Solution Manual For Modern Control Systems, 12th 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.ExercisesE1.1A microprocessor controlled laser system:ControllerErrorCurrent i(t)PoweroutDesiredpoweroutputMeasuredpower-LaserProcessprocessorMicro-PowerSensorMeasurementE1.2A driver controlled cruise control system:DesiredspeedFoot pedalActualautospeedVisual indicationof speedController-ProcessMeasurementDriverCar andEngineSpeedometerE1.3Although 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 (the1

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2CHAPTER 1Introduction to Control Systemscurrent 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.Desiredposition ofthe flyActualpositionof the flyVisual indicationof the position ofthe flyFly-fisherWinddisturbanceController-ProcessMeasurementMind andbody of thefly-fisherRod, line,and castVision ofthe fly-fisherE1.4An autofocus camera control system:One-way trip time for the beamDistance to subjectLens focusingmotorK1LensConversion factor(speed of light orsound)Emitter/ReceiverBeamBeam returnSubject

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Exercises3E1.5Tacking a sailboat as the wind shifts:DesiredsailboatdirectionActualsailboatdirectionMeasured sailboat directionWindError-ProcessMeasurementActuatorsControllerSailboatGyro compassRudder andsail adjustmentSailorE1.6An automated highway control system merging two lanes of traffic:DesiredgapActualgapMeasured gapError-ProcessMeasurementActuatorsControllerActivevehicleBrakes, gas orsteeringEmbeddedcomputerRadarE1.7Using the speedometer, the driver calculates the difference between themeasured speed and the desired speed. The driver throotle knob or thebrakes as necessary to adjust the speed. If the current speed is not toomuch over the desired speed, the driver may let friction and gravity slowthe motorcycle down.DesiredspeedVisual indication of speedActualmotorcyclespeedError-ProcessMeasurementActuatorsControllerThrottle orbrakesDriverMotorcycleSpeedometer

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4CHAPTER 1Introduction to Control SystemsE1.8Human biofeedback control system:MeasurementDesiredbodytempActualbodytempVisual indication ofbody temperatureMessage toblood vessels-ProcessControllerBody sensorHypothalumusHuman bodyTV displayE1.9E-enabled aircraft with ground-based flight path control:Corrections to theflight pathControllerGc(s)AircraftG(s)-DesiredFlightPathFlightPathCorrections to theflight pathControllerGc(s)AircraftG(s)-DesiredFlightPathFlightPathGround-Based Computer NetworkHealthParametersHealthParametersMeteorologicaldataMeteorologicaldataOptimalflight pathOptimalflight pathLocationand speedLocationand speedE1.10Unmanned aerial vehicle used for crop monitoring in an autonomousmode:Gc(s)G(s)-CameraGroundphotoControllerUAVSpecifiedFlightTrajectoryLocation withrespect to the groundFlightTrajectoryMapCorrelationAlgorithmTrajectoryerrorSensor

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Exercises5E1.11An inverted pendulum control system using an optical encoder to measurethe angle of the pendulum and a motor producing a control torque:ErrorAngleDesiredangleMeasuredangle-PendulumProcessOpticalencoderMeasurementMotorActuatorTorqueVoltageControllerE1.12In the video game, the player can serve as both the controller and the sen-sor. The objective of the game might be to drive a car along a prescribedpath. The player controls the car trajectory using the joystick using thevisual queues from the game displayed on the computer monitor.ErrorGameobjectiveDesiredgameobjective-Video gameProcessPlayer(eyesight, tactile, etc.)MeasurementJoystickActuatorPlayerController

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6CHAPTER 1Introduction to Control SystemsProblemsP1.1An automobile interior cabin temperature control system block diagram:Desiredtemperatureset by thedriverAutomobilecabin temperatureMeasured temperatureError-ProcessMeasurementControllerAutomobilecabinTemperaturesensorThermostat andair conditioningunitP1.2A human operator controlled valve system:Desiredfluidoutput *Error *Fluidoutput* = operator functionsVisual indicationof fluid output *-ProcessMeasurementControllerValveMeterTankP1.3A chemical composition control block diagram:DesiredchemicalcompositionErrorChemicalcompositionMeasured chemicalcomposition-ProcessMeasurementControllerValveMixer tubeInfrared analyzer

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Problems7P1.4A nuclear reactor control block diagram:Desiredpower levelOutputpower levelErrorMeasured chemicalcomposition-ProcessMeasurementControllerIonization chamberReactorand rodsMotor andamplifierP1.5A light seeking control system to track the sun:LighintensityDesiredcarriagepositionLightsourcePhotocellcarriagepositionMotorinputsError-ProcessControllerMotor,carriage,and gearsKControllerTrajectoryPlannerDualPhotocellsMeasurementP1.6If you assume that increasing worker’s wages results in increased prices,then by delaying or falsifying cost-of-living data you could reduce or elim-inate the pressure to increase worker’s wages, thus stabilizing prices. Thiswould work only if there were no other factors forcing the cost-of-livingup. Government price and wage economic guidelines would take the placeof additional “controllers” in the block diagram, as shown in the blockdiagram.InitialwagesPricesWage increasesMarket-based pricesCost-of-living-ControllerIndustryGovernmentpriceguidelinesK1GovernmentwageguidelinesControllerProcess

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8CHAPTER 1Introduction to Control SystemsP1.7Assume that the cannon fires initially at exactly 5:00 p.m.. We have apositive feedback system. Denote by ∆tthe time lost per day, and thenet time error byET. Then the follwoing relationships hold:∆t= 4/3 min.+ 3 min.= 13/3 min.andET= 12 days×13/3 min./day.Therefore, the net time error after 15 days isET= 52 min.P1.8The student-teacher learning process:DesiredknowledgeErrorLecturesKnowledgeMeasured knowledge-ControllerProcessTeacherStudentMeasurementExamsP1.9A human arm control system:Visual indication ofarm locationzyueds-ControllerProcessMeasurementDesiredarmlocationArmlocationNerve signalsEyes andpressurereceptorsBrainArm &musclesPressure

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Problems9P1.10An aircraft flight path control system using GPS:Desiredflight pathfrom air trafficcontrollersFlightpathMeasured flight pathError-ProcessMeasurementActuatorsControllerAircraftGlobal PositioningSystemComputerAuto-pilotAilerons, elevators,rudder, andengine powerP1.11The accuracy of the clock is dependent upon a constant flow from theorifice; the flow is dependent upon the height of the water in the floattank. The height of the water is controlled by the float. The control systemcontrols only the height of the water. Any errors due to enlargement ofthe orifice or evaporation of the water in the lower tank is not accountedfor. The control system can be seen as:Desiredheight ofthe waterin float tankActualheight-ProcessControllerFlow fromupper tankto float tankFloat levelP1.12Assume that the turret and fantail are at 90◦, ifθw6=θF-90◦. The fantailoperates on the error signalθw-θT, and as the fantail turns, it drives theturret to turn.xyWind**qWqTqFFantailTurret= Wind angle= Fantail angle= Turret angleqWqTqFTorqueqTqWError-ProcessControllerGears & turretFantail

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10CHAPTER 1Introduction to Control SystemsP1.13This scheme assumes the person adjusts the hot water for temperaturecontrol, and then adjusts the cold water for flow rate control.Desired watertemperatureActualwater temperatureand flow rateColdwaterDesired waterflow rateMeasured water flowMeasured water temperatureError-ProcessController-MeasurementHuman: visualand touchValve adjustValve adjustHot watersystemCold watersystemHotwaterP1.14If the rewards in a specific trade is greater than the average reward, thereis a positive influx of workers, sinceq(t) =f1(c(t)−r(t)).If an influx of workers occurs, then reward in specific trade decreases,sincec(t) =−f2(q(t)).-Error-ProcessControllerf1(c(t)-r(t))f2(q(t))q(t)Total ofrewardsc(t)Averagerewardsr(t)P1.15A computer controlled fuel injection system:DesiredFuelPressureFuelPressureMeasured fuel pressure-ProcessMeasurementControllerFuel PressureSensorElectronicControl UnitHigh Pressure FuelSupply Pump andElectronic FuelInjectors

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Problems11P1.16With the onset of a fever, the body thermostat is turned up. The bodyadjusts by shivering and less blood flows to the skin surface. Aspirin actsto lowers the thermal set-point in the brain.BodytemperatureDesired temperatureor set-point from bodythermostat in the brainMeasured body temperature-ProcessMeasurementControllerInternal sensorBodyAdjustmentswithin thebodyP1.17Hitting a baseball is arguably one of the most difficult feats in all of sports.Given that pitchers may throw the ball at speeds of 90 mph (or higher!),batters have only about 0.1 second to make the decision to swing—withbat speeds aproaching 90 mph. The key to hitting a baseball a long dis-tance is to make contact with the ball with a high bat velocity. This ismore important than the bat’s weight, which is usually around 33 ounces(compared to Ty Cobb’s bat which was 41 ounces!). Since the pitcher canthrow a variety of pitches (fast ball, curve ball, slider, etc.), a batter mustdecide if the ball is going to enter the strike zone and if possible, decidethe type of pitch. The batter uses his/her vision as the sensor in the feed-back loop. A high degree of eye-hand coordination is key to success—thatis, an accurate feedback control system.P1.18Define the following variables:p= output pressure,fs= spring force=Kx,fd= diaphragm force =Ap, andfv= valve force =fs-fd.The motion of the valve is described by ¨y=fv/mwheremis the valvemass. The output pressure is proportional to the valve displacement, thusp=cy ,wherecis the constant of proportionality.Screwdisplacementx(t)yValve positionOutputpressurep(t)fs-Diaphragm areacValveConstant ofproportionalityAKSpringfvfd

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12CHAPTER 1Introduction to Control SystemsP1.19A control system to keep a car at a given relative position offset from alead car:ThrottlePosition offolloweruReferencephotoRelativepositionDesired relative positionPositionof lead-ControllerVideo camera& processingalgorithmsFollowercarActuatorFuelthrottle(fuel)Lead car-P1.20A control system for a high-performance car with an adjustable wing:DesiredroadadhesionRoadadhesionMeasured road adhesionRoadconditions-ProcessMeasurementControllerTire internalstrain gaugesRace CarKActuatorAdjustablewingComputerP1.21A control system for a twin-lift helicopter system:Desired altitudeAltitudeMeasured altitudeSeparation distanceDesired separationdistanceMeasured separationdistance--MeasurementMeasurementRadarAltimeterControllerPilotProcessHelicopter

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Problems13P1.22The desired building deflection would not necessarily be zero. Rather itwould be prescribed so that the building is allowed moderate movementup to a point, and then active control is applied if the movement is largerthan some predetermined amount.DesireddeflectionDeflectionMeasured deflection-ProcessMeasurementControllerKBuildingHydraulicstiffenersStrain gaugeson truss structureP1.23The human-like face of the robot might have micro-actuators placed atstrategic points on the interior of the malleable facial structure. Coopera-tive control of the micro-actuators would then enable the robot to achievevarious facial expressions.DesiredactuatorpositionVoltageActuatorpositionMeasured positionError-ProcessMeasurementControllerAmplifierPositionsensorElectro-mechanicalactuatorP1.24We might envision a sensor embedded in a “gutter” at the base of thewindshield which measures water levels—higher water levels correspondsto higher intensity rain. This information would be used to modulate thewiper blade speed.Desiredwiper speedWiperbladespeedMeasured water level-ProcessMeasurementControllerKWater depthsensorWiper bladeand motorElectronicControl Unit

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14CHAPTER 1Introduction to Control SystemsP1.25A feedback control system for the space traffic control:Desiredorbit positionActualorbit positionMeasured orbit positionJetcommandsAppliedforcesError-ProcessMeasurementActuatorControllerSatelliteReactioncontrol jetsControllawRadar or GPSP1.26Earth-based control of a microrover to point the camera:MicroroverCamera positioncommandControllerGc(s)Camera position commandCameraPositionReceiver/TransmitterRoverpositionCameraMeasured camera positionG(s)Measured camerapositionSensorP1.27Control of a methanol fuel cell:Methanol watersolutionControllerGc(s)RechargingSystemGR(s)Fuel CellG(s)-ChargeLevelDesiredChargeLevelMeasured charge levelSensorH(s)

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AdvancedProblems15AdvancedProblemsAP1.1Control of a robotic microsurgical device:ControllerGc(s)Microsurgicalrobotic manipulatorG(s)-End-effectorPositionDesiredEnd-effectorPositionSensorH(s)AP1.2An advanced wind energy system viewed as a mechatronic system: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 SYSTEMSAP1.3The automatic parallel parking system might use multiple ultrasoundsensors to measure distances to the parked automobiles and the curb.The sensor measurements would be processed by an on-board computerto determine the steering wheel, accelerator, and brake inputs to avoidcollision and to properly align the vehicle in the desired space.

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