DEGREE PROJECT IN TECHNOLOGY, FIRST CYCLE, 15 CREDITS STOCKHOLM, SWEDEN 2016

Advanced RC car

Avancerad radiostyrd bil

FILIP LENSUND

JOHAN ERKERS

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

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BachelorThesisMMKB2016:31MDAB092

AdvancedRCcar

FilipLensund JohanErkers

Approved

2016-06-07Examiner

MartinEdinGrimhedenSupervisor

NihadSubasic

ABSTRACT This report contains improvementsof the radiocontrolledcarwhich isdevelopinganelectronic differential and a speed controller. The report contains theory of enginemodelling, steering and testing of these theories. Ackerman steering is used to getdifferentsteeringradiusoftheinnerandouterwheelwhencornering.Inordertoregulatethe velocity of the rearwheels they are individually controlled by implementing twoseparatecontrollersoneforeachwheel.TocontrolthesystemPD-controllersisusedforafastrisetime,twotypesofPD-controllersaretested,feed-backandfeed-forward.Ademonstratorwasconstructedtoexecutethetwotests,oneofthetestwastodeterminetheelectronicdifferentialsefficiencybymeasuringthecorneringabilityofthecarwithandwithoutdifferentialatdifferentspeeds.Thesecondtestwasperformedtodeterminewhich regulator gave the fastest controlling of the speed. This by exposing bothcontrollerswithdifferenttestscenarios.Based on our tests the conclusion is drawn that the electronic differential had a verypositiveimpactontheturningradius.Whiletesting,thecontrollersshowedonlyasmalldifference,wherethefeed-forwardcontrollerwasslightlyfasterinsomeofthetests.

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KandidatarbeteMMKB2016:31MDAB092

Avanceradradiostyrdbil

FilipLensundJohanErkers

Godkänt

2016-06-07Examinator

MartinEdinGrimhedenHandledare

NihadSubasic

SAMMANFATTNING Rapportenbehandlarförbättringaravdenradiostyrdabilenmedfokuspåutvecklingavenelektroniskdifferentialsamtregleringavhastigheten.Irapportenkommerteorikringmotormodellering och styrning, samt tester av dessa teorier. Ackerman-styrninganvändesförattfåolikaradiepåinnerochytterhjulenvidkurvtagning.Förattkunnareglerahasighetenpåbakhjulenindividuelltimplementeradestvåseparataregulatorer.FörregleringavhastighetpåbakhjulenanvändesPD-regulatorerförensnabbstigtid,tvåtyperavPD-regulatorertestadesenfeed-backochenfeed-forward.En demonstratör konstruerades för att möjliggöra tester av forskningsfrågorna. Detförstatestetutfördesförattundersökadenelektroniskadifferentialaxelnsinverkanpåbilens förmåga att ta kurvor i olika hastigheter. Det andra testet genomfördes för attundersöka vilken regulator som gav den snabbade regleringen av hastigheten. Dettagenomattutsättaregulatorernaförolikatestsenarior.Utifråntesternakundeslutsatsendrasattdenelektroniskadifferentialenharenmycketstorpositivinverkanpåbilenssvängradie.Medantesternaavregulatorernaendastgaven marginell skillnad men Feed-Forward regulator var något snabbare i en del avtesterna.

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PREFACE Wewould like to thankour supervisorNihad Subasic for feedbackandour dear friendsSimonGärtnerandAntonDahlquistforthehelpandsupport.

FilipLensund&JohanErkers

Stockholm,June2016

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NOMENCLATURE Fortheconvenienceofthereaderallthesymbolsandabbreviationshavebeengatheredunderthischapter.

Symbols

Symbol Description

𝜃 Angle of the Ackerman-Steering (degrees)

𝐿# lengthbetweenwheelaxis(m) 𝐿$ lengthbetweenfrontwheels(m)𝑅# Radius outer wheel (m)

𝑅$ Radius inner wheel (m)

𝑋' Estimation(position)𝐾' KalmanGain𝑍' Measuredvalue

𝑋'*# Previousestimation(position)U Voltage(V)R Resisters(ohm)i Current(A)L Inductance(H)𝑒,-. Backelectromotiveforce(V)

𝜏- Torqueproducedbymotor(Nm)𝜏0 TorqueproducedbyWheel(Nm)𝜑- Angle(rad)𝜑- Angularvelocity(rad/s)𝐾2 Armatureconstant(Nm/A)𝐾, Motortorqueconstant(V/A)𝜑0 Velocitywheel(rad/s)𝜑0 Accelerationwheel(rad/s2)𝑟 Radius(m)𝑣 Speed(m/s)𝐽0 Momentofinertiaforwheel(kgm2)𝐽- Momentofinertiaformotor(kgm2)𝑑 Dynamicfrictioncoefficient(𝜇)

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N Gearratio𝐾8 Proportionalpartparameter𝐾9 Derivativepartparameter

Abbreviations

CAD ComputerAidedDesignDC DirectcurrentDMP DigitalMotionProcessorDPS Degreespersecond𝐼$𝐶 Inter-integratedCircuitIMU InternalMeasurementUnitKTH KungligaTekniskaHögskolan(RoyalInstituteofTechnology)MATLAB ComputerAidedEngineeringPWM Pulse-widthModulationRC RadiocontrolledRpm Revolutionperminute

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CONTENTS ABSTRACT........................................................................................................................................................IISAMMANFATTNING......................................................................................................................................IVPREFACE..........................................................................................................................................................VINOMENCLATURE........................................................................................................................................VIIICONTENTS........................................................................................................................................................X1 INTRODUCTION....................................................................................................................................11.1 BACKGROUND.......................................................................................................................................................11.2 PURPOSE...............................................................................................................................................................11.3 SCOPE....................................................................................................................................................................11.4 METHOD................................................................................................................................................................2

2 THEORY...................................................................................................................................................32.1 ELECTRONICDIFFERENTIAL..............................................................................................................................32.2 ACKERMANSTEERING........................................................................................................................................42.3 IMU........................................................................................................................................................................42.4 ENCODER..............................................................................................................................................................52.5 KALMANFILTER..................................................................................................................................................52.6 SMOOTHFILTER...................................................................................................................................................52.7 MODELOFTHESYSTEM......................................................................................................................................52.7.1 ModeloftheDC-motor................................................................................................................................62.7.2 ModeloftheGearboxandWheel............................................................................................................6

2.8 PD-CONTROLLER.................................................................................................................................................72.8.1 TransferfunctionPD-controller.............................................................................................................82.8.2 Pol-placement.................................................................................................................................................92.8.3 Implementation............................................................................................................................................10

3 DEMONSTRATOR................................................................................................................................113.1 PROBLEMFORMULATION...............................................................................................................................113.2 SOFTWARE.........................................................................................................................................................113.2.1 Thesoftwarestructureforthehandunit.........................................................................................113.2.2 Thesoftwarestructureinthecarunit...............................................................................................11

3.3 ELECTRONICS....................................................................................................................................................123.3.1 Microcontroller............................................................................................................................................123.3.2 Battery.............................................................................................................................................................123.3.3 InternalmeasurementunitorIMU.....................................................................................................123.3.4 Xbee...................................................................................................................................................................123.3.5 H-bridge...........................................................................................................................................................133.3.6 DC-motorandgearbox..............................................................................................................................133.3.7 Servomotor....................................................................................................................................................133.3.8 Encoder............................................................................................................................................................133.3.9 Blockdiagram...............................................................................................................................................13

3.4 HARDWARE.......................................................................................................................................................143.4.1 Lasercut..........................................................................................................................................................143.4.2 3D-printed......................................................................................................................................................143.4.3 Soldering.........................................................................................................................................................14

3.5 THEDEMONSTRATOR......................................................................................................................................143.5.1 SteeringwiththeIMU................................................................................................................................143.5.2 Thehandandcarunit...............................................................................................................................15

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4 RESULTS................................................................................................................................................164.1 RESULTSFROMTHECORNERINGTEST.........................................................................................................164.2 RESULTSFROMTHETESTOFTHECONTROLLERS.......................................................................................17

5 DISCUSSIONANDCONCLUSIONS...................................................................................................185.1 DISCUSSION.......................................................................................................................................................185.1.1 Partsusedintheproject...........................................................................................................................185.1.2 Results..............................................................................................................................................................185.1.3 Errorsources.................................................................................................................................................18

5.2 CONCLUSIONS....................................................................................................................................................186 RECOMMENDATIONSANDFUTUREWORK...............................................................................196.1 RECOMMENDATIONS.......................................................................................................................................196.2 FUTUREWORK..................................................................................................................................................19

REFERENCES..................................................................................................................................................20APPENDIXA:DATAFROMCORNERINGTEST.....................................................................................22APPENDIXB:DATAFROMCONTROLLERTEST.................................................................................23

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1 INTRODUCTION This chapter contains an introduction to the project. It will introduce the background,purpose,scopeandmethod.

1.1 Background Theradiocontrolledcar,orRCcarwasinventedin1966byanItaliancompanynamedElettronicaGiocattio.InthebeginningtheRCcarswererunbygasolineornitrogen[1].Todaythecarsrunonelectricityorgasolineandarepopular,funandexcitingtoys.Eversincethebeginning,thecarshavebeencontrolledwithleversorawheelonahandheldremote.TheideaistomakeanewwaytocontrolthecarandotherRC-toysandimplementan electronic differential instead of the classicmechanic differential and implement acontroller for the speed on the rear wheels. Research has been done in the area ofcontrollingthecarwhitanIMUandafewsimilarhobbyprojects[2]havebeenfoundbutnoscientificstudies.

1.2 Purpose Thepurposeofthisprojectistodesignanelectronicdifferential,acontrollerforthespeedofthebackwheelsandanewwaytocontrolaRCcarandotherremotecontrolledvehicles,for example boats and airplanes. The static controller is replaced with an IMU andWirelesscommunicationplacedonthedriver’sarm.ThenewcontrolunitconsistsofanXbee,ArduinoNANOandanIMU[3].TheArduinoandXbeeareplacedontheforearmsonoextraweight isputonthehandwheretheIMUisplaced,thiswillmakeiteasiertomovethehand.Whenthehandistiltedforwardthecarwillgoforwardandifthehandistiltedtoeithersidethecarwillturnrightorleft.TodrivethecarforwardtwoDC-motorsare used. For an exact steering the DC-motors will act as an electronic differential,meaningthatthebackwheelswillhavedifferentspeedswhenturning.Thisthesiswillcoverthefollowingresearchquestions:

• Howwilltheelectronicdifferentialeffectcorneringatdifferentspeeds?• Which control theory will be best for the task, a feed-back or a feed-forward

controller?

1.3 Scope ThisprojectiscompletedforaBachelorthesisatKTHandextendsoveraperiodof16weeks.Theprojectbudgetis1000Swedishcrowns.TocontrolthesystemanArduinoUNOisprovidedbyKTHandisanopensourceplatform.TheArduinoNANO,IMU,H-bridge,DC-motors,servoandwheelshavebeenpurchased.TheKalmanfilter,smoothfilter,encodercounterand𝐼$𝐶bushavebeenobtainedfromopensourcelibraries,andareredesignedsothattheywillworkwiththeelectronicsthatareused.Theobtainedopensourcelibrarieswillbeexplainedbriefly,sincetheyareverycomplex.Thefocusinthisprojectwillbetocreateacontroller(chapter2.7)andmakeanelectronicdifferential.

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1.4 Method Theprojectstartedwitharesearchabouthowthecomponentsisusedinanefficientandsmartway.Twounitsareincorporated,onehandunitfortheremotecontrolandonecarunit.Betweenthemthereisawirelessconnectiontotransferdatafromtheremotecontrolto the car unit using an Xbee (chapter 3.3.4). To be able to investigate the researchquestionsademonstratorwasmade.Todeterminehowthecarsturningradius isaffectedbyanelectronicdifferential, fourdifferentspeedsweretestedwiththesamesteeringangleandnodifferential.Toachievethefourdifferentspeeds,thePWMsignalweresetto255(maxspeed),205,155and105.10 testwasperformed for each speedand the radiusof the cars routewasmeasured(figure1).Forthetestwithelectronicdifferentialthesamespeedwassetasinthefirsttesttotheouterwheel.Fortheinnerwheelthespeedwassettomatchtheinnerradiusoftheturningcircle.

Figure1.Testoftheturningradius

Thesecondtestwastodeterminewhichcontrollerisbestsuitedforcontrollingthespeedontherearwheels,afeed-backorfeed-forwardcontroller.Thetestwasdividedintofourdifferentscenarios,duringtheteststimeandspeedwasmeasuredusinganencoderandArduinosbuiltintimer.Thefirstscenariowasexecutedbylettingthecaraccelerateduptomaximumspeedfromastandstill.Thesecondtestwastoletthecaraccelerateto50%ofthemaxspeedformastandstill.Thethirdtestwasaccelerationfromaconstantspeedat50%oftopspeeddowntoastop.Thelasttestwasaccelerationfromconstanttopspeedtoastandstill.Allfourscenariosweretestedfivetimesinordertoprovidemoreeventestresults.

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2 THEORY Thischapterdescribesallthetheorybehindtheproject.Itgivesanunderstandingofhowthedifferentpartswork.

2.1 Electronic differential Whencornering theouterwheel travels a greaterdistance then the innerwheel.Thismeansthattheouterwheelneedsagreaterangularvelocitythentheinnerwheel.Tosolvethisproblemadifferentialisused.Thetwoaxesshaftsinfigure2canrotateatdifferentspeedthankstothedifferentialpiniongear.Thetheorybehinditisthatifoneoftheaxleshaftsrotatesslowerthedifferentialsidegearandpiniongearforcestheotheraxletorotatefaster[4].

Figure2.Mechanicaldifferential[4]

Theelectronicdifferentialusesthesametheoryasthemechanical,butinsteadofusingamechanicaldifferentialtheelectronicusesanindividualelectricmotorforeachwheel.

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2.2 Ackerman steering TheAckermann-principleisbasedonthattheaxesofthesteeringknucklealwayscuttingthe rearaxis at the samepoint (figure3).Whencornering, the frontwheelswillhavedifferent turning radius, the principle is that thewheelswill have different angels toprevent them from sliding on the surface [5]. To enforce this the angle is calculatedbetweenthesteeringknuckleandthewheelarch(equation1).

𝜃 = arctan𝐿$2 ∙ 𝐿#

(1)

Figure3.Ackermansteeringprincipal.

TheradiusoftheouterandinnerwheelwasdeterminedusingSolidedgeCADandiscalculatedto286mm.

2.3 IMU AnIMUisanelectroniccomponentthatmeasuresthespecificforceandangularrate.TheIMU uses combinations of an accelerometer, which measures force and a gyroscope,whichmeasuresangularvelocitytodeterminethesensormovement.Thesensorsreadthemovementsaroundallthreeaxes.Themovementsaredefinedasroll,pitchandyaw,seefigure4.TheIMUusesadigitalmotionprocessor(DMP)toprocessthedatafromthesensors[3].

Figure4.HowRoll,YawandPitchisdefined.

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2.4 Encoder Theencoderusestwopulsestodeterminethedirectionoftheturningwheel.TheAandBpulseusesanoffsetasseeninfigure5todeterminewhichwaytheencoderisturning.If theApulsechangesfromhighto lowwhiletheBpulse is lowthemotionis likethearrowinfigure5.IftheApulsechangesfromhightolowandtheBpulseishighthemotionisreversed[6].

Figure5.Pulsetrainoftheencoder[6].

Therearedifferentwaystocountpulses.InthewaydescribedaboveonepulseiscountedwhentheApulsechangesfromhightolow,thisiscalledFalling.ThesecondwaytocountpulsesiswhenAchangesstatefromlowtohigh,thisiscalledRising.ThethirdwayistocountoneverychangesofstateontheApulseandthisiscalledChange.Thebenefitofcountingonchangeisthatthepulsesofeachrevelationwilldouble.

2.5 Kalman filter TheKalmanfilterisanalgorithmthatusesaseriesofmeasurementstomakeapredictionofwhatthenextmeasuredvaluewillbe.Thisisusefulwhenthemeasuredvaluehasalotoffluctuations.TheKalmanfilterusesameanvaluewhichisthevaluethatisthemostlikelyandavariance.Theestimatedvaluetendstobemoreprecisethanthemeasured.Byimplementingequation(2)totheIMU,anaveragemeasurementisreceived[7]

𝑋' = 𝐾'. 𝑍' + 1 − 𝐾' . 𝑋'*# (2)

where the𝐾' is the Kalman gain𝑍' is themeasured value and𝑋'*# is the previousestimation.TheKalmanfilterisusedforfilteringthesignalfromtheIMU.

2.6 Smooth filter SincethedatareceivedfromtheXbee(chapter3.3.4)containsnoise,aSmoothfilter[8]isimplemented.TheSmooth filter isadigital low-pass filter forsmoothingout the inputsignal to the servo. An internal buffer stores data and limits the amount of new dataenteringthesystem.

2.7 Model of the system To be able to calculate the control parameters for the feed-back and feed-forwardcontrollers,amodelofthesystemwasdeveloped.

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2.7.1 Model of the DC-motor

To describe the model of the DC-motor an example from Control Tutorials [9] wasfollowed.Figure6bellowshowstheDC-motorscircuit.

Figure6.ModelofaDC-motor.

The supplyvoltage isU.RandLare themotor resistanceand inductance,𝑒,-. is theinducedmotorvoltageandithecurrent.𝜏-isthetorqueproducedbythemotor,𝜑-theangleand𝜑-istheangularvelocity,bisthedynamicmotorfrictionandJmisthemotorsmomentofinertia.AccordingtoKirchhoff’slaw[9]thevoltageUcanbedescribedas

𝑈 = 𝑅𝐼 + 𝐿𝑑𝑖𝑑𝑡 − 𝑒,-.

(3)

andthetorqueisgivenby[9]

𝜏- = 𝐾2𝑖 (4) where𝐾2isthearmatureconstantandtheback𝑒,-.isgivenby

𝑒,-. = 𝐾,𝜑- (5)

where𝐾, isthemotortorqueconstantwhichisequalto𝐾2so𝐾 = 𝐾, = 𝐾2 .

2.7.2 Model of the Gearbox and Wheel

Theangularvelocity𝜑0onthewheelontheoutgoingaxisfromthegearboxisgivenby[8]

𝜑- = 𝑛𝜑0 (6) andthetorqueisgivenby

𝜏- =1𝑛 𝜏0

(7)

Figure7.Motoraxisintothegearboxandwheelaxisoutofthegearbox.

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where𝜑-istheanglevelocityonthemotorshaft,𝜑0istheanglevelocityonthewheelaxisand𝑛thegearratioofthegearbox.Forthewheelinfigure7thespeed𝑣andtorque𝜏0isgivenby[10][9]

𝑣 = r𝜑0 (8)

𝜏0 = 𝐽0𝜑0 + 𝑑𝜑0 (9)

whererbeingtheradiusofthewheel,𝐽0themomentofinertiaanddthedynamicfrictioncoefficientofthewheel.

Figure8.Aturningwheel.

Theparametersforthesystemcanbefoundintable1.

Table1.Motordata.

Symbol Value ReferenceResistance R 4Ω MeasuredVoltageconstant 𝐾, 176,9 ∗ 10*T𝑉/𝐴 CalculatedArmatureconstant 𝐾2 176,9 ∗ 10*T𝑁𝑚/𝐴 CalculatedMotormomentofinertia 𝐽- 212,1 ∗ 10*T𝐾𝑔𝑚$ SolidedgeCADWheelmomentofinertia 𝐽0 51013 ∗ 10*T𝐾𝑔𝑚$ SolidedgeCADGearratio N 48 Datasheet

2.8 PD-controller ThereasontouseaPD-controllerwasthatthedriverwillcorrectanytypeofstaticerrorand a fast rise time is required. Two types of control theorywill be tested, feed-backcontrolfigure9andfeed-forwardcontrolfigure10.Boththeoriesareusingtheerror𝑒(𝑡)whichisthedifferencebetweenthereferencesignal𝑟(𝑡)fromtheIMUandthecalculatedspeed𝑦(𝑡).Thedifferencebetweenthetwotheoriesisthatfeed-forwardnotonlyusestheerror𝑒(𝑡),italsomakesaneducatedguessaboutwhattheoutputsignal𝑢(𝑡)shouldbe.Thecontrolfunctionforthefeed-forwardis𝐹.. 𝑠 = 1/𝐺(𝑠).Theoutputsignal𝑢 𝑡 foraPD-controlleris[11]

𝑢 𝑡 = 𝐾8𝑒 𝑡 + 𝐾9𝑑𝑑𝑡 𝑒(𝑡)

(10)

𝐾8and𝐾9areparametersthatcanbechangedtogetthesystemtobehaveasdesired.

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Theparameter𝐾8determineshowthecontrollerreactsproportionaltotheerrorand𝐾9determineshowthecontrollerreactsonthederivativeoftheerror.Thetransferfunction𝐺(𝑠)andhowtoobtainitisdescribedandcalculatedinchapter2.8.1.

Figure9.Feed-backcontrol.

Figure10.Feed-forwardcontrol.

2.8.1 Transfer function PD-controller

Thetransferfunctionis

𝐺 𝑠 =𝑉 𝑠𝑈 𝑠

(11)

where𝑉 𝑠 isthevelocityand𝑈 𝑠 istheoutputvoltage.Toobtainthetransferfunctionthemodelandequationsinchapter2.7areused.Thetorqueofthemotorcanbewrittenas[9]

𝜏- = 𝐽-𝜑- + 𝑏𝜑- (12)

Equations3,4,5and12areused,withtheassumptionthattheinduction𝐿 ≈ 0thenthemotionofthemotorcanbedescribedas

𝐽-𝜑- + 𝑏𝜑- =𝐾𝑅 𝑈 + 𝐾𝜑- (13)

Todescribethemotionofthewheeltheequations6,7,8and9areusedin13

𝜑0 + 𝜑0𝑛𝐾$ + 𝑑

𝐽0= 𝑈

𝑛𝐾𝐽0𝑅

(14)

Laplacetransformation[12]ofequation8and13gives

𝑉(𝑠) = 𝑟𝑠𝜑0(𝑠) (15)

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𝑠$𝜑0 𝑠 + 𝑠𝜑0 𝑠𝑛𝐾$ + 𝑑

𝐽0= 𝑈 𝑠

𝑛𝐾𝐽0𝑅

(16)

byusingandsimplifyingequation11,15and16thetransferfunctionisobtained

𝐺 𝑠 = fghijklml(gnmo)

- (17)

2.8.2 Pol-placement

Therequirements for thecontroller is tomake it as fastaspossible,withouthavingasystemthatoscillates.Theclosedloopsystemcanbedescribedas[13]

Figure11.Feed-backcontrol.

Thetransferfunctionisequalto[13]

𝐺ph 𝑠 =𝑆𝐴

𝐴𝑅 + 𝐵𝑆 =𝑆𝐴𝐴-𝐴s

. (18)

wheretheoutputsignalfromtheregulatorcanbewrittenas

𝑢 𝑡 =𝑆𝑅 (𝑟 𝑡 − 𝑦(𝑡)) (19)

Equation17andfigure9gives

𝐵𝐴 =

𝑛𝐾𝑟𝑠𝐽0𝑅 + 𝑅(𝐾$ + 𝑑) (20)

andforthecontrollerfunctionforthefeed-back𝐹.t(𝑠)

𝑆𝑅 =

𝑃𝑠 + 𝐷𝑠 + 𝑟s

(21)

Fromthistheequation22isobtained

𝐴wx = 𝐴𝑅 + 𝐵𝑆 (22) were𝐴-isapolynomialthathavethesameorderasAand𝐴wx isapolynomialofthesameorderas𝐴-𝐴s.Thepoles𝛼and𝛽canthenbechosenas

𝐴- = 𝑠 + 𝛼 (23)

𝐴s = 𝑠 + 𝛽 (24)

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Bychoosing𝛼 = 1and𝛽 = 5thesystemhasarisetimeof6,58 ∗ 10*|secondsthismeetstherequirementsofthedesiredsystem.Infigure12,astepresponsefortheclosedloopsystemisshown.

Figure12.Stepresponsefortheclosedloopsystem.

2.8.3 Implementation

Themicrocontrollerworksindiscretetimestepssothecontrollerfunctionforthefeed-backandfeed-forwardmustbediscretized.ThisisdoneusingTustinsapproximation[14]

𝑑𝑢𝑑𝑡 = Δ2𝑢(𝑡) (25)

whereΔ2𝑢(𝑡)is

12 (Δ2𝑢 𝑡 + Δ2𝑢 𝑡 − 𝑇 ) =

1𝑇 (𝑢 𝑡 + 𝑢 𝑡 − 𝑇 ) (26)

wereTbeingthesampletime.WhitcalculationsinMATLABthisgivesthediscretesystemforthefeed-back(equation27)andfeed-forward(equation28)

𝑢.t = 𝑎#𝑒 𝑡 + 𝑏#𝑒 𝑡 − 𝑇 − 𝑐#𝑢(𝑡 − 𝑇) (27)

𝑢.. = 𝑎$𝑒 𝑡 + 𝑏$𝑒 𝑡 − 𝑇 − 𝑐$𝑢(𝑡 − 𝑇) (28)

weretheconstantscanbefoundintable2.

Table2.constantsoftheoutputsignalforfeed-backandfeed-forward.

𝑎# 14,47𝑏# -14,10𝑐# 0,65𝑎$ 0,08𝑏$ 0,02𝑐$ 1

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3 DEMONSTRATOR Thischapterdescribestheproblemswhichwillbefacedwhenbuildingthedemonstrator,anditdescribesthesoftware,electronicsandhardwarethatareused.

3.1 Problem Formulation Togetafunctionaldemonstratorthefollowingproblemsweretobesolved.

• Theweightofthehandunitmustbelight.• Thepartsonthecarmustbestrongsotheydonotshatterwhencollidingwith

objects.• Thefrontwheelsmusthavedifferentturningradius.• Thespeedmustbeindividuallycontrolledonthebackwheels.

3.2 Software Thesoftwareisdividedintotwosubsystems,oneforthehandunitandoneforthecar.ThePrograminglanguagesforbothunitswasprimarilyC.

3.2.1 The software structure for the hand unit

ThesoftwareforthehandunitrunsonanArduinoNANO.Thehandunitstartstoreadtheroll (X-axis)andthepitch(Y-axis) fromthe IMUgyroscopeandaccelerometer therollrepresentingthesteeringandthepitchrepresentingthedrivingsignals.The incomingdatafromtheIMUisfilteredthroughanopensourceKalman-filter(chapter2.5).Therolland pitch angle is rescaled to PWM-signals and transmitted to the car by the Xbeetransmitter(figure13).

Figure13.Flowchartoftheprogramonthehandunit.

3.2.2 The software structure in the car unit

ThesignalsfromtheXbeetransmitterarereceivedbytheXbeereceiver.ThePWM-signalsarethensmoothedoutthroughanopen-sourcelowpassfilter(chapter2.6)toeliminateanynoisecausedbytheXbeecommunication.ThePWM-signalforcontrollingthesteeringisprocessedand sent to the servo (chapter3.3.7).Whencornering,both steeringanddrivinginputsarenecessaryforcalculatingtheindividuallyspeedforeachbackwheeltocreatetheelectronicsdifferential(chapter2.1).ThebacktiresareindividuallycontrolledbytwoPD-controllersforthespeedcontrolthatwasdevelopedandtestedinMatlab.Theoverallstructureofthesystemisdescribedintheflowchartbelow(figure14).

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Figure14.Flowchartofthecarprogram.

3.3 Electronics Oneachunitthereisacoupleofelectricalcomponents.Below,allelectricalcomponentswill be reviewed. In chapter 3.3.9 are two figures which contains flowcharts of thecomponentsoneachunit.

3.3.1 Microcontroller

TocontrolthesystemonthecaranArduinoUNO[15]isuse.ItisanopensourceplatformandusesC/C++languageandhasaclockspeedof16MHz.Theboardhas14digitalpinswhichcanbeusedasinputsoroutputs,italsohas6analoginputs.OnthehandunitanArduinoNANO[16] isusedandtheNANOboardhasthesamelayoutastheUNO.ThedifferencebetweentheboardsisthattheNANOhas8analogpins.TheUNOispoweredwith7,4VandtheNANOwith9V.

3.3.2 Battery

Astandard9ValkalinebatterywillpowertheArduinoNANOonthehandunit.Thebatteryonthecarisa7,4VlithiumbatteryandwillpowerthemotorsandtheArduinoUNO.

3.3.3 Internal measurement unit or IMU

TheIMUisaninertialmeasurementunitoftypeMPU-6050[3]andcanmeasureanglesandaccelerationupto±2000𝑑𝑝𝑠(degreespersecond)and±16𝑔inthreeaxes.Thisismuchfaster thannecessarysotherefreshratewasset to±200𝑑𝑝𝑠and±2𝑔 togiveamore exact reading. The IMU has six degrees of freedombut to solve the problem ofdrivingandsteeringthecaronly fourwillbeneeded(twoangles in theplaneandtheacceleration).

3.3.4 Xbee

ForthewirelesscommunicationasystemoftwoXbeesseries2[17]areused.OneoftheXbeesisconfiguredascoordinatorandthisunitreceivesthedatatothemicrocontroller.Theotheroneisconfiguredasendpoint,thisXbeetransmittheoutputsfromtheArduino

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NANO.TheXbeesareusingZigbeeforthewirelesscontrolwithafrequencyat2,4GHz.Thesemodulesareveryenergyefficientandhavearangeof40metersindoorsandupto100metersoutdoors.

3.3.5 H-bridge

TheH-bridge[18]isadualmotordriveandmakesitpossibletodrivethemotorsinbothdirections.Ithas2inputsand2outputsforeachmotor.ByusingthePWMsignal[19]thevoltagetothemotorcanbecontrolled.Withcontinuousdriving,theoutputcurrentcanbeupto1,5Ampereandpeakscanbeupto2Ampereforashortperiodoftime.

3.3.6 DC-motor and gearbox

TheDC-motorsandgearbox[20]areoftypeDG02Sandcanbedrivenonvoltagesfrom0-8Vandhaveanoloadcurrentof125mAandanoloadspeedof140rpm.Thegearboxhasagearratioof48:1.

3.3.7 Servo motor

Theservomotor[21]isusedforthesteeringofthecar.IntheservothereisaDC-motorandgearboxwithahighgearratio.Tocontroltheoutputangle,theservousesitsowncontroller.Theservohasarangeof180degreesandrunsat5V.

3.3.8 Encoder

TomeasurerthespeedofeachwheelanencoderoftypeM,512CPT[22]isplacedontheaxisofthewheel.Ithas2channelsandanA-,andB-pulsewith512pulsesperrevolution.Thismakesispossibletodeterminewhichwaythewheelsareturningandhowfastbycountingthepulsespertimeunit.

3.3.9 Block diagram

Figure15andfigure16showsablockdiagramofalltheelectronicpartsonthehandunitandcarunitandhowtheyworktogether.

Figure15.Handunitwiththecomponents.

Figure16.Carunitwiththecomponents.

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3.4 Hardware Themethodsofcreatingthedifferentcomponents forthedemonstratorarepresentedbelow.Thefourwheelsandthegearsfortheencoderwerepurchased.

3.4.1 Laser cut

Thebaseofthecarwasmadefrom6mmthickacrylicplastic.Theshapeandsizeofitisoptimisedsothatallthecomponentswillhaveanarrowfitandthecariskeptsmall.

3.4.2 3D-printed

TheholderfortheArduinoUNO,servoandbatteryis3D-printed.Tofastentheholderonto thebaseof thecar theholder isglued.Theholder for theXbee,ArduinoNANOandbatteryare3D-printedaswellastheholderfortheIMU.Thebenefitsof3D-printingarethatthepiecesarelightandeasytomake.

3.4.3 Soldering

Thecircuitboardforthehandandcarunitwasmadefromaperfboard.Theperfboardisforprototypingelectricalcircuits.Ithaspremadeholesandhasgoodfunctionality.

3.5 The demonstrator 3.5.1 Steering with the IMU

Figure17showshowtooperatethecarwiththeIMUplacedonthehand.

Figure17.Topleft:forward,topright:rightturn,bottomleft:break/back,bottomright:leftturn.

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3.5.2 The hand and car unit

Thefinalresultofthehandandcarunitisshownbelowinfigure18.

Figure18.Handandcarunit

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4 RESULTS Theresultsofthetwotestarepresentedinthischapter.

4.1 Results from the cornering test Infigure19thetestresultsfromnoelectronicdifferentialarepresented.All10differenttestsofeachspeedisdisplayedaswellastheaverageturningradius.

Figure19Turningradiuswithoutelectronicdifferential.

All10differenttestisdisplayedandtheaverageturningradiusisdisplayedinfigure20.Onlyonetestwasexecuted,thisbecauseofthenearperfectresultatmaximumspeed.Testsatlowerspeedswasunnecessary.

Figure20Turningradiuswithelectronicdifferential.

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Table3.Averageturningradiusandpercentimprovementwithdifferential.

AverageradiusNodifferential[mm]

Averageradiuswithdifferential[mm]

Percentimprovementwithdifferential[%]

PWM255 846 298 64,8Table3showstheaverageradiusinthetwodifferenttestsformaximumspeed.ForallmeasureddataseeappendixA.

4.2 Results from the test of the controllers Theresultsfromthetestsofthecontrollersperformanceareshowninfigure21.Thebluelines represent the feed-back controllers average test performance and the red linesrepresentthefeed-forwardsaveragetestperform.Theplotoftest1isfrom0%to100%ofthemaxspeed,test2isfrom0%to50%ofthemaxspeed,test3isfrom50%ofthemaxspeedto0%andtest4isfrom100%ofmaxspeedto0%.Withtimeinmillisecondsonthex-axisandspeedmeasuredinrad/sonthey-axis.TheexactdatafromthetestscanbefoundinappendixB.

Figure21.Plotoftheaveragetestresultsfromthefeed-errorandfeed-backcontroller.

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5 DISCUSSION AND CONCLUSIONS Inthischapterconclusionsaredrawnfromthetestsinpreviouschapterandtheprojectisdiscussed.

5.1 Discussion 5.1.1 Parts used in the project

• The DC-motors that drives the car should have been of better quality. It wasdifficult to find information and a datasheet of the motors. The associatedgearboxesforthemotorshasahighgearratio,whichleadstoalowspeed.

• Thebatteryusedon the car is large andhas ahigh capacity.Thebetter choicewouldbetohaveasmallerbatterytosavespaceandweightonthecar.

• The angle velocity for the servo is low, this means that the steering is not soresponsive.

5.1.2 Results

• IntheorytheFeed-forwardcontrollershouldperformbetter[23]becauseitusesboththefeed-backandfeed-forwardsignalasdescribedinchapter2.8.Onereasonfor thismay be bad components and primarily themotors due to inconsistentperformance,anotherreasonisthatthemodelofthesystemisnotentirelycorrect.

• The variation in the test results of the electronic differential could have beenaffectedbythesurfacethecarwastestedon.

5.1.3 Error sources

• The two different motors have different speeds for the same PWM-signal orvoltage,thereforetheresultsofdrivingwhiteoutdifferentialonaconstantPWM-signalcanhaveanerrormargininthemeasurements.

• Formodellingofthesystemthemomentofinertiaforboththemotorandwheelare calculated in Solid edge CAD. The partsmade in Solid edge CAD are not aperfectreplicaoftherealmotorsandthisaffecttheparametersofthecontroller.

5.2 Conclusions Conclusionsafterconductingtestsonthedemonstratorandanalysingthedata.

Howwilltheelectronicdifferentialeffectcorneringindifferentspeeds?

Fromthetestinchapter4.1theconclusiontobedrawnisthattheelectronicdifferentialwillclearlyhelpthecartotakethecornerataradiusclosertothecalculatedturning

radius.

Whichcontroltheorywillbebestforthetask,afeed-errororafeed-forwardcontroller?

Fromthetestinchapter4.2theconclusionisthatthereisnotabigdifferenceinresults,partfromtest2figure21whereitisclearthattheFeed-forwardcontrolleris

75Msfastertoachieve50%ofmaxspeedandmorestable.

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6 RECOMMENDATIONS AND FUTURE WORK Recommendationsformakingtherobotandthingsthatcouldbemadeinthefuture.

6.1 Recommendations ForbuildingademonstratorlikethisanArduinoisrecommendedduetotheopen-sourcelibraries.ItiseasytofindcodefortheXbee,IMUandotherelectricalcomponents.Itisfuntomakethemechanicalpartsforthedemonstratorbutitrequires3D-printersandlasercutters, if not available the parts can be bought in various stores. When selectingelectronicparts,itisrecommendedtobuyqualityproductsthatareaccurateratherthencheapercopies.ForchoosingDc-motorsforaprojectlikethisitisrecommendedtochoosemotorsofgoodqualityandgooddatasheets.

6.2 Future work Thebaseofthecarunitcouldbewidersothatthecargetsalowercentreofgravity.Theclearinginbetweenthepartsofthesteeringcouldbetighter,thiswillgiveamoreexactsteering.Anothertypeofconstructionofthesteeringcouldbechosensothatthesteeringwould be faster. For a greater speed of the car a DC-motor with higher rpm isrecommended.Topreventthecarfromdrivingintoobjectsanultrasonicsensorcouldbefittedtotheroofonthecar.Thehandunitcouldusea flexiblecablebetweentheIMUholderandthebattery/Xbee/ArduinoNANOholder.Theholderforthebattery,XbeeandArduinoNANOcouldbesmallersothatitwillbelighterandmorecomfortable.Tomakethecontrollerfaster,astatespacecontrollercouldbeconstructed.

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REFERENCES 1. HistoryofRadioControlledCars.Availableat:

http://www.classic.rc-junkies.net/?page_id=637[Accessed:2016-02-23]

2. Inspirationproject,2015-11-03.Availableat:https://developer.mbed.org/users/Xiaofei/notebook/imu-controlled-robot/[Accessed:2016-02-23]

3. Invensense,MPU-6050,2011-10-24.Availableat:https://cdn.sparkfun.com/datasheets/Components/General%20IC/PS-MPU-6000A.pdf[Accessed:2016-02-23]

4. Mechanicaldifferential.Availableat:http://constructionmanuals.tpub.com/14050/css/Figure-11-17-Typical-differential-and-axle-assembly-with-ring-and-pinion-272.htm

5. Encodertheory.Availableat:

https://www.pjrc.com/teensy/td_libs_Encoder.html[Accessed:2016-04-23]

6. Ackermansteering.Availableat:http://www.rctek.com/technical/handling/ackerman_steering_principle.html[Accessed:2016-04-25]

7. KalmanFilter,2015-08-11.Availableat:http://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/[Accessed:2016-04-16]

8. SmoothFilter,2007.Availableat:http://playground.arduino.cc/Main/Smooth[Accessed:2016-03-12]

9. ControlTutorialDC-motor.Availableat:http://ctms.engin.umich.edu/CTMS/index.php?example=MotorSpeed&section=SystemModeling[Accessed:2016-04-10]

10. MaskinelementHANDBOK2008vol.1.Instutionenförmaskinkonstuktion,KTH. pp.7

11. Reglerteknik,grundläggandeteori2015vol.4:13.TorkelGlad&LennartLjung. pp.19

12. Reglerteknik,GrundläggandeTeori.2015vol.4:13.TorkelGlad&LennartLjung.pp.232

13. DynamicsandmotioncontrolLieFenghttps://www.kth.se/social/files/56b9a1f9f2765457b115e464/C3_Feedback_2016.pdf

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14. Reglerteknik,GrundläggandeTeori.2015vol.4:13.TorkelGlad&LennartLjung.pp.211

15. ArduinoUNOBoard.Availableat:https://www.arduino.cc/en/main/arduinoBoardUno[Accessed:2016-02-10]

16. ArduinoNANOBoard.Availableat:https://www.arduino.cc/en/Main/ArduinoBoardNano[Accessed:2016-02-10]

17. BuildingWirelessSensorNetworks.2011vol1.RobertFaludipp3,25-31.

18. H-bridgeDatasheet,2015-07.Availableat:http://www.ti.com/lit/ds/symlink/drv8833.pdf[Accessed:2016-04-25]

19. PWMsignalAvailableat:https://www.arduino.cc/en/Tutorial/PWM[Accessed:2016-04-28]

20. DC-motor.Availableat:http://www.dagurobot.com/goods.php?id=86[Accessed:2016-04-28]

21. Servomotor,2011-10-24.Availableat:https://www.parallax.com/sites/default/files/downloads/900-00005-Standard-Servo-Product-Documentation-v2.2.pdf[Accessed:2016-03-10]

22. Encoder,2015-04.Availableat:http://www.maxonmotor.com/medias/sys_master/root/8816813441054/15-353-354-EN.pdf[Accessed:2016-04-27]

23. ControlSystemDesignLecturenotesforKarlJohanÅström,EngineeringUniversityofCalifornia,SantaBarbara2002.http://www.boti.oil.gov.iq/book/english%20ebooks/%D8%A7%D9%84%D9%83%D9%87%D8%B1%D8%A8%D8%A7%D8%A1/control%20sys/CSYS%20%203-Control%20System%20Design.pdf[Accessed:2016-03-10]

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APPENDIX A: DATA FROM CORNERING TEST Datafromthecorneringtest.

WithoutDIFF(mm)

WithDIFF(mm)

Testnr

PWM255

PWM205

PWM155

PWM105 PWM255

1 1305 1010 630 294 3202 1374 976 617 280 3003 1354 1005 636 270 2954 1522 943 643 268 3105 1499 947 605 276 3156 1535 920 575 258 2807 1350 962 570 280 2958 1390 1022 576 284 2959 1060 947 578 260 30510 1070 945 572 268 270

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APPENDIX B: DATA FROM CONTROLLER TEST Datafromthecontrollertest.

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TRITA MMKB 2016:31 MDAB092

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