in the third signals which would occur without the secondary vibration.

10. A system as claimed in claim 2, 3, 4, 5, 6, 7, 8 or 9, wherein the cross-correlation matrix of the first signals is stored in the controller.

11. A system as claimed in claim 2, 3, 4, 5, 6, 7, 8, 9 or 10, wherein the cross-correlation matrix between the first and third signals is stored in the controller.

12. A system as claimed in claim 2, 3, 4, 5, 6, 7, 8, 9, 10 or 11, wherein the cross-correlation matrix of the first signals is estimated during operation of the controller.

13. A system as claimed in claim 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12, wherein the cross-correlation matrix between the first and third signals is estimated during operation of the controller.

14. A system as claimed in claim 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 or 13, wherein the response of the input sensors to the secondary vibration is subtracted from their output so that the first signals are substantially insensitive to the secondary vibration.

15. A system as claimed in claim 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 or 14, wherein part of at least one of the output waveform generators is a filter which has a time-base synchronized to the rotation rate or timing of one of the vibration sources.

16. A system as claimed in claim 15, wherein part of at least one of the output waveform generators receives an additional signal related to the relative phase or timing of another vibration source.

17. A system as claimed in claim 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 or 16, wherein part of at least one of the output waveform generators is a filter which operates on a uniform time-base and which receives a signal related to the phase or timing of one vibration source.