Solution Manual for Modern Control Systems, 13th Edition

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CHAPTER1Introduction to Control SystemsThere are, in general, no unique solutions to the following exercises andproblems. Other equally valid block diagrams may be submitted by thestudent.ExercisesE1.1Describe typical sensors that can measure each of the following:a.Linear position→ultrasonic transducerb.Velocity (or speed)→Doppler radarc.Non-gravitational acceleration→inertial measurement unitd.Rotational position (or angle)→rotary encodere.Rotational velocity→gyroscopef.Temperature→thermocoupleg.Pressure→barometerh.Liquid (or gas) flow rate→velocimeteri.Torque→torquemeterj.Force→load cellk.Earth's magnetic field→magnetometerl.Heart rate→electrocardiographE1.2Describe typical actuators that can convert the following:a.Fluidic energy to mechanical energy→hydraulic cylinderb.Electrical energy to mechanical energy→electric motorc.Mechanical deformation to electrical energy→piezoelectric actuatord.Chemical energy to kinetic energy→automobile enginee.Heat to electrical energy→thermoelectric generator1

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2CHAPTER 1Introduction to Control SystemsE1.3A microprocessor controlled laser system:ControllerErrorCurrent i(t)PoweroutDesiredpoweroutputMeasuredpower-LaserProcessprocessorMicro-PowerSensorMeasurementE1.4A driver controlled cruise control system:DesiredspeedFoot pedalActualautospeedVisual indicationof speedController-ProcessMeasurementDriverCar andEngineSpeedometerE1.5Although the principle of conservation of momentum explains much ofthe process of fly-casting, there does not exist a comprehensive scientificexplanation of how a fly-fisher uses the small backward and forward mo-tion of the fly rod to cast an almost weightless fly lure long distances (thecurrent world-record is 236 ft). The fly lure is attached to a short invisibleleader about 15-ft long, which is in turn attached to a longer and thickerDacron line. The objective is cast the fly lure to a distant spot with dead-eye accuracy so that the thicker part of the line touches the water firstand then the fly gently settles on the water just as an insect might.WinddisturbanceController-ProcessMeasurementRod, line,and cast

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Exercises3E1.6Anautofocuscameracontrolsystem:One-way trip time for the beamDistance to subjectLens focusingmotorK1LensConversion factor(speed of light orsound)Emitter/ReceiverBeamBeam returnSubjectE1.7Tackingasailboatasthewindshifts:DesiredsailboatdirectionActualsailboatdirectionMeasured sailboat directionWindError-ProcessMeasurementActuatorsControllerSailboatGyro compassRudder andsail adjustmentSailorE1.8Anautomatedhighwaycontrolsystemmergingtwolanesoftraffic:DesiredgapActualgapMeasured gapError-ProcessMeasurementActuatorsControllerActivevehicleBrakes, gas orsteeringEmbeddedcomputerRadar

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4CHAPTER 1Introduction to Control SystemsE1.9Askateboardridermaintainingverticalorientationanddesiredspeed:Desiredverticalorientation& speedRiderorientation& speedErrors-ProcessMeasurementActuatorsControllerRiderrepositioning& propellingRiderRider &SkateboardRiderE1.10Humanbiofeedbackcontrolsystem:MeasurementDesiredbodytempActualbodytempVisual indication ofbody temperatureMessage toblood vessels-ProcessControllerBody sensorHypothalumusHuman bodyTV displayE1.11E-enabledaircraftwithground-basedflightpathcontrol:Corrections to theflight pathControllerGc(s)AircraftG(s)-DesiredFlightPathFlightPathCorrections to theflight pathControllerGc(s)AircraftG(s)-DesiredFlightPathFlightPathGround-Based Computer NetworkHealthParametersHealthParametersMeteorologicaldataMeteorologicaldataOptimalflight pathOptimalflight pathLocationand speedLocationand speed

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Exercises5E1.12Unmannedaerialvehicleusedforcropmonitoringinanautonomousmode:Gc(s)G(s)-CameraGroundphotoControllerUAVSpecifiedFlightTrajectoryLocation withrespect to the groundFlightTrajectoryMapCorrelationAlgorithmTrajectoryerrorSensorE1.13An invertedpendulum controlsystem using anopticalencoder tomeasuretheangleofthependulumandamotorproducingacontroltorque:ErrorAngleDesiredangleMeasuredangle-PendulumProcessOpticalencoderMeasurementMotorActuatorTorqueVoltageControllerE1.14Inthevideogame,theplayercanserveasboththecontrollerandthesen-sor.Theobjectiveofthegamemightbetodriveacaralongaprescribedpath.Theplayercontrolsthecartrajectoryusingthejoystickusingthevisualqueuesfromthegamedisplayedonthecomputermonitor.ErrorGameobjectiveDesiredgameobjective-Video gameProcessPlayer(eyesight, tactile, etc.)MeasurementJoystickActuatorPlayerController

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6CHAPTER 1Introduction to Control SystemsProblemsP1.1Anautomobileinteriorcabintemperaturecontrolsystemblockdiagram:Desiredtemperatureset by thedriverAutomobilecabin temperatureMeasured temperatureError-ProcessMeasurementControllerAutomobilecabinTemperaturesensorThermostat andair conditioningunitP1.2Ahumanoperatorcontrolledvalvesystem:Desiredfluidoutput *Error *Fluidoutput* = operator functionsVisual indicationof fluid output *-ProcessMeasurementControllerValveMeterTankP1.3Achemicalcompositioncontrolblockdiagram:DesiredchemicalcompositionErrorChemicalcompositionMeasured chemicalcomposition-ProcessMeasurementControllerValveMixer tubeInfrared analyzer

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Problems7P1.4Anuclearreactorcontrolblockdiagram:Desiredpower levelOutputpower levelErrorMeasured chemicalcomposition-ProcessMeasurementControllerIonization chamberReactorand rodsMotor andamplifierP1.5Alightseekingcontrolsystemtotrackthesun:LighintensityDesiredcarriagepositionLightsourcePhotocellcarriagepositionMotorinputsError-ProcessControllerMotor,carriage,and gearsKControllerTrajectoryPlannerDualPhotocellsMeasurementP1.6Ifyouassumethatincreasingworker’swagesresultsinincreasedprices,thenbydelayingorfalsifyingcost-of-livingdatayoucouldreduceorelim-inatethepressuretoincreaseworker’swages,thusstabilizingprices.Thiswouldworkonlyiftherewerenootherfactorsforcingthecost-of-livingup.Governmentpriceandwageeconomicguidelineswouldtaketheplaceofadditional“controllers”intheblockdiagram,asshownintheblockdiagram.InitialwagesPricesWage increasesMarket-based pricesCost-of-living-ControllerIndustryGovernmentpriceguidelinesK1GovernmentwageguidelinesControllerProcess

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8CHAPTER 1Introduction to Control SystemsP1.7Assumethatthecannonfiresinitiallyatexactly5:00p.m..Wehaveapositivefeedbacksystem.Denoteby∆tthetimelostperday,andthenettimeerrorbyET.Thenthefollwoingrelationshipshold:∆t=4/3min.+ 3min.=13/3min.andET=12days×13/3min./day.Therefore,thenettimeerrorafter15daysisET=52min.P1.8Thestudent-teacherlearningprocess:DesiredknowledgeErrorLecturesKnowledgeMeasured knowledge-ControllerProcessTeacherStudentMeasurementExamsP1.9Ahumanarmcontrolsystem:Visual indication ofarm locationzyueds-ControllerProcessMeasurementDesiredarmlocationArmlocationNerve signalsEyes andpressurereceptorsBrainArm &musclesPressure

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Problems9P1.10AnaircraftflightpathcontrolsystemusingGPS:-ProcessMeasurementActuatorsControllerAircraftGlobal PositioningSystemComputerAuto-pilotAilerons, elevators,rudder, andengine powerDesiredflight pathfrom air trafficcontrollersFlightpathMeasured flight pathErrorP1.11Theaccuracyoftheclockisdependentuponaconstantflowfromtheorifice;theflowisdependentupontheheightofthewaterinthefloattank.The height of the wateris controlledby the float.The controlsystemcontrolsonlytheheightofthewater.Anyerrorsduetoenlargementoftheorificeorevaporationofthewaterinthelowertankisnotaccountedfor.Thecontrolsystemcanbeseenas:Desiredheight ofthe waterin float tankActualheight-ProcessControllerFlow fromupper tankto float tankFloat levelP1.12Assumethattheturretandfantailareat90◦,ifθw=θF-90◦.⁄Thefantailoperatesontheerrorsignalθw-θT,andasthefantailturns,itdrivestheturrettoturn.xyWind**WTFFantailTurret= Wind angle= Fantail angle= Turret angleWTFTorqueTWError-ProcessControllerGears & turretFantail

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10CHAPTER 1Introduction to Control SystemsP1.13Thisschemeassumesthepersonadjuststhehotwaterfortemperaturecontrol,andthenadjuststhecoldwaterforflowratecontrol.Desired watertemperatureActualwater temperatureand flow rateColdwaterDesired waterflow rateMeasured water flowMeasured water temperatureError-ProcessController-MeasurementHuman: visualand touchValve adjustValve adjustHot watersystemCold watersystemHotwaterP1.14Iftherewardsinaspecifictradeisgreaterthantheaveragereward,thereisapositiveinfluxofworkers,sinceq(t)=f1(c(t)−r(t)).Ifaninfluxofworkersoccurs,thenrewardinspecifictradedecreases,sincec(t)=−f2(q(t)).-Error-ProcessControllerf1(c(t)-r(t))f2(q(t))q(t)Total ofrewardsc(t)Averagerewardsr(t)P1.15Acomputercontrolledfuelinjectionsystem:DesiredFuelPressureFuelPressureMeasured fuel pressure-ProcessMeasurementControllerFuel PressureSensorElectronicControl UnitHigh Pressure FuelSupply Pump andElectronic FuelInjectors

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Problems11P1.16Withtheonsetofafever,thebodythermostatisturnedup.Thebodyadjustsbyshiveringandlessbloodflowstotheskinsurface.Aspirinactstolowersthethermalset-pointinthebrain.BodytemperatureDesired temperatureor set-point from bodythermostat in the brainMeasured body temperature-ProcessMeasurementControllerInternal sensorBodyAdjustmentswithin thebodyP1.17Hitting a baseball is arguably one of the most difficult featsin allof sports.Giventhatpitchersmaythrowtheballatspeedsof90mph(orhigher!),battershaveonlyabout0.1secondtomakethedecisiontoswing—withbatspeedsaproaching90mph.Thekeytohittingabaseballalongdis-tanceistomakecontactwiththeballwithahighbatvelocity.Thisismoreimportantthanthebat’sweight,whichisusuallyaround33ounces.Since the pitcher can throw a varietyof pitches (fast ball, curve ball, slider,etc.),abattermustdecideiftheballisgoingtoenterthestrikezoneandifpossible,decidethetypeofpitch.Thebatteruseshis/hervisionasthesensorinthefeedbackloop.Ahighdegreeofeye-handcoordinationiskeytosuccess—thatis,anaccuratefeedbackcontrolsystem.P1.18Definethefollowingvariables:p=outputpressure,fs=springforce=Kx,fd=diaphragmforce=Ap,andfv=valveforce=fs-fd.Themotionofthevalveisdescribedby¨y=fv/mwheremisthevalvemass.Theoutputpressureisproportionaltothevalvedisplacement,thusp=cy,wherecistheconstantofproportionality.Screwdisplacementx(t)yValve positionOutputpressurep(t)fs-Diaphragm areacValveConstant ofproportionalityAKSpringfvfd

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12CHAPTER 1Introduction to Control SystemsP1.19Acontrolsystemtokeepacaratagivenrelativepositionoffsetfromaleadcar:ThrottlePosition offolloweruReferencephotoRelativepositionDesired relative positionPositionof lead-ControllerVideo camera& processingalgorithmsFollowercarActuatorFuelthrottle(fuel)Lead car-P1.20Acontrolsystemforahigh-performancecarwithanadjustablewing:DesiredroadadhesionRoadadhesionMeasured road adhesionRoadconditions-ProcessMeasurementControllerTire internalstrain gaugesRace CarKActuatorAdjustablewingComputerP1.21Acontrolsystemforatwin-lifthelicoptersystem:Desired altitudeAltitudeMeasured altitudeSeparation distanceDesired separationdistanceMeasured separationdistance--MeasurementMeasurementRadarAltimeterControllerPilotProcessHelicopter

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Problems13P1.22Thedesiredbuildingdeflectionwouldnotnecessarilybezero.Ratheritwouldbeprescribedsothatthebuildingisallowedmoderatemovementuptoapoint,andthenactivecontrolisappliedifthemovementislargerthansomepredeterminedamount.DesireddeflectionDeflectionMeasured deflection-ProcessMeasurementControllerKBuildingHydraulicstiffenersStrain gaugeson truss structureP1.23Thehuman-likefaceoftherobotmighthavemicro-actuatorsplacedatstrategicpointsontheinteriorofthemalleablefacialstructure.Coopera-tivecontrolofthemicro-actuatorswouldthenenabletherobottoachievevariousfacialexpressions.DesiredactuatorpositionVoltageActuatorpositionMeasured positionError-ProcessMeasurementControllerAmplifierPositionsensorElectro-mechanicalactuatorP1.24Wemightenvisionasensorembeddedina“gutter”atthebaseofthewindshieldwhichmeasureswaterlevels—higherwaterlevelscorrespondstohigherintensityrain.Thisinformationwouldbeusedtomodulatethewiperbladespeed.Desiredwiper speedWiperbladespeedMeasured water level-ProcessMeasurementControllerKWater depthsensorWiper bladeand motorElectronicControl Unit

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14CHAPTER 1Introduction to Control SystemsP1.25Afeedbackcontrolsystemforthespacetrafficcontrol:Desiredorbit positionActualorbit positionMeasured orbit positionJetcommandsAppliedforcesError-ProcessMeasurementActuatorControllerSatelliteReactioncontrol jetsControllawRadar or GPSP1.26Earth-basedcontrolofamicrorovertopointthecamera:MicroroverCamera positioncommandControllerGc(s)Camera position commandCameraPositionReceiver/TransmitterRoverpositionCameraMeasured camera positionG(s)Measured camerapositionSensorP1.27Controlofamethanolfuelcell:Methanol watersolutionControllerGc(s)RechargingSystemGR(s)Fuel CellG(s)-ChargeLevelDesiredChargeLevelMeasured charge levelSensorH(s)

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AdvancedProblems15AdvancedProblemsAP1.1Controlofaroboticmicrosurgicaldevice:ControllerGc(s)Microsurgicalrobotic manipulatorG(s)-End-effectorPositionDesiredEnd-effectorPositionSensorH(s)AP1.2Anadvancedwindenergysystemviewedasamechatronicsystem:WIND ENERGYSYSTEMPhysical System ModelingSignals and SystemsSensors and ActuatorsComputers andLogic SystemsSoftware andData AcquisitionCOMPUTER EQUIPMENT FOR CONTROLLING THE SYSTEMSAFETY MONITORING SYSTEMSCONTROLLER ALGORITHMSDATA ACQUISTION: WIND SPEED AND DIRECTIONROTOR ANGULAR SPEEDPROPELLOR PITCH ANGLECONTROL SYSTEM DESIGN AND ANALYSISELECTRICAL SYSTEM DESIGN AND ANALYSISPOWER GENERATION AND STORAGESENSORSRotor rotational sensorWind speed and direction sensorACTUATORSMotors for manipulatiing the propeller pitchAERODYNAMIC DESIGNSTRUCTURAL DESIGN OF THE TOWERELECTRICAL AND POWER SYSTEMSAP1.3Theautomaticparallelparkingsystemmightusemultipleultrasoundsensorstomeasuredistancestotheparkedautomobilesandthecurb.Thesensormeasurementswouldbeprocessedbyanon-boardcomputertodeterminethesteeringwheel,accelerator,andbrakeinputstoavoidcollisionandtoproperlyalignthevehicleinthedesiredspace.

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