Introduction to Modern Control Theory中英文.docx

Introduction to Modern Control Theory中英文.docx

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IntroductiontoModernControlTheory中英文

IntroductiontoModernControlTheory

Severalfactorsprovidedthestimulusforthedevelopmentofmoderncontroltheory:

a.Thenecessaryofdealingwithmorerealisticmodelsofsystem.

b.Theshiftinemphasistowardsoptimalcontrolandoptimalsystemdesign.

c.Thecontinuingdevelopmentsindigitalcomputertechnology.

d.Theshortcomingofpreviousapproaches.

e.Recognitionoftheapplicabilityofwell-knownmethodsinotherfieldsofknowledge.

Thetransitionfromsimpleapproximatemodels,whichareeasytoworkwith,tomorerealisticmodels,producestwoeffects.First,alargenumberofvariablesmustbeincludedinthemodels.Second,amorerealisticmodelismorelikelytocontainnonlinearitiesandtime-varyingparameters.Previouslyignoredaspectsofthesystem,suchasinteractionswithfeedbackthroughtheenvironment,aremorelikelytobeincluded.

Withanadvancingtechnologicalsociety,thereisatrendtowardsmoreambitiousgoals.Thisalsomeansdealingwithcomplexsystemwithalargenumberofinteractingcomponents.Theneedforgreateraccuracyandefficiencyhaschangertheemphasisoncontrolsystemperformance.Theclassicalspecificationsintermsofpercentovershoot,settingtime,bandwidth,etc.haveinmanycasesgivenwaytooptimalcriteriasuchasminimumenergy,minimumcost,andminimumtimeoperation.Optimizationofthesecriteriamakesitevenmoredifficulttoavoiddealingwithunpleasantnonlinearities.Optimalcontroltheoryoftendictatesthatnonlineartime-varyingcontrollawsareused,evenifthebasicsystemislinearandtime-invariant.

Thecontinuingadvancesincomputertechnologyhavehadthreeprincipaleffectsonthecontrolsfield.Oneoftheserelatestothegiganticsupercomputers.Thesizeandtheclassoftheproblemsthatcannowbemodeled,analyzed,andcontrolledareconsiderablylargethantheywerewhenthefirsteditionofthisbookwaswritten.

ThesecondimpactofthecomputertechnologyhastosowiththeproliferationandwideavailabilityofthemicrocomputersinhomesandItheworkplace,classicalcontroltheorywasdominatedbygraphicalmethodsbecauseatthetimethatwastheonlywaytosolvecertainproblems,Noweverycontroldesignerhaseasyaccesstopowerfulcomputerpackagesforsystemsanalysisanddesign.Theoldgraphicalmethodshavenotyetdisappeared,buthavebeenautomated.Theysurvivebecauseoftheinsightandintuitionthattheycanprovide,somedifferenttechniquesareoftenbettersuitedtoacomputer.Althoughacomputercanbeusedtocarryouttheclassicaltransform-inversetransformmethods,itisusedusuallymoreefficientforacomputertointegratedifferentialequationsdirectly.

Thethirdmajorimpactofthecomputersisthattheyarenowsocommonlyusedasjustanothercomponentinthecontrolsystems.Thismeansthatthediscrete-timeanddigitalsystemcontrolnowdeservesmuchmoreattentionthanitdidinthepast.

Moderncontroltheoryiswellsuitedtotheabovetrendsbecauseitstime-domaintechniquesanditsmathematicallanguage（matrices,linearvectorspaces,etc.）areidealwhendealingwithacomputer.Computersareamajorreasonfortheexistenceofstatevariablemethods.

Mostclassicalcontroltechniquesweredevelopedforlinearconstantcoefficientsystemswithoneinputandoneoutput（perhapsafewinputsandoutputs）.ThelanguageofclassicaltechniquesistheLaplaceorZ-transformandtransferfunctions.Whennonlinearitiesadtimevariationsarepresent,theverybasisfortheseclassicaltechniquesisremoved.Somesuccessfultechniquessuchasphase-planemethods,describingfunctions,andotheradhocmethods,havebeendevelopedtoalleviantthisshortcoming.

However,thegreatestsuccesshasbeenlimitedtolow-ordersystems.Thestatevariableapproachofmoderncontroltheoryprovidesauniformandpowerfulmethodofrepresentingsystemsofarbitraryorder,linearornonlinear,withtime-varyingorconstantcoefficient.Itprovidesanidealformulationforcomputerimplementationandisresponsibleformuchoftheprogressinoptimizationtheory.

Moderncontroltheoryisarecentdevelopmentinthefieldofcontrol.Therefore,thenameisjustifiedatleastasadescriptivetitle.However,thefoundationsofmoderncontroltheoryaretobefoundinotherwell-establishedfields.RepresentingasystemintermsofstatevariablesisequivalenttotheapproachofHamiltonianmechanics,usinggeneralizedcoordinatesandgeneralizedmoment.Theadvantagesofthisapproachhavebeenwell-knownIclassicalphysicsformanyyears.Theadvantagesofusingmatriceswhendealingwithsimultaneousequationsofvariouskindshavelongbeenappreciatedinappliedmathematics.Thefieldoflinearalgebraalsocontributesheavilytomoderncontroltheory.Thisisduetotheconcisenotation,thegeneralityoftheresults,andtheeconomyofthoughtthatlinearalgebraprovides.

MechanismofSurfaceFinishProduction

Therearebasicallyfivemechanismswhichcontributetotheproductionofasurfacewhichhavebeenmachined.Thereare:

（1）Thebasicgeometryofthecuttingprocess.In,forexample,singlepointturningthetoolwilladvanceaconstantdistanceaxiallyperrevolutionoftheworkpieceandtheresultantsurfacewillhaveonit,whenviewedperpendicularlytothedirectionoftoolfeedmotion,aseriesofcuspswhichwillhaveabasicformwhichreplicatestheshapeofthetoolincut.

（2）Theefficiencyofthecuttingoperation.Ithasalreadybeenmentionedthatcuttingwithunstablebuilt-up-edgeswillproduceasurfacewhichcontainshardbuilt-up-edgefragmentswhichwillresultinadegradationofthesurfacefinish.Itcanalsobedemonstratedthatcuttingunderadverseconditionssuchasapplywhenusinglargefeedssmallrakeanglesandlowcuttingspeeds,besidesproducingconditionswhichcontinuousshearoccurringintheshearzone,tearingtakesplace,discontinuouschipsofuneventhicknessareproduced,andtheresultantsurfaceispoor.Thissituationisparticularlynoticeablewhenmachiningveryductilematerialssuchascopperandaluminum.

（3）Thestabilityofthemachinetool.Undersomecombinationsofcuttingconditions:

workpiecesize,methodofclamping,andcuttingtoolrigidityrelativetothemachinetoolstructure,instabilitycanbesetupinthetoolwhichcausesittovibrate.Undersomeconditionsthevibrationwillbuiltupandunlesscuttingisstoppedconsiderabledamagetoboththecuttingtoolandworkpiecemayoccur.Thisphenomenonisknownaschatterandinaxialturningischaracterizedbylongpitchhelicalbandsontheworkpiecesurfaceandshortpitchundulationsonthetransientmachinedsurface.

（4）Theeffectivenessofremovingsward.Indiscontinuouschipproductionmachining,suchasmillingorturningofbrittlematerials,itisexpectedthatthechip（sward）willleavethecuttingzoneeitherundergravityorwiththeassistanceofajetofcuttingfluidandthattheywillnotinfluencethecutsurfaceinanyway.However,whencontinuouschipproductionisevident,unlessstepsatetakentocontroltheswarfitislikelythatitwillimpingeonthecutsurfaceandmarkit.Inevitably,thismarkingbesidealookingunattractive,oftenresultsinapoorersurfacefinishing,

（5）Theeffectiveclearanceangleonthecuttingtool.Forcertaingeometriesofminorcuttingedgereliefandclearanceanglesitispossibletocutonthemajorcuttingedgeandburnishontheminorcuttingedge.Thiscanproduceagoodsurfacefinishbut,ofcourse,itisstrictlyacombinationofmetalcuttingandmetalformingandisnottoberecommendedasapracticalcuttingmethod.However,duetocuttingtoolwear,theseconditionsoccasionallyariseandleadtoamarkedchangeinthesurfacecharacteristics.

SurfaceFinishingandDimensionalControl

Productsthathavebeencompletedtotheirpropershapeandsizefrequentlyrequiresometypeofsurfacefinishingtoenablethantosatisfactorilyfulfilltheirfunction.Insomecases,titisnecessarytoimprovethephysicalpropertiesofthesurfacematerialforresistancetopenetrationorabrasion.Inmanymanufacturingprocesses,theproductsurfaceisleftwithdirt,chips,grease,orotherharmfulmaterialuponit.Assembliesthataremadeofdifferentmaterials,orfromthesamematerialsprocessedindifferentmanners,manyrequiresomespecialsurfacetreatmenttoprovideuniformityofappearance.

Surfacefinishingmanysometimesbecomeanintermediatestepprocessing.Forinstance,cleaningandpolishingareusuallyessentialbeforeanykindofplatingprocess.Someofthecleaningproceduresarealsousedforimprovingsurfacesmoothnessonmatingpartsandforremovingburrsandsharpcorners,whichmightbeharmfulinlateruse.Anotherimportantneedforsurfacefinishingisforcorrosionprotectioninavarietyofenvironments.Thetypeofprotectionprocedurewilldependlargelyupontheanticipatedexposure,withdueconsiderationtothematerialbeingprotectedandtheeconomicfactorsinvolved.

Satisfyingtheaboveobjectivesnecessitatestheuseofmainsurface-finishingmethodsthatinvolvechemicalchangeofthesurfacemechanicalworkaffectingsurfaceproperties,cleaningbyavarietyofmethods,andtheapplicationofprotectivecoatings,organicandmetallic.

Intheearlydaysofengineering,thematingofpartswasachievedbymachiningonepartasnearlyaspossibletotherequiredsize,machiningthematingpartnearlytosize,andthencompletingitsmachining,continuallyofferingtheotherparttoit,untilthedesiredrelationshipwasobtained.Ifitwasinconvenienttoofferonepartotheotherpartduringmachining,thefinalworkwasd