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askelandphulenotes-ch19printable

Course: ME 2733, Fall 2010
School: LSU
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TheScienceandEngineeringof Materials,4thed DonaldR.AskelandPradeepP.Phul Chapter19MagneticMaterials 1 ObjectivesofChapter19 Tostudythefundamentalbasisforresponsesof certainmaterialstothepresenceofmagnetic fields. Toexaminethepropertiesandapplicationsof differenttypesofmagneticmaterials. 2 ChapterOutline 19.1ClassificationofMagneticMaterials 19.2MagneticDipolesandMagneticMoments...

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TheScienceandEngineeringof Materials,4thed DonaldR.AskelandPradeepP.Phul Chapter19MagneticMaterials 1 ObjectivesofChapter19 Tostudythefundamentalbasisforresponsesof certainmaterialstothepresenceofmagnetic fields. Toexaminethepropertiesandapplicationsof differenttypesofmagneticmaterials. 2 ChapterOutline 19.1ClassificationofMagneticMaterials 19.2MagneticDipolesandMagneticMoments 19.3Magnetization,Permeability,andthe MagneticField 19.4Diamagnetic,Paramagnetic,Ferromagnetic, Ferrimagnetic,andSuperparamagnetic Materials 19.5DomainStructureandtheHysteresisLoop 19.6TheCurieTemperature 19.7ApplicationsofMagneticMaterials 19.8MetallicandCeramicMagneticMaterials 3 Section19.1 ClassificationofMagneticMaterials Ferromagnetism Ferrimagnetism Diamagnetism Antiferromagnetism Hardmagnet 4 Section19.2Magnetic DipolesandMagneticMoments Themagneticbehaviorofmaterialscanbetracedtothe structureofatoms. BohrmagnetonThestrengthofamagneticmomentofan electron(B)duetoelectronspin. 5 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.1Originofmagneticdipoles:(a)Thespinoftheelectron producesamagneticfieldwithadirectiondependentonthequantum numberms.(b)ElectronsElectronsorbitingaroundthenucleuscreatea magneticfieldaroundtheatom. 6 7 Section19.3 Magnetization,Permeability,andtheMagnetic Field MagneticpermeabilityTheratiobetweeninductanceor magnetizationandmagneticfield.Itisameasureoftheease withwhichmagneticfluxlinescanflowthroughamaterial. MagnetizationThetotalmagneticmomentperunitvolume. MagneticsusceptibilityTheratiobetweenmagnetizationand theappliedfield. 8 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.2AcurrentpassingthroughacoilsetsupamagneticfieldHwith afluxdensityB.Thefluxdensityishigherwhenamagneticcoreisplaced withinthecoil. 9 10 Example19.1 TheoreticalandActualSaturationMagnetization inFe Calculatethemaximum,orsaturation,magnetizationthatweexpectin iron.ThelatticeparameterofBCCironis2.866.Comparethisvalue with2.1tesla(avalueofsaturationfluxdensityexperimentallyobserved forpureFe.) Example19.1SOLUTION Basedontheunpairedelectronicspins,weexpecteachironatomto havefourelectronsthatactasmagneticdipoles.Thenumberofatoms perm3inBCCironis: 11 Example19.1SOLUTION(Continued) Themaximumvolumemagnetization(Msat)isthetotalmagnetic momentperunitvolume: ToconvertthevalueofsaturationmagnetizationMintosaturationflux densityBintesla,weneedthevalueof0M.Inferromagneticmaterials 0M>>0Handtherefore,B0M. Saturationinductionintesla=Bsat=0Msat. 12 Section19.4 Diamagnetic,Paramagnetic,Ferromagnetic, Ferrimagnetic,andSuperparamagnetic Materials FerromagnetismAlignmentofthemagneticmomentsofatoms inthesamedirectionsothatanetmagnetizationremainsafter themagneticfieldisremoved. FerrimagnetismMagneticbehaviorobtainedwhenionsina materialhavetheirmagneticmomentsalignedinanantiparallel arrangementsuchthatthemomentsdonotcompletelycancel outandanetmagnetizationremains. DiamagnetismTheeffectcausedbythemagneticmomentdue totheorbitingelectrons,whichproducesaslightoppositionto theimposedmagneticfield. 13 Section19.4(Continued) AntiferromagnetismArrangementofmagneticmomentssuch thatthemagneticmomentsofatomsorionscanceloutcausing zeronetmagnetization. HardmagnetFerromagneticorferrimagneticmaterialthathas acoercivity>104A.m1. 14 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.3Theeffect ofthecorematerialon thefluxdensity.The magneticmoment opposesthefieldin diamagneticmaterials. Progressivelystronger momentsarepresentin paramagnetic, ferrimagnetic,and ferromagneticmaterials forthesameapplied field. 15 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.4Thecrystal structureofMn0consists ofalternatinglayersof {111}typeplanesof oxygenandmanganese ions.Themagnetic momentsofthe manganeseionsinevery other(111)planeare oppositelyaligned. Consequently,Mn0is antiferromagnetic. 16 Example19.2 Design/MaterialsSelectionforaSolenoid Wewanttoproduceasolenoidcoilthatproducesaninductance ofatleast2000gausswhena10mAcurrentflowsthroughthe conductor.Duetospacelimitations,thecoilshouldbecomposed of10turnsovera1cmlength.Selectacorematerialforthecoil. 17 18 Example19.2SOLUTION ThemagneticfieldHproducedbythecoil. Thepermeabilityofthecorematerialmustbe: Therelativepermeabilityofthecorematerialmustbeatleast: FromTable194,wefindthat479permalloyhasamaximum relativepermeabilityof80,000andmightbeagoodselectionforthe corematerial. 19 Section19.5Domain Structureandthe HysteresisLoop DomainsSmallregionswithinasingleorpolycrystallinematerial inwhichallofthemagnetizationdirectionsarealigned. BlochwallsTheboundariesbetweenmagneticdomains. SaturationmagnetizationWhenallofthedipoleshavebeen alignedbythefield,producingthemaximummagnetization. RemananceThepolarizationormagnetizationthatremainsina materialafterithasbeenremovedfromthefield. HysteresisloopThelooptracedoutbymagnetizationina ferromagneticorferrimagneticmaterialasthemagneticfieldis cycled. 20 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.5(a)Aqualitativesketchofmagneticdomainsina polycrystallinematerial.Thedashedlinesshowdemarcationbetween differentmagneticdomains;thedarkcurvesshowthegrainboundaries. (b)Themagneticmomentsinadjoiningatomschangedirection continuouslyacrosstheboundarybetweendomains. 21 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.6Whenamagneticfieldisfirstappliedtoamagneticmaterial, magnetizationinitiallyincreasesslowly,thenmorerapidlyasthedomains begintogrow.Later,magnetizationslows,asdomainsmusteventuallyrotate toreachsaturation.Noticethepermeabilityvaluesdependuponthe magnitudeofH. 22 Figure19.7(a)TheferromagnetichysteresisMHloopshowingtheeffectofthe magneticfieldoninductanceormagnetization.Thedipolealignmentleadsto saturationmagnetization(point3),aremanance(point4),andacoercivefield (point5).(b)ThecorrespondingBHloop.NoticetheendoftheBHloop,theB valuedoesnotsaturatesinceB=0H+0M.(Source:AdaptedfromPermanent Magnetism,byR.SkomskiandJ.M.D.Coey,p.3,Fig.11.EditedbyJ.M.D.Coey andD.R.Tilley.Copyright1999InstituteofPhysicsPublishing.Adaptedby permission.) 23 Section19.6The CurieTemperature CurietemperatureThetemperatureabove(Tc)which ferromagneticorferrimagneticmaterialsbecomeparamagnetic. 24 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.8Theeffectoftemperatureon(a)thehysteresisloopand(b) theremanance.FerromagneticbehaviordisappearsabovetheCurie temperature. 25 26 Example19.3 Design/MaterialsSelectionfora HighTemperatureMagnet Selectapermanentmagnetforanapplicationinanaerospacevehicle thatmustreenterEarthsatmosphere.Duringreentry,themagnetmay beexposedtomagneticfieldsashighas600oerstedandmaybriefly reachtemperaturesashighas500oC.Wewantthematerialtohavethe highestpowerpossibleandtomaintainitsmagnetizationafterreentry. 27 28 Example19.3SOLUTION Itisfirstnecessarytoselectpotentialmaterialshavingsufficient coercivefieldHcandCurietemperaturethatreentrywillnot demagnetizethem. TheCo5SmhasfourtimesthepoweroftheAlnico5and,basedon performance,mightbeourbestchoice. 29 Section19.7 ApplicationsofMagneticMaterials SoftMagneticMaterialsFerromagneticmaterialsareoftenused toenhancethemagneticfluxdensity(B)producedwhenan electriccurrentispassedthroughthematerial.Applications includecoresforelectromagnets,electricmotors,transformers, generators,andotherelectricalequipment. DataStorageMaterialsMagneticmaterialsareusedfordata storage. PermanentMagnetsMagneticmaterialsareusedtomake strongpermanentmagnets PowerThestrengthofapermanentmagnetasexpressedby themaximumproductoftheinductanceandmagneticfield. 30 Figure19.9(a)Comparisonofthehysteresisloopsfor threeapplicationsofferromagneticandferrimagnetic materials. 31 Figure19.9(b)Saturationmagnetizationandcoercivityvaluesfordifferent magneticmaterials.(Source:AdaptedfromMagneticMaterials:An Overview,BasicConcepts,MagneticMeasurements,Magnetostrictive Materials,byG.Y.Chinetal.InD.Bloor,M.Flemings,andS.Mahajan (Eds.),EncyclopediaofAdvancedMaterials,Vol.1,1994,p.1423,Fig.1. Copyright1994PergamonPress.Reprintedbypermissionoftheeditor.) 32 33 34 35 Figure19.10(a)Thelargestrectangledrawninthesecondorfourthquadrantof theBHcurvegivesthemaximumBHproduct.(BH)maxisrelatedtothepower,or energy,requiredtodemagnetizethepermanentmagnet.(b)Developmentof permanentmagnetmaterials,maximumenergyproductisshownontheyaxis. (Source:AdaptedfromPermanentMagnetism,byR.SkomskiandJ.M.D.Coey,p. 23,Table12.EditedbyJ.M.D.CoeyandD.R.Tilley.Copyright 1999Instituteof PhysicsPublishing.Adaptedbypermission.) 36 Example19.4Energy ProductforPermanentMagnets 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Determinethepower,orBHproduct,forthemagneticmaterialwhose propertiesareshowninFigure19.11. Figure19.11Thefourthquadrant oftheBHcurveforapermanent magneticmaterial(forExample 19.4) 37 Example19.4SOLUTION Severalrectangleshavebeendrawninthefourthquadrantofthe BHcurve.TheBHproductineachis: Thus,thepowerisabout4.2 106gauss.oersted. 38 Example19.5 Design/SelectionofMagneticMaterials Selectanappropriatemagneticmaterialforthefollowingapplications:a highelectricalefficiencymotor,amagneticdevicetokeepcupboard doorsclosed,amagnetusedinanammeterorvoltmeter,andmagnetic resonanceimaging. Example19.5SOLUTION Highelectricalefficiencymotor:Tominimizehysteresislosses, wemightuseanorientedsiliconiron,takingadvantageofits anisotropicbehavioranditssmallhysteresisloop. Magnetforcupboarddoors:Themagneticlatchesusedto fastencupboarddoorsmustbepermanentmagnets;however,lowcost isamoreimportantdesignfeaturethanhighpower.Aninexpensive ferriticsteeloralowcostferritewouldberecommended. 39 Example19.5SOLUTION(Continued) Magnetsforanammeterorvoltmeter:Forthese applications,Alnicoalloysareparticularlyeffective.Wefindthat thesealloysareamongtheleastsensitivetochangesin temperature,assuringaccuratecurrentorvoltagereadingsovera rangeoftemperatures. Magneticresonanceimaging:Oneoftheapplicationsfor MRIisinmedicaldiagnostics.Inthiscase,wewantaverypowerful magnet.ANd2Fe12Bmagneticmaterial,whichhasanexceptionally highBHproduct,mightberecommendedforthisapplication.We canalsomakeuseofverystrongelectromagnetsmadeusing superconductors. 40 Example19.6Lifting PowerofaMagnet CalculatetheforceinkNforonesquaremeterareaofapermanent magnetwhosesaturationmagnetizationis1.61tesla. Example19.6SOLUTION Wehavebeengiventhevalueof0M=1.61tesla.Wecanrewritethe equationthatprovidestheforceduetoapermanentmagnetasfollows. 41 Section19.8Metallic andCeramicMagneticMaterials MagnetocrystallineanisotropyInsinglecrystals,thecoercivity dependsuponcrystallographicdirectioncreatingeasyandhard axesofmagnetization. 42 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.12Informationcanbestoredorretrievedfromamagneticdiskby useofanelectromagnetichead.Acurrentintheheadmagnetizesdomainsin thediskduringstorage;thedomainsinthediskinduceacurrentinthehead duringretrieval. 43 Figure19.13Theinitialmagnetizationcurveforironishighly anisotropic;magnetizationiseasiestwhenthedirections100 arealignedwiththefieldandhardestalong[111].(Source:From PrinciplesofElectricalEngineeringMaterialsandDevices,byS.O. Kasap,p.623,Fig.824.Copyright1997Irwin.Reprintedby permissionofTheMcGrawHillCompanies.) 44 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.14DemagnetizingcurvesforCo5SmandCo5Ce,representinga portionofthehysteresisloop. 45 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.15(a)Thestructureofmagnetite,Fe304.(b)Thesubcellof magnetite.Themagneticmomentsofionsintheoctahedralsiteslineup withthemagneticfield,butthemagneticmomentsofionsintetrahedral sitesopposethefield.Anetmagneticmomentisproducedbythisionic arrangement. 46 Example19.7 MagnetizationinMagnetite(Fe3O4) Calculatethetotalmagneticmomentpercubiccentimeterinmagnetite. Calculatethevalueofthesaturationfluxdensity(Bsat)forthismaterial. Figure19.15(b)The subcellofmagnetite. 47 Example19.7SOLUTION Intheunitcelloverall,thereareeightsubcells,sothetotalmagnetic momentis32Bohrmagnetonspercell.Thesizeoftheunitcell, withalatticeparameterof8.37 108cm,is: Themagneticmomentpercubiccentimeteris: ThisexpressionrepresentsthemagnetizationMatsaturation(Msat). ThevalueofBsat0Msatwillbe=(4 107)(5.1 105)= 0.64Tesla. 48 49 Example19.8 Design/MaterialsSelectionfor aCeramicMagnet Designacubicferritemagnetthathasatotalmagneticmomentper cubicmeterof5.5 105A/m. 50 Example19.8SOLUTION AssumingthattheadditionofMnionsdoesnotappreciablyaffect thesizeoftheunitcell,wefindfromExample197that: LetxbethefractionofMn2+ionsthathavereplacedtheFe2+ions, whichhavenowbeenreducedto1x.Then,thetotalmagnetic momentis: Thereforeweneedtoreplace34.6at%oftheFe2+ionswithMn2+ ionstoobtainthedesiredmagnetization. 51 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.16 Hysteresiscurvefora hardmagneticmaterial (forProblem19.19). 52 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.17Hysteresiscurveforahardmagneticmaterial(for Problem19.30). 53 2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Figure19.14(RepeatedforProblem19.36.)Demagnetizingcurvesfor Co5SmandCo5Ce,representingaportionofthehysteresisloop. 54
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LSU - ME - 2733
TheScienceandEngineeringofMaterials,4thedDonaldR.AskelandPradeepP.PhulChapter20PhotonicMaterials1ObjectivesofChapter20Topresentasummaryoffundamentalprinciplesthathaveguidedapplicationsofopticalmaterials.Toexploretwoavenuesbywhichwecanusetheoptica
LSU - ME - 2733
TheScienceandEngineeringofMaterials,4thedDonaldR.AskelandPradeepP.PhulChapter21ThermalPropertiesofMaterials1ObjectivesofChapter21Todiscussheatcapacity,thermalexpansionproperties,andthethermalconductivityofmaterials.2ChapterOutline21.1HeatCapac
LSU - ME - 2733
TheScienceandEngineeringofMaterials,4thedDonaldR.AskelandPradeepP.PhulChapter22CorrosionandWear11ObjectivesofChapter22Tointroducetheprinciplesandmechanismsbywhichcorrosionandwearoccurunderdifferentconditions.Thisincludestheaqueouscorrosionofmeta
LSU - EE - 4580
Constant: K 20log[abs(k)] k>0 0 degrees k<0 -180 degrees Pole at Origin (Integrator) -20 dB/decade passing through 0 dB at w=1 -90 degrees Zero at Origin (Differentiator) +20 dB/decade passing through 0 dB at w=1 +90 degrees Real Pole
LSU - EE - 4580
MATLAB Tutorial IRepresentation of transfer function:b0 sm + b1sm,1 + bm:i T s = na0 s + a1 sn,1 + anMATLAB command isnum = b0 b1 bm ;den = a0 a1 an ;s , z1s , z2 s , zmii T s = K:s , p1s , p2 s , pnMATLAB command isK = ;Z = z1 z2 zm ;P =
LSU - EE - 4580
Classical Feedback ControlIn classical control, feedback is the key concept. In fact theconcept of feedback has been applied to many other branches ofscience.Question: Why feedback?Plant uncertainty: parameter variations, nonlinearities etc.Environm
LSU - EE - 4580
Procedure for Skecth of root locus page 260 of text:Example 1: Gs = s + 1=s2= z1 = ,1; p1 = p2 = 0 and n , m = 1.Step 1: Mark the poles and zeros on the s-plane.Step 2: Draw locus on the real axis: left of s = ,1.Step 3: Draw asymptotes: since n , m
LSU - EE - 4580
Zero-degree Loci for Negative KWe considersm + b1sm,1 + + bm :KGs = ,jK j sn + a sn,1 + + a1nBy convention, we have1 + KGs = 0; K = 0 ! ,1:The angle of Gs is 0o + 360o lChange: 180o + 360o is replaced by 0o + 360o l.On real axis: the number of p
LSU - EE - 4580
x6. Frequency-Response Design Methods1. Frequency Response:We recall inverse Laplace transform:23K5K4L,1 6 s , j! + s + j! 7 = 2jK j cos!ot + 6 K :ooConsider sinusoidal input signalut = Au cos!otapplied to a plant Gs. Then the output in s-dom
LSU - EE - 4580
GL90P.M.180
LSU - EE - 4580
Example Prob. 6.50 on page 456:K:s1 + s=51 + s=20Design a compensator such thatKGs =ess 0:01 for unit ramp input.P.M.= 45o 3o.ess 1=250 for sinusoidal input with !0:2.Noise be attenuated by a factor of 100 for ! 100.Analysis:essto 1=250 for
LSU - EE - 4580
F-planes-planeD DAABCBC
LSU - EE - 4580
Modeling of Inverted PendulumWe consider line movement for simplication. This example hasapplications to the launch of rocket or missiles. We will demonstrate the use of Lagrange mechanics in modeling.vyvmvzLu(t)My Step 1: Total kinetic energy
LSU - EE - 4580
Iterative Design AlgorithmWe consider an iterative design method: (a) Design zy , z , and Ky > 0, such that the three zeros of(s) = 0 are in the right locations.z5.67zy5.67 (b) Design Kgy and pg such that the roots of (s) = (s + pg )denp(s) + 3.2
LSU - EE - 4580
Course Title:Control System Design.Course Number:EE4580 | Fall 2002.Instructor:Dr. Guoxiang Gu, ECE 329, Tel : 578-5534, Email: ggu@ee.lsu.edu.O ce Hour:7:30 10:00 AM M. W. at ECE 329.Estimated ABET:Engineering Science: 1 credit; Engineering Desi
LSU - EE - 4580
LSU - EE - 4580
LSU - EE - 4580
LSU - EE - 4580
LSU - EE - 4580
Homework 1 of EE 4002 Spring 2004Solution:Solution:
LSU - EE - 4580
Solution to Homework 2 of EE4002, Spring 2004
LSU - EE - 4580
Solution to Homework 6 of EE4002 Spring 2004
LSU - EE - 4580
Solution to Homework 7EE4002, Spring 2004
LSU - EE - 4580
Solution to Homework 8 of EE4002 Spring 2004
LSU - EE - 4580
Project 2: Digital Control of the Ball-Beam SystemThis project is based on Project 1 using mainly Simulink toolbox to validate yourdesign. The project consists of the following: Program the continuous-time nonlinear ball-beam model using the Simulink t
LSU - EE - 4580
Solution to Homework 9 of EE4002 Spring 2004
LSU - EE - 4580
Solution to Midterm Test1. For the lead compensator, we havedB20.2220200degree45.2220200For the lag compensator, we havedB20.2220200220200degree.204512. (a) For the gain plot, we choose L = 0.1, and H = 1000. Hence we have at
LSU - EE - 4580
H0=zpk([],[0,-1,-5,-10],1);H1=zpk([-2],[0,-1,-5,-10],1);H2=zpk([-2,-6],[0,-1,-5,-10],1);H3=zpk([-2,-4],[0,-1,-5,-10],1);H4=tf([1],[1 3 10]);H5=tf([1],[1 3 10 0]);H6=tf([1 2 8],[1 2 10 0]);H7=tf([1 2 12],[1 2 10 0]);H8=tf([1 0 1],[1 0 4 0]);H9=tf(
LSU - EE - 4580
LSU - EE - 4580
LSU - EE - 4580
Matlab Section of Question 3.41For the lower boundary I chose the number zero to indicate that the number was stillnegative, and then I choose a number smaller than zero to prove that the roots arepositive. This helped me show that the poles are in the
LSU - EE - 4580
LSU - EE - 4580
MATLAB REQUIREMENT FOR HW#2PART 1.The code below is what I used to get the transfer function, zero/pole form, and a graph of the step function.> num1=[500 2500];> den1= conv([1 12 100],[1 25]);> gtf1=tf(num1,den1)Transfer function:500 s + 2500-s^3
LSU - EE - 4580
MATLAB COMMANDS TO GET PLOTS ON THE NEXT PAGE FOR 4.4 a,b,c,d> numA=[1];> numB=[1 2];> numC=[1 8 12];> numD=[1 6 8];> denALL=[1 16 65 50 0];> sysA=tf(numA,denALL)Transfer function:1-s^4 + 16 s^3 + 65 s^2 + 50 s> sysB=tf(numB,denALL)Transfer fun
LSU - EE - 4580
Solution to HW2 EE4580 Fall04
LSU - EE - 4580
Solution to Homework 3 of EE 4580 Fall 04
LSU - EE - 4580
HW #3 MATLAB SECTION OF 5.65.6-AMATLAB INSTRUCTIONS> numA=[1];> denA=[1 8 0 0];> sysA=tf(numA,denA)Transfer function:1-s^3 + 8 s^2> rlocus(sysA)RESULTING GRAPHRoot Locus1510Imag Ax is50-5-10-15-20-15-10-5Real Axis055.6-CMATLAB
LSU - EE - 4580
HW #3 MATLAB SECTION OF 5.65.7-BMATLAB INSTRUCTIONS> numB=[1 2];> denB=[1 16 85 250 0 0];> sysB=tf(numB,denB)Transfer function:s+2-s^5 + 16 s^4 + 85 s^3 + 250 s^2> rlocus(sysB)RESULTING GRAPHRoot Locus201510Imag Ax is50-5-10-15-20-20
LSU - EE - 4580
HW #3 MATLAB SECTION OF 5.85.8-BMATLAB INSTRUCTIONS> numB=[1 2];> denB=[1 10 -1 -10];> sysB=tf(numB,denB)Transfer function:s+2-s^3 + 10 s^2 - s - 10> rlocus(sysB)RESULTING GRAPHRoot Locus1510Imag Ax is50-5-10-15-10-8-6-4Real Axis-
LSU - EE - 4580
Correction to 5-11 of HW4 EE4580 Fall041) The closed-loop transfer function is10 K1Y ( s)Gc ( s ) ==(1)R( s ) s ( s + )( s + 10) + s ( s + ) + 2 K1 s + 10 K1You can use direct computation, Masons rule or block diagram simplification methodto get
LSU - EE - 4580
MATLAB PART OF 5.29PART Dsys29d2 = zpk([-1 -0.5],[0 -1 -10 -55.6 -0.04],10)rlocus(sys29d2);grid on;Root Locus1500.620.480.360.240.120.76140120100100800.886050400.97Imaginary Ax is200200.9740-50600.8880-1001001200.760.6
LSU - EE - 4580
Solution to HW5 of EE4580 Fall04
LSU - EE - 4580
6.4a6.4b6.4c6.4d
LSU - EE - 4580
6.5a6.5b6.5c6.5d6.5e-GAVE ME A WARNING SIGN6.5f- GAVE ME A WARNING SIGN
LSU - EE - 4580
6.7a6.7b6.7c6.7d6.7e
LSU - EE - 4580
Solution to Homework 6 of EE4580 Fall04
LSU - EE - 4580
Solution to Homework 7 of EE4580 Fall04
LSU - EE - 4580
Solution to Homework 8 of EE4580 Fall04
LSU - EE - 4580
ZOOMED IN PLOTS FROM LAST SEMESTERS HOMEWORK 5.5A,C,E
LSU - EE - 4580
LSU - EE - 4580
Solution7Ch6_5,7,30,316.5 Solution:(a) L ( s ) = #s102110+310s +150P ha se ( d eg)0-50-100-150-20010-110010F r eq uency ((b) L(s) =s110s102+310 s1102r a d/sec)+1-50P hase (deg)-100-150-200-250-30010-1100
LSU - EE - 4580
Solution8 Ch6_43,45,(47),50,576.43 Solution:(a) The frequency response is obtained by letting s = j ,D (j ) = KT j + 1T j + 1The phase is given by, = tan1 (T ) tan1 (T )(b) Using the trigonometric relationship,tan(A B ) =tan(A) tan(B )1 + tan(A)
LSU - EE - 4580
Solution9 Ch6_18,19,37,396.18 Solution:(a)1s2Note that the portion of the Nyquist diagram on the right side belowthat corresponds to the bode plot is from B to C. The large loopfrom F to A to B arises from the detour around the 2 poles at theorigi
LSU - EE - 4580
LSU - EE - 4580
EEE 480HW # 6 SOLUTIONSProblem 5.21The root-locus asymptotes for pure-gain compensation are at 2:5. Since the required closed-loop polelocations are 1 j , we need to introduce a lag compensator. Observe that asymptotes at 1 are obtained forpoles at 0
LSU - EE - 4580
LSU - EE - 4580
Solution to Homework 6 of EE4002 Spring 2004
LSU - EE - 4580
Problem 6.25Using the MATLAB command[GM PM]=margin(sys) we findGM = 1.57 and PM = 100.55From the Bode plot it can be observedthat the gain margin is so small that aslight increase in gain may result inunstable closed loop system. The phase onthe o
LSU - EE - 4580
EEE 480HW # 8 SOLUTIONSNOTE: Ballpark computations relating bandwidth (wBW ) and crossover frequency (wGC ).In classical compensator designs, it is often useful to convert closed-loop bandwidth specications to crossover specpications. The closed-loop
LSU - EE - 4580
Problem 6Problem 6.25Using theMATLABcommand[GM PM]=margin(sys)we findGM = 1.57 andPM = 100.55From the Bodeplot it can beobserved thatthe gainmargin is sosmall that aslight increasein gain mayresult inunstableclosed loopsystem. Thepha