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