樓宇第04次課-樓宇第01次課-CHAPTER-1-CONTROL-FUNDAMENTALS-4課件

CHAPTER1CONTROLFUNDAMENTALS(4)CHAPTER11StepControl

Stepcontrollersoperateswitchesorrelaysinsequencetoenableordisablemultipleoutputs,orstages,oftwo-positiondevicessuchaselectricheatersorreciprocatingrefrigerationcompressors.Stepcontrolusesananalogsignaltoattempttoobtainproportionaloutputfromequipmentthatistypicallyeitheronoroff.Figures25and26showthatthestagesmaybearrangedtooperatewithorwithoutoverlapoftheoperating(on/off)differentials.Ineithercase,thetypicaltwo-positiondifferentialsstillStepControl2Fig.25.ElectricHeatStages.existbutthetotaloutputisproportioned.Fig.25.ElectricHeatStages.3Fig.26.StagedReciprocatingChillerControl.Fig.26.StagedReciprocating4

Figure27showsstepcontrolofsequencedDXcoilsandelectricheat.Onariseintemperaturethroughthethrottlingrangeatthethermostat,theheatingstagessequenceoff.Onafurtherriseafteradeadband,thecoolingstagesturnoninsequence.Avariationofstepcontrolusedtocontrolelectricheatisstepplus-proportionalcontrol,whichprovidesasmoothtransitionbetweenstages.ThiscontrolmoderequiresoneofthestagestobeaproportionalmodulatingoutputFigure27showsstep5andtheothers,two-position.Formostefficientoperation,theproportionalmodulatingstageshouldhaveatleastthesamecapacityasonetwo-positionstage.andtheothers,two-position.6Fig.27.StepControlwithSequencedDXCoilsandElectricHeat.Fig.27.StepControlwithSeq7

Startingfromnoload,astheloadontheequipmentincreases,themodulatingstageproportionsitsloaduntilitreachesfulloutput.Then,thefirsttwo-positionstagecomesfullonandthemodulatingstagedropstozerooutputandbeginstoproportionitsoutputagaintomatchtheincreasingload.Whenthemodulatingstageagainreachesfulloutput,thesecondtwo-positionstagecomesfullon,themodulatingstagereturnstozero,andthesequencerepeatsuntilallstagesrequiredtomeettheloadconditionareon.Onadecreaseinload,theprocessreverses.Startingfromnoloa8

FloatingControlFloatingcontrolisavariationoftwo-positioncontrolandisoftencalled"three-positioncontrol".Floatingcontrolisnotacommoncontrolmode,butisavailableinmostmicroprocessor-basedcontrolsystems.Avariationoffloatingcontrolisproportional-speed-floatingcontrol.Floatingcontrolrequiresaslow-movingactuatorandafastrespondingsensorselectedaccordingtotherateofresponseinthecontrolledsystem.Iftheactuatorshouldmovetooslowly,thecontrolledFloatingControl9systemwouldnotbeabletokeeppacewithsuddenchanges;iftheactuatorshouldmovetooquickly,two-positioncontrolwouldresult.Floatingcontrolkeepsthecontrolpointnearthesetpointatanyloadlevel,andcanonlybeusedonsystemswithminimallagbetweenthecontrolledmediumandthecontrolsensor.Floatingcontrolisusedprimarilyfordischargecontrolsystemswherethesensorisimmediatelydownstreamfromthecoil,damper,ordevicethatitcontrols.Anexampleoffloatingcontrolistheregulationofstaticsystemwouldnotbeab10Fig.28.FloatingStaticPressureControl.pressureinaduct(Fig.28).Fig.28.FloatingStaticPress11Inatypicalapplication,thecontrolpointmovesinandoutofthedeadband,crossingtheswitchdifferential(Fig.29).Adropinstaticpressurebelowthecontrollersetpointcausestheactuatortodrivethedampertowardopen.Thenarrowdifferentialofthecontrollerstopstheactuatorafterithasmovedashortdistance.Thedamperremainsinthispositionuntilthestaticpressurefurtherdecreases,causingtheactuatortodrivethedamperfurtheropen.Inatypicalapplication,12Fig.29.FloatingControl.Fig.29.FloatingControl.13Onariseinstaticpressureabovethesetpoint,thereverseoccurs.Thus,thecontrolpointcanfloatbetweenopenandclosedlimitsandtheactuatordoesnotmove.Whenthecontrolpointmovesoutofthedeadband,thecontrollermovestheactuatortowardopenorcloseduntilthecontrolpointmovesintothedeadbandagain.Inproportional-speedfloatingcontrol,thefartherthecontrolpointmovesbeyondthedeadband,thefastertheactuatormovestocorrectthedeviation.Onariseinstaticpressu14

ProportionalControlGENERALProportionalcontrolproportionstheoutputcapacityoftheequipment(e.g.,thepercentavalveisopenorclosed)tomatchtheheatingorcoolingloadonthebuilding,unliketwo-positioncontrolinwhichthemechanicalequipmentiseitherfullonorfulloff.Inthisway,proportionalcontrolachievesthedesiredheatreplacementordisplacementrate.Inachilledwatercoolingsystem,forexample(Fig.30),thesensorisplacedintheProportionalControl15dischargeair.Thesensormeasurestheairtemperatureandsendsasignaltothecontroller.Ifacorrectionisrequired,thecontrollercalcula-testhechangeandsendsanewsignaltothevalveactuator.Theactuatorrepositionsthevalvetochangethewaterflowinthecoil,andthusthedischargetemperature.Fig.30.ProportionalControlLoop.dischargeair.Thesensor16Inproportionalcontrol,thefinalcontrolelementmovestoapositionproportionaltothedeviationofthevalueofthecontrolledvariablefromthesetpoint.Thepositionofthefinalcontrolelementisalinearfunctionofthevalueofthecontrolledvariable(Fig.31).Thefinalcontrolelementisseldominthemiddleofitsrangebecauseofthelinearrelationshipbetweenthepositionofthefinalcontrolelementandthevalueofthecontrolledvariable.Inproportionalcontrolsystems,thesetInproportionalcontrol,thef17pointistypicallythemiddleofthethrottlingrange,sothereisusuallyanoffsetbetweencontrolpointandsetpoint.pointistypicallythemiddle18Fig.31.FinalControlElementPositionasaFunctionoftheControlPoint(CoolingSystem).Fig.31.FinalControlElement19

Anexampleofoffsetwouldbetheproportionalcontrolofachilledwatercoilusedtocoolaspace.Whenthecoolingloadis50percent,thecontrollerisinthemiddleofitsthrottlingrange,theproperlysizedcoilvalveishalf-open,andthereisnooffset.Astheout-doortemperatureincreases,theroomtemperaturerisesandmorecoolingisrequiredtomaintainthespacetemperature.Thecoilvalvemustopenwidertodelivertherequiredcoolingandremaininthatpositionaslongastheincreasedrequirementexists.BecausetheAnexampleofoffset20positionofthefinalcontrolelementisproportionaltotheamo-untofdeviation,thetemperaturemustdeviatefromthesetpointandsustainthatdeviationtoopenthecoilvalveasfarasrequired.Figure32showsthatwhenproportionalcontrolisusedinaheatingapplication,astheloadconditionincreasesfrom50percent,offsetincreasestowardcooler.Astheloadconditiondecreases,offsetincreasestowardwarmer.Theoppositeoccursinacoolingapplication.positionofthefinalcontrol21Fig.32.RelationshipofOffsettoLoad(HeatingApplication).Fig.32.RelationshipofOffse22

Thethrottlingrangeistheamountofchangeinthecontrolledvariablerequiredforthecontrollertomovethecontrolleddevicethroughitsfulloperatingrange.TheamountofchangeisexpressedindegreesCelsiusfortemperature,inpercentagesforrelativehumidity,andinkilopascalsforpressure.Forsomecontrollers,throttlingrangeisreferredtoas"proportionalband".Proportionalbandisthrottlingrangeexpressedasapercentageofthecontrollersensorspan:Thethrottlingrange23

"Gain"isatermoftenusedinindustrialcontrolsystemsforthechangeinthecontrolledvariable.Gainisthereciprocalofproportionalband:

Theoutputofthecontrollerisproportionaltothedeviationofthecontrolpointfromsetpoint.Aproportionalcontrollercanbemathematicallydescribedby:V=KE+M

"Gain"isatermofte24Where:V=outputsignalK=proportionalityconstant(gain)E=deviation(controlpoint-setpoint)M=valueoftheoutputwhenthedeviationiszero(Usuallytheoutputvalueat50percentorthemiddleoftheoutputrange.Thegeneratedcontrolsignalcorrectionisaddedtoorsubtractedfromthisvalue.Alsocalled"bias"or"manualreset".)Where:25

Althoughthecontrolpointinaproportionalcontrolsystemisrarelyatsetpoint,theoffsetmaybeaccept-able.Compensation,whichistheresettingofthesetpointtocompensateforvaryingloadconditions,reducestheeffectofoffsetformoreaccuratecontrol.Anexampleofcompensationisresettingboilerwatertemperaturebasedonoutdoorairtemperature.Compensationisalsocalled"resetcontrol"or"cascadecontrol".Althoughthecontrol26CompensationControlGENERAL

Compensationisacontroltechniqueavailableinproportionalcontrolinwhichasecondary,orcompen-sation,sensorresetsthesetpointoftheprimarysensor.AnexampleofCompensationwouldbetheoutdoortemperatureresettingthedischargetemperatureofafansystemsothatthedischargetemperatureincreasesastheoutdoortemperaturedecreases.ThefollowingsampleresetscheduleisshowngraphicallyinFigure33.CompensationControl27Figure34showsacontroldiagramforthesampleresetsystem.Figure34showsacontrol28Fig.33..TypicalResetScheduleforDischargeAirControlFig.33..TypicalResetSchedu29Fig.34.DischargeAirControlLoopwithReset.Fig.34.DischargeAirControl30

Compensationcaneitherincreaseordecreasethesetpointasthecompensationinputincreases.increasingthesetpointbyaddingresetonanincreaseinthecompen-sationvariableisoftenreferredtoaspositiveorsummercompensation.Increasingthesetpointbyaddingresetonadecreaseinthecompensationvariableisoftenreferredtoasnegativeorwintercompensation.Compensationismostcommonlyusedfortemperaturecontrol,butcanalsobeusedwithahumidityorothercontrolsystem.Compensationcaneithe31

Somecontrollersprovidecompensationstartpointcapability.Compensationstartpointisthevalueofthecompensationsensoratwhichitstartsresettingthecontrollerprimarysensorsetpoint.

Somecontrollersprov32

Proportional-Integral(PI)ControlIntheproportional-integral(PI)controlmode,resetofthecontrolpointisautomatic.PIcontrol,alsocalled"proportionalplus-reset"control,virtuallyeliminatesoffsetandmakestheproportionalbandnearlyinvisible.Assoonasthecontrolledvariabledeviatesaboveorbelowthesetpointandoffsetdevelops,theproportionalbandgraduallyandautomaticallyshifts,andthevariableisbroughtbacktothesetpoint.ThemajordifferencebetweenProportional-Integral(PI)33proportionalandPIcontrolisthatproportionalcontrolislimitedtoasinglefinalcontrolelementpositionforeachvalueofthecontrolledvariable.

PIcontrolchangesthefinalcontrolelementpositiontoaccommodateloadchangeswhilekeepingthecontrolpointatorverynearthesetpoint.

proportionalandPIcontrol34

Theresetactionoftheintegralcomponentshiftstheproportionalbandasnecessaryaroundthesetpointastheloadonthesystemchanges.ThegraphinFigure36showstheshiftoftheproportionalbandofaPIcontrollercontrollinganormallyopenheatingvalve.Theshiftingoftheproportionalbandkeepsthecontrolpointatsetpointbymakingfurthercorrectionsinthecontrolsignal.Becauseoffsetiseliminated,theproportionalbandisusuallysetfairlywidetoensuresystemstabilityunderalloperatingconditions.Theresetactionoft35Fig.35.ProportionalBandShiftDuetoOffset.Fig.35.ProportionalBandShi36Resetofthecontrolpointisnotinstanta-neous.Whenevertheloadchanges,thecontrolledvariablechanges,producinganoffset.Theproportionalcontrolmakesanimmediatecorrection,whichusuallystillleavesanoffset.Theintegralfunctionofthecontrollerthenmakescontrolcorrectionsovertimetobringthecontrolpointbacktosetpoint(Fig.36).Inadditiontoaproportionalbandadjustment,thePIcontrolleralsohasaresettimeadjustmentthatdeterminestherateatwhichtheproportionalbandshiftswhenthecontrolledvariabledeviatesanygivenamountfromthesetpoint.Resetofthecontrol37Fig.36.Proportional-IntegralControlResponsetoLoadChanges.ResettimeisproportionaltothedeviationofthecontrolledFig.36.Proportional-Integral38

variable.Forexample,afour-percentdeviationfromthesetpointcausesacontinuousshiftoftheproportionalbandattwicetherateofshiftforatwo-percentdeviation.Resetisalsoproportionaltothedurationofthedeviation.Resetaccumulatesaslongasthereisoffset,butceasesassoonasthecontrolledvariablereturnstothesetpoint.WiththePIcontroller,therefore,thepositionofthefinalcontrolelementdependsnotonlyuponthelocationofthecontrolledvariablewithintheproportionalband(proportionalbandadjustment)variable.Forexample,afo39butalsouponthedurationandmagnitudeofthedeviationofthecontrolledvariablefromthesetpoint(resettimeadjustment).Understeadystateconditions,thecontrolpointandsetpointarethesameforanyloadconditions,asshowninFigure36.PIcontroladdsacomponenttotheproportionalcontrolalgorithmandisdescribedmathematicallyby:butalsouponthedurationand40Where:V=outputsignalK=proportionalityconstant(gain)E=deviation(controlpoint-setpoint)T1=resettimeK/T1=resetgaindt=differentialoftime(incrementintime)M=valueoftheoutputwhenthedeviationiszeroWhere:41

Integralwindup,oranexcessiveovershootcondition,canoccurinPIcontrol.Integralwindupiscausedbytheintegralfunctionmakingacontinuedcorrectionwhilewaitingforfeedbackontheeffectsofitscorrection.Whileintegralactionkeepsthecontrolpointatsetpointduringsteadystateconditions,largeovershootsarepossibleatstart-uporduringsystemupsets(e.g.,setpointchangesorlargeloadchanges).Onmanysystems,shortresettimesalsocauseovershoot.Integralwindup,or42

Integralwindupcanbeavoidedanditseffectsdiminished.Atstart-up,somesystemsdisableintegralactionuntilmeasuredvariablesarewithintheirrespectiveproportionalbands.Systemsoftenprovideintegrallimitstoreducewindupduetoloadchanges.Theintegrallimitsdefinetheextenttowhichintegralactioncanadjustadevice(thepercentoffulltravel).Thelimitistypicallysetat50percent.Integralwindupcanb43

Proportional-Integral-Derivative(PID)Control（作業(yè)）Fig.37.ProportionalControlFig.38.Proportional-IntegralControl.Fig.37.ProportionalContr44Fig.39.Proportional-Integral-DerivativeControlFig.39.Proportional-Integral45

AdaptiveControlAdaptivecontrolisavailableinsomemicroprocessor-basedcontrollers.Adaptivecontrolalgorithmsenableacontrollertoadjustitsresponseforoptimumcontrolunderallloadconditions.Acontrollerthathasbeentunedtocontrolaccuratelyunderonesetofconditionscannotalwaysrespondwellwhentheconditionschange,suchasasignificantloadchangeorchangeoverfromheatingtocooling.AdaptiveControl46Anadaptivecontrolalgorithmmonitorstheperformanceofasystemandattemptstoimprovetheperformancebyadjustingcontrollergainsorparameters.Onemeasurementofperformanceistheamountoftimethesystemrequirestoreacttoadisturbance:usuallytheshorterthetime,thebettertheperformance.Themethodsusedtomodifythegainsorparametersaredeterminedbythetypeofadaptivealgorithm.Anadaptivecontrola47AnexampleofagoodapplicationforadaptivecontrolisdischargetemperaturecontrolofthecentralsystemcoolingcoilfunctionaVAVsystem.Thetimeconstantofasensorvariesasafunctionofthevelocityoftheair(orotherfluid).ThusthetimeconstantofthedischargeairsensorinaVAVsystemisconstantlychanging.Thechangeinsensorresponseaffectthesystemcontrolsotheadaptivecontrolalgorithmadjustssystemparameterssuchastheresetandratesettingstomaintainoptimumsystemperformance.Anexampleofagood48Adaptivecontrolisalsousedinenergymanagementprogramssuchasoptimumstart.TheoptimumstartprogramenablesanHVACsystemtostartaslateaspossibleinthemorningandstillreachthecomfortrangebythetimethebuildingisoccupied.Todeterminetheamountoftimerequiredtoheatorcoolthebuilding,theoptimumstartprogramusesfactorsbasedonpreviousbuildingresponse,HVACsystemcharacteristics,andcurrentweatherconditions.Adaptivecontrolisa49Thealgorithmmonitorscontrollerperformancebycomparingtheactualandcalculatedtimerequiredtobringthebuildingintothecomfortrangeandtriestoimprovethisperformancebycalculatingnewfactors.Thealgorithmmonitors50CHAPTER1CONTROLFUNDAMENTALS(4)CHAPTER151StepControl

Stepcontrollersoperateswitchesorrelaysinsequencetoenableordisablemultipleoutputs,orstages,oftwo-positiondevicessuchaselectricheatersorreciprocatingrefrigerationcompressors.Stepcontrolusesananalogsignaltoattempttoobtainproportionaloutputfromequipmentthatistypicallyeitheronoroff.Figures25and26showthatthestagesmaybearrangedtooperatewithorwithoutoverlapoftheoperating(on/off)differentials.Ineithercase,thetypicaltwo-positiondifferentialsstillStepControl52Fig.25.ElectricHeatStages.existbutthetotaloutputisproportioned.Fig.25.ElectricHeatStages.53Fig.26.StagedReciprocatingChillerControl.Fig.26.StagedReciprocating54

Figure27showsstepcontrolofsequencedDXcoilsandelectricheat.Onariseintemperaturethroughthethrottlingrangeatthethermostat,theheatingstagessequenceoff.Onafurtherriseafteradeadband,thecoolingstagesturnoninsequence.Avariationofstepcontrolusedtocontrolelectricheatisstepplus-proportionalcontrol,whichprovidesasmoothtransitionbetweenstages.ThiscontrolmoderequiresoneofthestagestobeaproportionalmodulatingoutputFigure27showsstep55andtheothers,two-position.Formostefficientoperation,theproportionalmodulatingstageshouldhaveatleastthesamecapacityasonetwo-positionstage.andtheothers,two-position.56Fig.27.StepControlwithSequencedDXCoilsandElectricHeat.Fig.27.StepControlwithSeq57

Startingfromnoload,astheloadontheequipmentincreases,themodulatingstageproportionsitsloaduntilitreachesfulloutput.Then,thefirsttwo-positionstagecomesfullonandthemodulatingstagedropstozerooutputandbeginstoproportionitsoutputagaintomatchtheincreasingload.Whenthemodulatingstageagainreachesfulloutput,thesecondtwo-positionstagecomesfullon,themodulatingstagereturnstozero,andthesequencerepeatsuntilallstagesrequiredtomeettheloadconditionareon.Onadecreaseinload,theprocessreverses.Startingfromnoloa58

FloatingControlFloatingcontrolisavariationoftwo-positioncontrolandisoftencalled"three-positioncontrol".Floatingcontrolisnotacommoncontrolmode,butisavailableinmostmicroprocessor-basedcontrolsystems.Avariationoffloatingcontrolisproportional-speed-floatingcontrol.Floatingcontrolrequiresaslow-movingactuatorandafastrespondingsensorselectedaccordingtotherateofresponseinthecontrolledsystem.Iftheactuatorshouldmovetooslowly,thecontrolledFloatingControl59systemwouldnotbeabletokeeppacewithsuddenchanges;iftheactuatorshouldmovetooquickly,two-positioncontrolwouldresult.Floatingcontrolkeepsthecontrolpointnearthesetpointatanyloadlevel,andcanonlybeusedonsystemswithminimallagbetweenthecontrolledmediumandthecontrolsensor.Floatingcontrolisusedprimarilyfordischargecontrolsystemswherethesensorisimmediatelydownstreamfromthecoil,damper,ordevicethatitcontrols.Anexampleoffloatingcontrolistheregulationofstaticsystemwouldnotbeab60Fig.28.FloatingStaticPressureControl.pressureinaduct(Fig.28).Fig.28.FloatingStaticPress61Inatypicalapplication,thecontrolpointmovesinandoutofthedeadband,crossingtheswitchdifferential(Fig.29).Adropinstaticpressurebelowthecontrollersetpointcausestheactuatortodrivethedampertowardopen.Thenarrowdifferentialofthecontrollerstopstheactuatorafterithasmovedashortdistance.Thedamperremainsinthispositionuntilthestaticpressurefurtherdecreases,causingtheactuatortodrivethedamperfurtheropen.Inatypicalapplication,62Fig.29.FloatingControl.Fig.29.FloatingControl.63Onariseinstaticpressureabovethesetpoint,thereverseoccurs.Thus,thecontrolpointcanfloatbetweenopenandclosedlimitsandtheactuatordoesnotmove.Whenthecontrolpointmovesoutofthedeadband,thecontrollermovestheactuatortowardopenorcloseduntilthecontrolpointmovesintothedeadbandagain.Inproportional-speedfloatingcontrol,thefartherthecontrolpointmovesbeyondthedeadband,thefastertheactuatormovestocorrectthedeviation.Onariseinstaticpressu64

ProportionalControlGENERALProportionalcontrolproportionstheoutputcapacityoftheequipment(e.g.,thepercentavalveisopenorclosed)tomatchtheheatingorcoolingloadonthebuilding,unliketwo-positioncontrolinwhichthemechanicalequipmentiseitherfullonorfulloff.Inthisway,proportionalcontrolachievesthedesiredheatreplacementordisplacementrate.Inachilledwatercoolingsystem,forexample(Fig.30),thesensorisplacedintheProportionalControl65dischargeair.Thesensormeasurestheairtemperatureandsendsasignaltothecontroller.Ifacorrectionisrequired,thecontrollercalcula-testhechangeandsendsanewsignaltothevalveactuator.Theactuatorrepositionsthevalvetochangethewaterflowinthecoil,andthusthedischargetemperature.Fig.30.ProportionalControlLoop.dischargeair.Thesensor66Inproportionalcontrol,thefinalcontrolelementmovestoapositionproportionaltothedeviationofthevalueofthecontrolledvariablefromthesetpoint.Thepositionofthefinalcontrolelementisalinearfunctionofthevalueofthecontrolledvariable(Fig.31).Thefinalcontrolelementisseldominthemiddleofitsrangebecauseofthelinearrelationshipbetweenthepositionofthefinalcontrolelementandthevalueofthecontrolledvariable.Inproportionalcontrolsystems,thesetInproportionalcontrol,thef67pointistypicallythemiddleofthethrottlingrange,sothereisusuallyanoffsetbetweencontrolpointandsetpoint.pointistypicallythemiddle68Fig.31.FinalControlElementPositionasaFunctionoftheControlPoint(CoolingSystem).Fig.31.FinalControlElement69

Anexampleofoffsetwouldbetheproportionalcontrolofachilledwatercoilusedtocoolaspace.Whenthecoolingloadis50percent,thecontrollerisinthemiddleofitsthrottlingrange,theproperlysizedcoilvalveishalf-open,andthereisnooffset.Astheout-doortemperatureincreases,theroomtemperaturerisesandmorecoolingisrequiredtomaintainthespacetemperature.Thecoilvalvemustopenwidertodelivertherequiredcoolingandremaininthatpositionaslongastheincreasedrequirementexists.BecausetheAnexampleofoffset70positionofthefinalcontrolelementisproportionaltotheamo-untofdeviation,thetemperaturemustdeviatefromthesetpointandsustainthatdeviationtoopenthecoilvalveasfarasrequired.Figure32showsthatwhenproportionalcontrolisusedinaheatingapplication,astheloadconditionincreasesfrom50percent,offsetincreasestowardcooler.Astheloadconditiondecreases,offsetincreasestowardwarmer.Theoppositeoccursinacoolingapplication.positionofthefinalcontrol71Fig.32.RelationshipofOffsettoLoad(HeatingApplication).Fig.32.RelationshipofOffse72

Thethrottlingrangeistheamountofchangeinthecontrolledvariablerequiredforthecontrollertomovethecontrolleddevicethroughitsfulloperatingrange.TheamountofchangeisexpressedindegreesCelsiusfortemperature,inpercentagesforrelativehumidity,andinkilopascalsforpressure.Forsomecontrollers,throttlingrangeisreferredtoas"proportionalband".Proportionalbandisthrottlingrangeexpressedasapercentageofthecontrollersensorspan:Thethrottlingrange73

"Gain"isatermoftenusedinindustrialcontrolsystemsforthechangeinthecontrolledvariable.Gainisthereciprocalofproportionalband:

Theoutputofthecontrollerisproportionaltothedeviationofthecontrolpointfromsetpoint.Aproportionalcontrollercanbemathematicallydescribedby:V=KE+M

"Gain"isatermofte74Where:V=outputsignalK=proportionalityconstant(gain)E=deviation(controlpoint-setpoint)M=valueoftheoutputwhenthedeviationiszero(Usuallytheoutputvalueat50percentorthemiddleoftheoutputrange.Thegeneratedcontrolsignalcorrectionisaddedtoorsubtractedfromthisvalue.Alsocalled"bias"or"manualreset".)Where:75

Althoughthecontrolpointinaproportionalcontrolsystemisrarelyatsetpoint,theoffsetmaybeaccept-able.Compensation,whichistheresettingofthesetpointtocompensateforvaryingloadconditions,reducestheeffectofoffsetformoreaccuratecontrol.Anexampleofcompensatio