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04/07/2014, 05:28
... involved inthe design of a
satisfactory control system.To understand and use a computer-aided analysis
and design package, one must first a chieve a conceptual understanding of the
theory and processes ... theenigmaticcontrolsystem.Toprovideacoherentdevelopmentofthesub-
ject,weeschewformalproofsandlemmas,insteadusinganorganizationthat
drawstheperceptivestudentsteadilyandsurelytothedemandingtheoryof
multivariablecontrolsystems.Designexamplesareincludedthroughouteach
chaptertoreinforcethestudentsunderstandingofthematerial.Astudentwho
hasreachedthispointisfullyequippedtoundertakethechallengesofmore
advancedcontroltheories,aspresentedinadvancedcontroltheorytextbooks.
Chapter2 setsforththeappropriatedifferentialequationstodescribethe
performanceofphysicalsystems,networks,anddevices.Theblockdiagram,the
transferfunction,andthestatespace(theessentialconceptofmodern
controltheory)arealsointroduced.Theapproachusedforthestatespaceis
thesimultaneousderivationofthestate-vectordifferentialequationwiththe
SISOdifferentialequationforachosenphysicalsystem.Thechapteralsoshows
howtoderivethemathematicaldescriptionofaphysicalsystemusing
LaGrangeequations.
Chapter3 presentstheclassicalmethodofsolvingdifferentialequations.
Oncethestate-variableequationhasbeenintroduced,acarefulexplanationof
itssolutionisprovided.Therelationshipofthetransferfunctiontothestate
equationofthesystemispresentedinChapter14.Theimportanceofthestate
transitionmatrixisdescribed,andthestatetransitionequationisderived.
Theideaofeigenvaluesisexplainednext;thistheoryisusedwiththeCayley^
HamiltonandSylvestertheoremstoevaluatethestatetransitionmatrix.
TheearlypartofChapter4presentsacomprehensivedescriptionof
Laplacetransformmethodsandpole-zeromaps.Somefurtheraspectsofmatrix
algebraareintroducedasbackgroundforsolvingthestateequationusing
Laplacetransforms.Finally,theevaluationoftransfermatricesisclearly
explained.
Chapter5 beginswithsystemrepresentationbytheconventionalblock-
diagramapproach.Thisisfollowedbyadiscussionofsimulationdiagramsand
thedeterminationofthestatetransitionequationusingsignalflowgraphs.The
chapteralsoexplainshowtoderiveparallelstatediagramsfromsystemtransfer
functions,establishingtheadvantagesofhavingthestateequationinuncoupled
form.
Chapter6 introducesbasicfeedbacksystemcharacteristics.Thisincludes
therelationshipbetweensystemtypeandtheabilityofthesystemtofollowor
trackpolynomialinputs.
Chapter7 presentsthedetailsoftheroot-locusmethod.Chapters 8and9
describethefrequency-responsemethodusingbothlogandpolarplots.These
chaptersaddressthefollowingtopics:theNyquiststabilitycriterion;thecorre-
lationbetweenthes-plane,frequencydomain,andtimedomain;andgainset-
tingtoachieveadesiredoutputresponsepeakvaluewhiletrackingpolynomial
commandinputs.Chapters1 0and1 1describethemethodsforimproving
Copyright ... heavier,moveddown,therebyclosingthedoor.Thisoccursaslongasthe
bucketishigherthanthecontainer.Thedevicewasprobablyactuatedwhen
therulerandhisentouragestartedtoascendthetemplesteps.Thesystemfor
openingthedoorwasnotvisibleorknowntothemasses.Thus,itcreatedan
airofmysteryanddemonstratedthepoweroftheOlympiangods.
JamesWatt’sflyballgovernorforcontrollingspeed,developedin1788,
canbeconsideredthefirstwidelyusedautomaticfeedbackcontrolsystem.
Maxwell,in1868,madeananalyticstudyofthestabilityoftheflyball
governor.Thiswasfollowedbyamoredetailedsolutionofthestabilityofa
third-orderflyballgovernorin1876bytheRussianengineerWischnegradsky
[13].Minorskymadeoneoftheearlierdeliberateapplicationsofnonlinear
elementsinclosed-loopsystemsinhisstudyofautomaticshipsteeringabout
1922[14].
Asignificantdateinthehistoryofautomaticfeedbackcontrolsystemsis
1934,whenHazen’spaper‘‘TheoryofServomechanisms’’waspublishedin
theJournaloftheFranklinInstitute,markingthebeginningoftheveryintense
interestinthisnewfield.Itwasinthispaperthatthewordservomechanism
originated,fromthewordsservant(orslave)andmechanism.Black’simportant
paperonfeedbackamplifiersappeared[15]inthesameyear.AfterWorldWar
II,controltheorywasstudiedintensivelyandapplicationshaveproliferated.
Manybooksandthousandsofarticlesandtechnicalpapershavebeenwritten,
andtheapplicationofcontrolsystemsintheindustrialandmilitaryfieldshas
beenextensive.Thisrapidgrowthoffeedbackcontrolsystemswasacceler-
atedbytheequallyrapiddevelopmentandwidespreaduseofcomputers.
Anearlymilitaryapplicationofafeedbackcontrolsystemistheantiair-
craftradartrackingcontrolsystemshowninFig.1.12.Theradarantenna
detectsthepositionandvelocityofthetargetairplane,andthecomputer
takesthisinformationanddeterminesthecorrectfiringangleforthegun.
Thisangleincludesthenecessaryleadanglesothattheshellreachesthe
projectedpositionatthesametimeastheairplane.Theoutputsignalofthe
computer,whichisafunctionofthefiringangle,isfedintoanamplifierthat
providespowerforthedrivemotor.Themotorthenaimsthegunatthe
necessaryfiringangle.Afeedbacksignalproportionaltothegunposition
ensurescorrectalignmentwiththepositiondeterminedbythecomputer.
Sincethegunmustbepositionedbothhorizontallyandvertically,thissystem
hastwodrivemotors,whicharepartsoftwocoordinatedfeedbackloops.
Theadventofthenuclearreactorwasamilestoneintheadvancementof
scienceandtechnology.Forproperoperationthepowerlevelofthereactor
mustbemaintainedatadesiredvalueormustvaryinaprescribedmanner.
Thismustbeaccomplishedautomaticallywithminimumhumansupervision.
Figure1.13isasimplifiedblockdiagramofafeedbackcontrolsystemfor
controlling...