Note: Descriptions are shown in the official language in which they were submitted.
CVO 90/13108 PGT/GB90/00617
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Title: Active Sound and/or Vibration control
Field of invention
This invention relates gem rally to systems for
controlling sound or vibration, and more especially to
active control systems which use a plurality of actuators
.,.... _~o produce a cr~n-trolling- sounc or vibration field anr~ a-..-
plurality of sensors to measure the residual field.
In contrast to previous systems aimed at controlling
periodic sound or vibration, the system of the invention
can be used even when the fundamental period of vibration
is changing rapidly. For example, it can be used to
control the engine noise in the interior of a vehicle.
The improved method in accordance with the invention uses
orthogonal trans'ormations to :educe a multichannel
control system to a series of single channel systems and
provides a method by which the output of each such system
can be adapted to maintain good performance of the control
system even when the fundamental frequency of the
vibration or sound source is changing.
8ackqround to the invention
The principles of active sound and vibration control have
been known for many years and there is a wealth of
published literature. Most parent specifications in this
field relate to methods applicable to particular
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situations. The method and system described herein relate
to the control o' periodic or almost periodic sound and
vibration. The two main approaches to this problem are:
(i) Wave shaping or filtering, eg US Patent No.
x,506,380 and published UK Patent Application No.
2,201.858. where a reference signal containing one or more
frequencies of the unwanted sound and vibration is
filtered to produce the signals to send to actuators which
in turn produce the desired sound or vibration.
" (ii)'cVaveform synthesis, where a waveform generator is
triggered by a signal derived from the source, eg UK
Patent Specification No. 1,517,322.
The two methods are equivalent only if the vibration
source is exactly periodic. If the source characteristics
are changing in time it is usual to use an adaptive
control system in which sensors in the region to be
controlled sense the residual sound or vibration and pass
th a information to a processor which alters the filter
coefficients or the synthesized waveform so as to provide
better control. Published UK Patent Application No.
2,201,858 describes methods nor adapting filter
coefficients. v:~ Patent Specification No. 1,577,322
recognises the need for adaption and a later patent
specification, UK Patent No. 2,107,960, describes a simple
technique for such a system using a single actuator and
sensor. This latter patent specification does not explain
how to control vibration where the period is changing,
except to suggest that in this case the transform
technique should produce frea_uency components from the
lowest expected frequency to the highest, rather than just
at freauencies corresponding to one harmonics of the
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source.
A further GB Patent Specification No. 2,122,052, White
et al., uses a waveform synthesis technique for vibration
control. In this method a sensor and actuator are placed at
each of a number of locations. This results in a system with
equal numbers of sensors and actuators and a method for
adapting the waveform is presented for this special case. In
most applications, however, the sources and sensors are not
co-located and usually more sensors than sources are used in
an effort to obtain a better measure of the resulting sound
or vibration.
Brief Description of the Drawings
The present invention will be described in conjunction with
the drawings in which:
Figs. 1-3 illustrate equations described in the specification;
Fig. 4 illustrates an active sound and vibration control
system according to one embodiment of the present invention.
Summarv of the Invention
In accordance with one aspect of the present invention there
is provided an active sound or vibration cancelling apparatus
for cancelling sound or vibration from a source thereof,
comprising: a. a source of sensing means, having an output,
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for producing a source signal related to the phase of
unwanted sound or vibration at the source; b. a distributed
plurality of sound or vibration sensors, each having an
output; c. a distributed plurality of sound or vibration
producing actuators; d. analogue-to-digital converter means
for sampling output signals of said sound or vibration
sensors in dependence on the source signal, said converted
means having an output; and e. processing means responsive to
the output of said analogue-to-digital converter means to
produce drive signals for said sound or vibration producing
actuators to effect cancellation of noise or vibration from
said source thereof; f. wherein said processing means uses
data in the form of singular values representing a singular
value decomposition of a matrix representing transfer
functions between said plurality of actuators and said
plurality of sensors to calculate said drive signals.
The Invention
The theoretical background to the present invention will now
be described. The numbered mathematical equations referred to
are set out in accompanying drawings.
The signal from each of a plurality of sensors is sampled
using an analogue to digital converter (ADC) triggered by a
signal related to the position of the source in its cycle.
The data may be averaged over several cycles to improve
accuracy. This gives an almost periodic sequence to which an
orthogonal transform, such as the discrete Fourier transform,
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can be applied. This process is well known for the analysis
of periodic signals, and is referred to as "order ratio
analysis" or "order locked analysis".
The sample signal from the i-th sensor is given by equation
(3.1), where Ii~(nT) is the response at sensor i, due to an
impulse at the j-th controller output, x~(m) is the
m-th value of the j-th controller output, yi(n) is the
WO 90/13108 PCT/GB90/00617
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n-th value of sensor signal in the absence of any control
and T is the sampling interval. 3 is the number of
controller outputs. A slightly more complicated
expression must be used if the length of the impulse
response is comparable with the time over which the
sampling period changes significantly. If ri is sampled N
times per cycle, then since x~ is periodic, equation (3.~)
is applicable, where NT is the fundamental period.
Equation (3.1) can then be written a$ equation (3.3),
where equation (3.4) defines the cyclic impulse response.
a
----_ _,- .. .- An orthogonal transform can be. used to simplify equation
(3.3).
An example of this is a discrete Fourier transform defined
by equation (3.5), where f=1/NT is the fundamental
frequency.
Equation (3.3) then becomes equation (3.6).
It is to be noted that, since Ri, Yi and X~ are sampled an
exact number of times per cycle, they do not depend on the
frequency, f. Equation (3.6) shows that each harmonic, k,
of the system can be considered separately.
The control problem is to find the components X~(k) which
produce the desired values of Ri(k). This problem is
complicated because all of the control outputs, X~(k)
interact to produce each sensor signal. It is possible,
however, to use a technique which transforms the set of
coupled equations (3.6) into a set of independent
equations. The technique employs a singular value
decomposition of the transfer function matrix Ai~(kf) for
each kf. This gives equation (3.7), where the asterisk
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denotes complex conjugation. The matrices with complex
components Uim and Vmj represent orthogonal
transformations and so have the properties given by
equations (3.8) and (3.9), where ~I is the number of
sensors and d~ m is the itronecker delta. The term Dm(kf)
is the m-th singular value at frequency kf. It is a real
quantity. The method of decomposition is described in
"Numerical recipes - the art of scientific computing" by w
Press and others, Cambridge University Press, 1986,
pages 52 to 64. Equation (3.&) can be multiplied by U*,.
:~ i
and summed over i to give equation (3.10), to which
equations (3.10:1) andw(3.10.2~) and (3.10.3) are .-
applicable.
These quantities are called the principal components of
the corresponding signals. Equation (3.10) is a single
equation for the component X~(kf) of the desired
controller output, which can be solved directly if YQ and
R~ are known or, since Y may be changing, can be solved
iteratively using standard adaption algorithms. If the
explicit dependence on ~, and kf is dropped, equation
(3.10) reduces to equation (3.11).
If the aim is to make R as small as possible, one
algorithm, at the n-th step, results in equation (3.12),
where a is a real convergence factor.
Using equation (3.11) end (3.12) gives equation (3.12.1),
and from equation (3.11), equation (3.12.2) results.
These can be combined to give equation (3. I3) and this
shows that the algorithm is stable provided equation
(3.14) is applicable, whereby optimal convergence is
obtained when uD = 1.
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;fence it is desirable that actuation (3.15) applies, that
is. a different convergence factor is used for each
frequency and each principal component.
In order to implement this algorithm it is necessary to
measure the transfer functions Aik(kf) at a number of
different frequencies, kf, This can be done durin:~ an
initial start-up or calibration phase and if necessary can
be adapted using a parameter estimator as described in UK
Patent Application 8825074.1. The transformation matrices
U(kf) and v(kf) and the sincular values D~(kf) a're
calculated from the measurec transfer functions and stored
for each frequency. During operation the frequency f (or,
equivalently, the period T) is measured so that the
appropriate transformation matrices and singular values
can be used. Since kf is unlikely to correspond exactly
to a value for which the transfer function was measured,
the nearest value is used, alternatively interpolation
between nearby values could be used to obtain more
accuracy, In order to mai:,~ain a given accuracy the
former method uses more memory and the latter uses more
computation time.
Once X (kf) has been found, equations (3.9) and (3.10.3)
can be used to give equatio~ (3.16).
It is then possible to apply an inverse discrete Fourier
transform to obtain x~(n). These control signals are sent
to digital to analogue conve_ters (DACs), then filtered
and amplified to provide the drive signals for the
actuators.
In some applications it is c~si:able that the actuators
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are not driven too hard, and it is important that the
signals to the DAC's are within the correct range. One
particular method of limiting the drive amplitudes is to
use a minimisation constraint, a in the algorithm given by
equation (3.17). The constraint \ can be adapted after
each iteration, that is ,\ is increased if any of the drive
signals x~ is too large or reduced if that' are all in the
desired range.
Description of embodiment
The invention is exemplified ~~~ita rs~e:ence to the
accompanying drawings, in which the single figure
following the invention shows one embodiment of apparatus
for implementing the method.
Digital values are stored in a memory device (1), which
may for example be a FIFO device. These values are sent
to a set of digital to analogue converters (DACs) (2)
which are triggered V times per cycle by a train of
electrical pulses from a sensor (3). These pulses relate
to the position of the sourca in its cycle. The analogue
signals from the DACs are passed through signal
conditioners (4) to provide the drive signals for a number
of actuators (5). The resul;.ing sound or vibration field
is measured by sensors (6). The signals from these
sensors are used to adapt the values stored in the memory
device (1) so that the sensor signals approach the desired
values. The sensor signals are passed through signal
conditioners (7) and then sampled in synchrony with the
source using analogue to dicital converters (8) which are
triggered by signals from the position sensor (3). These
sampled values are placed it memory device (9) and may be
averaged over a number of complete cycles to reduce the
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effects of signals unrelated to the source. A transform
module (10), which may use a discrete Fourier transform,
produces components related to the harmonic frequencies of
the source for each sensor. The components from the
different sensors are then combined in the transform
module (11) so as to produce the principal components of
sensor signals. Baeh of these inde;~endent components is
modified in the adaption module (12) to produce the
principal components of the new drive Signals. These are
combined with transform module (13) to produce the
frequency components of each drive signal which are then
converted to time values via an inverse transform module
(15). The new time values then replace those in the
memory device (1). The transform modules (11) and (13)
and the adaption modules (12) require knowledge of the
period or frequency of the source. This may be obtained
from the position signal via a frequency counter (14)
which contains a real time clock. This method can be used
in aircraft cabins where the source of the noise is the
propellers or propfans.
An important application of the method of active control
described above is in the control of engine related noise
in vehicles. A control system for controlling the "boom"
in automobile interiors is described in published UK
Patent Application 2,201,858. It uses the wave shaping or
filtering technique described above. The system is
designed to adapt on a time scale comparable with delays
associated with the propagation time of sound from the
actuators to the sensors. In an automobile interior,
however there is sound from many sources which are not
related to the engine; for example, road noise, wind
noise, sound from the in-car entertainment system. This
noise contaminates the sensor signals and degrades the
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performance of the system.
The method of this invention uses averaging of the
synchronously sampled signals over several cycles. This
reduces the level of contamination and improves the
performance of the system. However, the time taken for
averaging reduces the ability of the system to track
changes in the sound field due to changes in engine speed
and load. Therefore, for a given level of contaminating
noise, there will be an optimum number of cycles for
averaging which will depend upon the rate of change of
engine speed and load. The rate of change,o,f engine speed
may be obtained from the position signal and engine load
may be obtained from additional sensors, such as a
pressure sensor in the inlet manifold or throttle position
sensor. This information cari be used to control the rate
of adaption so that optimal performance of the system can
be obtained. This enables good performance to be obtained
over a whole range of conditions rather than just at
"boom" where the unwanted sound is much louder than the
contaminating noise. Most modern automobile engines use
computer controlled engine management systems. Some of
the sensors could be used both for the active control
system and the engine management system. Additionally,
the same microprocessor could be used to control both
systems.
