Adaptive Feed-Forward Control of Low Frequency Interior Noise

351 Pages·2012·10.161 MB·English

by  Thomas Kletschkowski (auth.)

Adaptive Feed-Forward Control of Low Frequency
Interior Noise
InternationalSerieson
INTELLIGENTSYSTEMS,CONTROL,ANDAUTOMATION:
SCIENCEANDENGINEERING
VOLUME56
Editor:
ProfessorS.G.Tzafestas,NationalTechnicalUniversityofAthens,Athens,Greece
EditorialAdvisoryBoard
ProfessorP.Antsaklis,UniversityofNotreDame,NotreDame,IN,USA
ProfessorP.Borne,EcoleCentraledeLille,Lille,France
ProfessorD.G.Caldwell,UniversityofSalford,Salford,UK
ProfessorC.S.Chen,UniversityofAkron,Akron,Ohio,USA
ProfessorT.Fukuda,NagoyaUniversity,Nagoya,Japan
ProfessorS.Monaco,UniversityLaSapienza,Rome,Italy
ProfessorG.Schmidt,TechnicalUniversityofMunich,Munich,Germany
ProfessorS.G.Tzafestas,NationalTechnicalUniversityofAthens,Athens,Greece
ProfessorF.Harashima,UniversityofTokyo,Tokyo,Japan
ProfessorN.K.Sinha,McMasterUniversity,Hamilton,Ontario,Canada
ProfessorD.Tabak,GeorgeMasonUniversity,Fairfax,Virginia,USA
ProfessorK.Valavanis,UniversityofDenver,Denver,Colorado,USA
Forfurthervolumes:
www.springer.com/series/6259
Thomas Kletschkowski
Adaptive Feed-
Forward Control
of Low Frequency
Interior Noise
ThomasKletschkowski
DepartmentofMechanicalEngineering,
Mechatronics
Helmut-Schmidt-University/University
oftheFederalArmedForcesHamburg
Holstenhofweg85
Hamburg22043
Germany
[email protected]
ISBN978-94-007-2536-2 e-ISBN978-94-007-2537-9
DOI10.1007/978-94-007-2537-9
SpringerDordrechtHeidelbergLondonNewYork
LibraryofCongressControlNumber:2011941767
©SpringerScience+BusinessMediaB.V.2012
Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby
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permissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurpose
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Coverdesign:VTeXUAB,Lithuania
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Preface
Thisbookfocusesonamechatronicapproachtoactivecontrolofinteriornoise.It
strives to comprehend the results of a five year research period as chief engineer
withthechairformechatronicsoftheHelmut-Schmidt-University/Universityofthe
FederalArmedForcesHamburg.
Althoughthebookstartswithfundamentalconcepts,thereaderisexpectedtobe
familiarwithengineeringmechanicsand/orengineeringacoustics(includingexper-
imentaltechniques),systemtheoryandnumericalmathematics.Thetargetaudience
thereforeconsistsofpostgraduatestudents,professionalengineers,andresearchers
workinginmechatronics,andespeciallyinthefieldofactiveinteriornoisecontrol.
Atthebeginningofeachnewchapter,anabstractcontainsbothashortsummary
and,asrecommendationsforfurtherreading,abriefcommentonliterature.Theim-
portantcontributionstothesubjectmatterarequotedthroughoutthetext.However,
the list of references is far from being complete. I therefore apologize to any col-
leaguesnotmentionedinspiteoftheirimportantcontributionstoacademicand/or
appliedresearchonactivenoiseandvibrationcontrol.
Hamburg,Germany ThomasKletschkowski
v
Acknowledgements
TheauthorgratefullyacknowledgesthesupportoftheHelmut-Schmidt-University/
UniversityoftheFederalArmedForcesHamburg.Thetop-levelconditionsforre-
search and teaching provided by this institution have been essential to finish my
Habilitationaswellastowritethisbook.
Veryspecialthanks,theauthorwouldliketoexpresstoDelfSachauwhomade
me familiar with Active Noise and Vibration Control in 2004 and since then has
continued to give much helpful advice. The author would also like to thank Udo
ZölzerandDetlefKrahèforalloftheircriticisms,commentsandsuggestions.Fur-
thermore, the author would like to thank Uwe Schomburg and Albrecht Bertram
whoalwaysencouragedmetofinishthiswork.
Many colleagues and friends also made useful comments and suggestions that
madeispossibletoimprovethisbook.TheauthorwouldliketothankStenBöhme,
HaraldBreitbach,MohamedBouhaj,ChristianGerner,JulianGreßkowski,Martin
Holters,NorbertHövelmann,KayKochan,RolfLammering,JörgLefèvre,Marian
Markiewicz, Günter Neuwirth, Oliver Pabst, Marek Pawelczyk, Bernd Samtleben,
HenningScheel,KaiSimanowski,JochenSommer,FabriceTeuma,MartinWandel
andMatthiasWeber.
Theacademiccareeroftheauthorwouldhavebeenimpossiblewithoutthesup-
portofhisfamilyinHamburg,SchwerinandDenHaag.Veryspecialthanksgoto
Ammerentie,RolandandKaroline,toBeateandReinhardaswellastoAdrianaand
Izaak.Theauthorisgratefultoallofthem.
vii
Notation
MathematicalOperationsandOperators
div Divergenceoperator
grad Gradientoperator
max Maximumoperator
min Minimumoperator
E Expectation
F Fouriertransform
F−1 InverseFouriertransform
F Fouriertransformofsampledsignals
d
F−1 InverseFouriertransformofsampledsignals
d
F DiscreteFouriertransform
DFT
F−1 InverseDiscreteFouriertransform
DFT
Im Givestheimaginarypartofacomplexnumber
Re Givestherealpartofacomplexnumber
T Transformation
◦–• Mappingfromtimedomaintofrequencydomain
•–◦ Mappingfromfrequencydomaintotimedomain
(cid:2) Waveoperator
(cid:2)(cid:3) Vectorwaveoperator
()T Transposition
()H Hermitianorconjugatetranspose(ofamatrix)
d() Totalderivative
∂() Partialderivative
() Arithmeticmean
tr() Traceofamatrix
(cid:4)(cid:4) Euclideannorm
2
ConventionsforSignalsandSystems
ConventionsforContinuous-TimeSignalsandSystems
t Time
f Frequency
ix
x Notation
ω Angularfrequency,i.e.2π timestheactualfrequencyinhertz
x(t) Continuous-timesignal
X(jω) Fouriertransformofx(t)
ConventionsforDiscrete-TimeSignalsandSystems
n Discretetimestep
T Samplingtime,sot=nT wherenisaninteger
x(n) Discrete-timesignal
X(ejωT) Fouriertransformofx(n)
X(n) Fouriertransformofx(n)atdiscretetimestepn
GeneralConventions
xˆ Realvaluedamplitudeofx orapproximation/modelofx
(cid:5)
x Filteredsignal
x∞ Steadystateofx
x¯ Arithmeticmeanofx
σ2 Varianceofx
x
x Rootmeansquareofx
RMS
δx Virtualsignal
ˆ
X ComplexamplitudeofXorapproximation/modelofX
(cid:5)
X Filteredsignal
X∞ SteadystateofX
E Meansignalenergy
x
Π Meansignalpower
x
r Autocorrelationofx
xx
r Crosscorrelationbetweenx andy
xy
h Impulseresponseofasystem
S Autospectraldensityofx
xx
S Crossspectraldensityforx andy
xy
G Single-sidedautospectraldensityofx
xx
G Single-sidedcrossspectraldensityforx andy
xy
H Transferfunctionofasystem
ConventionsforLinearAlgebra
ConventionsforScalars
x,X Scalarvariables
X RealpartofX,whereX =Re(X)
R R
X ImaginarypartofX,whereX =Im(X)
I I
X∗ ConjugatecomplexofX,whereX∗=X −jX
R I
|X|2 SquaredmagnitudeofX,where|X|2=X∗X
ConventionsforColumnMatrices
x Lower-caseboldvariablesarecolumnmatrices
xT Thetransposeofacolumnmatrixisarowmatrix
x Realpartofx,wherex =Re(x)
R R
x Imaginarypartofx,wherex =Im(x)
I I
xH Hermitianofx,wherexH =xT −jxT
R I
Notation xi
xHx Theinnerproductofx,whichisascalar
xxH Theouterproductofx,whosetracei√sequaltotheinnerproduct
(cid:4)x(cid:4) Euclideannormofx,where(cid:4)x(cid:4) = xHx
2 2
ConventionsforMatrices
X Upper-caseboldvariablesarematrices
XT ThetransposeofX
X RealpartofX,whereX =Re(X)
R R
X ImaginarypartofX,whereX =Im(X)
I I
XH HermitianofX,whereXH =XT −jXT
R I
X−1 TheinverseofX
X−H TheinverseofXH
tr(X) TraceofX
λi(X) Thei-theigenvalueofX (cid:2)
(cid:4)X(cid:4) EuclideannormofX,where(cid:4)X(cid:4) = tr(XHX)
2 2
I Theidentitymatrix
ConventionsforVectors
x(cid:3) Vectorvaluedvariablesuchaspositionvector
x(cid:3)·y(cid:3) Scalarproductbetweenvectors
CommentsonSymbols
Lower-CaseLatinSymbols
b Costfunctionparametercolumnmatrix
c Speedofsoundorcostfunctionparameter
d Disturbanceordistancebetweenanodeandcathode
e 2.718...,errorsignal,acousticenergydensityoradditivefilterederror
e Acoustickineticenergydensity
kin
e Acousticpotentialenergydensity
pot
f Frequency
f (ξ) Probabilitydensityfunctionofastochasticprocess
x(t)
f n-theigenfrequency
n
f n-thresonancefrequency
nR
f Loadcolumnmatrix
i Index,normalcomponentofsoundintensityorelectriccurrent
(cid:3)
i Soundintensityvector √
j Indexorimaginarynumber(j = −1)
k Index,wavenumber,discrete-timedelayorstiffness
(cid:5)
k Alternativeformofcomplexwavenumber
k Wavenumberforthen-thresonance
nR
l Indexorlength
m Index,discrete-timedelayormass
n Indexordiscretetimestep
n(cid:3) Normalvector
p Acousticpressure
p Totalpressure
tot
xii Notation
p∞ Equilibriumvalueoftotalpressure
p Primarynoise
p
p Anti-noise
s
q Sourcestrength,electricchargeorvolumevelocity
r Dampingcoefficientorradialdistance
r Residuumcolumnmatrix
Δr Changeinradialdistance
t Time
t Observationtimepoint
i
v Normalcomponentofacousticvelocity
v(cid:3) Acousticvelocity
v(cid:3) Totalvalueofacousticvelocity
tot
v(cid:3)∞ Equilibriumvalueofacousticvelocity
w Columnmatrixofcontrolfiltercoefficients
w mki-thcontrolfiltercoefficient
mki
wˆ mki-thauxiliarycoefficient
mki
x Signalorx-coordinate
Δx Separationdistance
x(cid:3) Positionvector
y Signalory-coordinate
z z-coordinate
Upper-CaseLatinSymbols
A Attenuationofanaloguefilter
A Costfunctionparametermatrix
B Electromagneticinduction
C Capacityofcondenser
C Stiffnessmatrixorcontrollermatrix
C Specificheatforconstantpressure
p
C Specificheatforconstantvolume
V
D Dimensionlessdampingratioofmechanicalsystems
D Dampingmatrix
E Error,EnergyorBulkmodulus
I Numberofcontrolfiltercoefficientsorinstantaneousintensity
¯
I Meanintensity
¯
I Measuredmeanintensity
M
¯
I Truemeanintensity
T
J Numberoffiltercoefficientsusedforplantmodelingorcostfunction
K Numberofreferencesignals
L Numberoferrorsignals,lengthorinductance
M Numberofcontrolleroutputsignalsormodaloverlap
M Massmatrix
N Numberoftimesteps
P Probabilityofastochasticprocess
w
R Complexreflectioncoefficient,electricresistanceorresiduum
R Impedanceboundary
Z