标签: zeros

EffectofRHPzerosandpolesonthesensitivityfunctionsinmultivariablesystems(SigurdSkogestad)

CancellationofDiscreteTimeUnstableZerosbyFeedforwardControl(MasayoshiTomizuka)

Thetwomaintechniquesinsignalprocessing,convolutionandFourieranalysis,teachthatalinearsystemcanbecompletelyunderstoodfromitsimpulseorfrequencyresponse.Thisisaverygeneralizedapproach,sincetheimpulseandfrequencyresponsescanbeofnearlyanyshapeorform.Infact,itistoogeneralformanyapplicationsinscienceandengineering.Manyoftheparametersinouruniverseinteractthroughdifferentialequations.Forexample,thevoltageacrossaninductorisproportionaltothederivativeofthecurrentthroughthedevice.Likewise,theforceappliedtoamassisproportionaltothederivativeofitsvelocity.Physicsisfilledwiththesekindsofrelations.Thefrequencyandimpulseresponsesofthesesystemscannotbearbitrary,butmustbeconsistentwiththesolutionofthesedifferentialequations.Thismeansthattheirimpulseresponsescanonlyconsistofexponentialsandsinusoids.TheLaplacetransformisatechniqueforanalyzingthesespecialsystemswhenthesignalsarecontinuous.Theztransformisasimilartechniqueusedinthediscretecase.CHAPTERTheLaplaceTransform32Thetwomaintechniquesinsignalprocessing,convolutionandFourieranalysis,teachthatalinearsystemcanbecompletelyunderstoodfromitsimpulseorfrequencyresponse.Thisisaverygeneralizedapproach,sincetheimpulseandfrequencyresponsescanbeofnearlyanyshapeorform.Infact,itistoogeneralformanyapplicationsinscienceandengineering.Manyoftheparametersinouruniverseinteractthroughdifferentialequations.Forexample,thevoltageacrossaninductorisproportionaltothederivativeofthecurrentthroughthedevice.Likewise,theforceappliedtoamassisproportionaltothederivativeofitsvelocity.Physicsisfilledwiththesekindsofrelations.Thefrequencyandimpulse……

TransmissionZerosinFilterDesignTransmissionZerosinFilterDesignByRandallW.RheaEaglewareCorporationoreeconomicandeffectivebandpassfilterscanbedesignedbycontrollingthelocationoftransmissionzeros.Whatdowemeanbytransmissionzeros?Considerthefifth-orderlowpassfilterinFigure1(a).Thereislittleattenuationatlowfrequenciesandincreasingattenuationabovethecutoff.Onlyatinfinitefrequencyistherenotransmission.Infact,atinfinitefrequency,eachinductorbecomesanopenandeachcapacitorbecomesashort.Thisfilterhasfivetransmissionzeros(TZs)atinfinitefrequency.ThefifthorderhighpassfilterinFigure1(b)hasfiveTZsatDC.Itisessentialthattheinductorsandcapacitorsalternate.Ifweweretoattempttobuildafifth-orderlowpasswithfiveseriesinducto……