Solutions Manual Feedback Control of Dynamic Systems Gene F. Franklin资料下载.pdf
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Solutions Manual Feedback Control of Dynamic Systems Gene F. Franklin资料下载.pdf
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thesensor?
theactuator?
theactuatoroutputsignal?
ThereferencesignalNoticethatinanumberofcasesthesamephysicaldevicemayper-formmorethanoneofthesefunctions.Solution:
(a)Amanualsteeringsystemforanautomobile:
101102CHAPTER1.ANOVERVIEWANDBRIEFHISTORYOFFEEDBACKCONTROL(b)Drebbelsincubator:
(c)Waterlevelregulator:
(d)Fly-ballgovernor:
1.1.PROBLEMSANDSOLUTIONS103(e)Automaticsteeringofaship:
(f)Apublicaddresssystem:
2.Identifythephysicalprinciplesanddescribetheoperationofthethermo-statinyourhomeoroce.Solution:
Athermostatisadeviceformaintainingatemperatureconstantatadesiredvalue.Itisequippedwithatemperaturesensorwhichdetectsdeviationfromthedesiredvalue,determineswhetherthetemperaturesettingisexceededornot,andtransmitstheinformationtoafurnaceorairconditionersothatthetermperatureintheroomisbroughtback104CHAPTER1.ANOVERVIEWANDBRIEFHISTORYOFFEEDBACKCONTROLThickstockConsistencymeterControllerWhitewaterCVRefinerMachinechestStoragechestWireMoisturemeterScreensandcleanersHeadboxDryingsectionPressesReelFigure1.1:
ApapermakingmachineFromKarlAstrom,(1970,page192)reprintedwithpermission.tothedesiredsetting.Examples:
Tubeslledwithliquidmercuryareattachedtoabimetallicstripwhichtiltthetubeandcausethemer-curytoslideoverelectricalcontacts.Abimetallicstripconsistsoftwostripsofmetalbondedtogether,eachofadierentexpansioncoecientsothattemperaturechangesbendthemetal.Insomecases,thebendingofbimetallicstripssimplycauseelectricalcontactstoopenorclosedi-rectly.Inmostcasestoday,temperatureissensedelectronicallyusing,forexample,athermistor,aresistorwhoseresistancechangeswithtempera-ture.Moderncomputer-basedthermostatsareprogrammable,sensethecurrentfromthethermistorandconvertthattoadigitalsignal.3.AmachineformakingpaperisdiagrammedinFig.1.12.Therearetwomainparametersunderfeedbackcontrol:
thedensityofbersascontrolledbytheconsistencyofthethickstockthatowsfromtheheadboxontothewire,andthemoisturecontentofthenalproductthatcomesoutofthedryers.Stockfromthemachinechestisdilutedbywhitewaterreturningfromunderthewireascontrolledbyacontrolvalve(CV).Ametersuppliesareadingoftheconsistency.Atthe“dryend”ofthemachine,thereisamoisturesensor.DrawasignalgraphandidentifythesevencomponentslistedinProblem1for(a)controlofconsistency(b)controlofmoistureSolution:
(a)Controlofpapermachineconsistency:
1.1.PROBLEMSANDSOLUTIONS105(b)Controlofpapermachinemoisture:
4.Manyvariablesinthehumanbodyareunderfeedbackcontrol.Foreachofthefollowingcontrolledvariables,drawagraphshowingtheprocessbeingcontrolled,thesensorthatmeasuresthevariable,theactuatorthatcausesittoincreaseand/ordecrease,theinformationpaththatcompletesthefeedbackpath,andthedisturbancesthatupsetthevariable.Youmayneedtoconsultanencyclopediaortextbookonhumanphysiologyforinformationonthisproblem.(a)bloodpressure(b)bloodsugarconcentration(c)heartrate(d)eye-pointingangle(e)eye-pupildiameterSolution:
Feedbackcontrolinhumanbody:
106CHAPTER1.ANOVERVIEWANDBRIEFHISTORYOFFEEDBACKCONTROLVariableSensorActuatorInformationpathDisturbancesa)Bloodpressure-Arterial-Cardiacoutput-Aerentnerve-Bleedingbaroreceptors-Arteriolar/venousbers-Drugsdilation-Stress,Painb)Bloodsugar-Pancreas-Pancreassecreting-Bloodowto-Dietconcentrationinsulinpancreas-Exercise(Glucose)c)Heartrate-Diastolicvolume-Electricalstimulation-Mechanicaldraw-Hormonereleasesensorsofsino-atrialnodeofbloodfromheart-Exercise-Cardiacsympatheticandcardiacmuscle-Circulatingnervesepinephrined)Eyepointing-Opticnerve-Extraocularmuscles-Cranialinnervation-Headmovementangle-Imagedetection-Muscletwitche)Pupildiameter-Rods-Pupillarysphincter-Autonomous-Ambientlightmusclessystem-Drugsf)Bloodcalcium-Parathyroidgland-Cafrombonestoblood-Parathormone-Caneedinbonesleveldetectors-Gastrointestinalhormoneaecting-Drugsabsorptioneectorsites5.Drawagraphofthecomponentsfortemperaturecontrolinarefrigeratororautomobileair-conditioningsystem.Solution:
Thisisthesimplestpossiblesystem.Moderncasesincludecomputercontrolasdescribedinlaterchapters.6.Drawagraphofthecomponentsforanelevator-positioncontrol.Indi-catehowyouwouldmeasurethepositionoftheelevatorcar.Consideracombinedcoarseandnemeasurementsystem.Whataccuraciesdoyousuggestforeachsensor?
Yoursystemshouldbeabletocorrectforthefactthatinelevatorsfortallbuildingsthereissignicantcablestretchasafunctionofcabload.Solution:
Acoarsemeasurementcanbeobtainedbyanelectroswitchlocatedbeforethedesiredoorlevel.Whentouched,thecontrollerreducesthemotorspeed.A“ne”sensorcanthenbeusedtobringtheelevatorpreciselytotheoorlevel.Withasensorsuchastheonedepictedinthegure,alinearcontrolloopcanbecreated(asopposedtotheon-otypeofthecoarsecontrol).Accuracyrequiredforthecourseswitchisaround5cm;
fortheneooralignment,anaccuracyofabout2mmisdesirabletoeliminateanynoticeablestepforthoseenteringorexitingtheelevator.1.1.PROBLEMSANDSOLUTIONS1077.Feedbackcontrolrequiresbeingabletosensethevariablebeingcontrolled.Becauseelectricalsignalscanbetransmitted,amplied,andprocessedeasily,oftenwewanttohaveasensorwhoseoutputisavoltageorcurrentproportionaltothevariablebeingmeasured.Describeasensorthatwouldgiveanelectricaloutputproportionalto:
(a)temperature(b)pressure(c)liquidlevel(d)owofliquidalongapipe(orbloodalonganartery)force(e)linearposition(f)rotationalposition(g)linearvelocity(h)rotationalspeed(i)translationalacceleration(j)torqueSolution:
Sensorsforfeedbackcontrolsystemswithelectricaloutput.Exam-ples(a)Temperature:
Thermistor-temperaturesensitiveresistorwithresis-tancechangeproportionaltotemperature;
Thermocouple;
Thyrister.Modernthermostatsarecomputercontrolledandprogrammable.(b)Pressure:
Strainsensitiveresistormountedonadiaphragmwhichbendsduetochangingpressure108CHAPTER1.ANOVERVIEWANDBRIEFHISTORYOFFEEDBACKCONTROL(c)Liquidlevel:
Floatconnectedtopotentiometer.Ifliquidisconductivetheimpedancechangeofarodimmersedintheliquidmayindicatetheliquidlevel.(d)Flowofliquidalongapipe:
Aturbineactuatedbytheowwithamagnettotriggeranexternalcountingcircuit.Halleectproducesanelectronicoutputinresponsetomagneticeldchanges.Anotherway:
Measurepressuredierencefromventuriintopressuresensorasingure;
Flowmeter.Forbloodow,anultrasounddevicelikeaSONARcanbeused.(e)Position.Whendirectmechanicalinteractionispossibleandfor“small”dis-placements,thesameideasmaybeused.Forexampleapotentiome-termaybeusedtomeasurepositionofamassinanaccelerator(h).Howeverinmanycasessuchasthepositionofanaircraft,thetaskismuchmorecomplicatedandmeasurementcannotbemadedirectly.Calculationmustbecarriedoutbasedonothermeasurements,forexampleopticalorelectromagneticdirectionmeasurementstoseveralknownreferences(stars,transmittingantennas.);
LVDTforlinear,RVDTforrotational.(f)Rotationalposition.Themostcommontraditionaldeviceisapote-niometer.Alsocommonaremagneticmachinesinshicharotatingmagnetproducesavariableoutputbasedonitsangle.(g)Linearvelocity.Foravehicle,aRADARcanmeasurelinearvelocity.Inothercases,arack-and-pinioncanbeusedtotranslatelineartorotationalmotionandanelectricmotor(tachometer)usedtomeasurethespeed.(h)Speed:
Anytoothedwheelorgearonarotatingpartmaybeusedtotriggeramagneticeldchangewhichcanbeusedtotriggeranelec-tricalcountingcircuitbyuseofaHalleect(magnetictoelectrical)sensor.Thepulsescanthenbecountedoverasettimeintervaltoproduceangularvelocity:
Rategyro;
Tachometer1.1.PROBLEMSANDSOLUTIONS109(i)Acceleration:
Amassmovementrestrainedbyaspringmeasuredbyapotentiometer.Apiezoelectricmaterialmaybeusedinstead(ama-terialthatproduceselectricalcurrentwithintensityproportionaltoacceleration).Inmodernairbags,anintegratedcircuitchipcontainsatinyleverandproofmasswhosemotionismeasuredgeneratingavoltageproportionaltoacceleration.(j)Force,torque:
Adynamometerbasedonspringorbeamdeections,whichmaybemeasuredbyapotentiometerorastrain-gauge.8.EachofthevariableslistedinProblem7canbebroughtunderfeedbackcontrol.Describeanactuatorthatcouldacceptanelectricalinputandbeusedtocontrolthevariableslisted.Givetheunitsoftheactuatoroutputsignal.Solution:
(a)Resistorwithvoltageappliedtoitormercuryarclamptogenerateheatforsmalldevices.afurnaceforabuilding.(b)Pump:
Pumpingairinoroutofachambertogeneratepressure.Else,atorquemotorproducesforce.(c)Valveandpump:
forcingliquidinoroutofthecontainer.(d)Avalveisnromallyusedtocontrolow.(e)Electricmotor(f)Electricmotor(g)Electricmotor(h)Electricmotor(i)Translationalacceler
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