Chapter4：Feedbackcontrolsystemcharacteristics

Aclosed-loopsystemisusedtotrackthesuntoobtainmaximumpowerfromaphotovoltaicarray.ThetrackingsystemmayberepresentedbyFigure1withH(s)=1and

,

Wheresecondsnominally.

Calculatethesensitivityofthissystemforasmallchangein.

Figure1.closed-loopcontrolsystemwithoutputnoise.

Amagneticdiskdriverequiresamotortopositionaread/writeheadovertracksofdataonaspinningdisk,asshowninFigure2.Themotorandheadmayberepresentedbythetransferfunction

,

Wheresecond.Thecontrollertakesthedifferenceoftheactualanddesiredpositionsandgeneratesanerror.ThiserrorismultipliedbyanamplifierK.

Whatisthesteady-statepositionerrorforastepchangeinthedesiredinput?

(b)CalculatetherequiredKinordertoyieldasteady-stateerrorof0.1mmforarampinputof10cm/s.

Figure2.Diskdrivecontrol.

Submersibleswithclearplastichullshavethepotentialtorevolutionizeunderwaterleisure.Onesmallsubmersiblevehiclehasadepth-controlsystemasillustratedinFigure3.

Determinetheclosed-looptransferfunctionT(s)=Y(s)/R(s).

(b)Determinethesensitivityand.

(c)Determinethesteady-stateerrorduetoadisturbance.

(d)Calculatetheresponsey(t)forastepinputR(s)=1/swhenand.Selectforthefastestresponse.

Figure3.Depthcontrolsystem.

Oneofthemostimportantvariablesthatmustbecontrolledinindustrialandchemicalsystemsistemperature.AsimplerepresentationofathermalcontrolsystemisshowninFigure4.ThetemperatureToftheprocessiscontrolledbytheheaterwitharesistanceR.Anapproximaterepresentationofthedynamiclinearlyrelatestheheatlossfromtheprocesstothetemperatutedifference.Thisrelationholdsifthetemperaturedifferenceisrelativelysmallandtheenergystorageoftheheaterandthevesselwallsisnegligible.Also,itisassumedthatthevoltageappliedtotheheaterisproportionaltoor,whereistheconstantoftheactuator.Thenthelinearizedopen-loopresponseofthesystemis

,

Where

,

M=massintank,

A=surfaceareaofrank,

=heattransferconstant,

C=specificheatconstant,

=adimensionalityconstant,and

=outputvoltageofthethermocouple.

Determineandcomparetheopen-loopandclosed-loopsystemsfor

(a)sensitivitytochangesintheconstant;

(b)theabilitytoreducetheeffectsofastepdisturbanceintheenvironmentaltemperature;and