Shaft Sensor-less FOC Control of an Induction Motor Using Neural Estimators
|
|
- Arlene Hart
- 6 years ago
- Views:
Transcription
1 Act Poltechnc Hngc Vol 9, No, Shft Senso-less FOC Contol of n Indcton Moto Usng Nel Estmtos Pete Gosý, Josl Tmo, Josl Žloá Deptment of Electcl Engneeng nd Mechtoncs, Techncl Unest of ošce, Letná 9, ošce, Slo Repblc petegos@tes, josltmo@tes, joslzlo@tes Abstct: The ppe dels th shft senso-less feld oented contol stcte fo n ndcton moto bsed on nel neto estmtos The fst pt pesents the theoetcl noledge The second pt pesents the smlton nd eslts of desgnng nel estmtos fo obseng the mgnetc fl nd the moto ngl speed fo ndcton moto feld oented contol n MATLAB-Smln Contolles fo smlton of shft senso-less feld oented contol he been desgned b stte spce method An cheed smlton eslt of the nel ngl speed estmto hs been efed b sstem of AC conete ndcton moto b Rel-Tme sstem eods: ndcton moto; nel neto; senso-less contol; ecto contol Intodcton Motos pl mpotnt oles n ndstl podcton nd n mn othe pplctons In the el ds, DC motos hd the dntge of pecse speed contol hen tlzed fo the ppose of ccte dng Hoee, DC motos he the dsdntge of bsh eoson, mntennce eqements, enonmentl effects, comple stctes nd poe lmts On the othe hnd, ndcton motos e obst, smll n sze, lo n cost, nd lmost mntennce-fee Hsse [9] nd Blsche [] deeloped feld oented contol theo to smplf the stcte of IM speed contol sed to de the DC moto In ecent es, the feld oented contol theo hs become moe fesble de to pogess n the deelopment of electoncs technqes nd hgh-speed mcopocessos Nonlne contol poblems cn often be soled f fll stte nfomton s lble; n the IM cse, the oto sttes e mmesble nd often t s too costl to monto the ngl speed of the oto In most pplctons, speed sensos e necess n the speed contol loop On the othe hnd, thee e pplctons hee loe pefomnce s eqed, cost edcton nd hgh elblt e necess, o hostle enonment does not
2 P Gosý et l Shft Senso-less FOC Contol of Indcton Moto Usng Nel Estmtos llo fo sng speed sensos In these felds, speed senso-less IM contol cn be sefll ppled Mn dffeent soltons fo the estmton of sttes bles o model pmetes he been poposed ecentl, fo emple, estmtos tlzng moto constcton popetes, estmtos bsed on the de dnmc model o estmtos bsed on tfcl ntellgence [7, 8,, 5, 6] Senso-less contolles he been poposed hch depend on dpte contol nd obsee theo, on optml obsee desgn b pplng lmn flte theo [, ], on sldng mode contol [, ], nd on sng tfcl ntellgence methods [,, 5, 6, ] At pesent, eqements on the dnmc pecson e not too stct nd tl o soft sensos e ltentel sccessfll tlzed Estmtos bsed on tfcl ntellgence e dded nto the follong gops: sstems bsed on the fzz logc, sstems bsed on nel netos, sstems bsed on hbd sstems, sstems bsed on eolton lgothms (genetc lgothms) Smlton Desgn of Nel Estmto fo Feld Oented Contol of Indcton Moto The nel modellng cn pefom estmton of the ndcton moto ngl speed o of othe non-mesble bles on the nel netos bse Nods, thee e feld oented contolled des bsed on dffeent soltons nd pefomnces hch e commonl sed n ndst Wth feld-oented technqes, the decoplng of fl nd toqe contol commnds of the IM s gnteed, nd the ndcton moto cn be contolled lnel, le septel ected DC moto The DC moto le pefomnce cn be obtned b peseng fed nd othogonl oentton beteen the feld nd mte felds n the ndcton moto b oentton of the stto cent th espect to the oto fl n ode to ttn ndependentl contolled fl nd toqe Usng the feld oented contol pncple, the stto cent component d s lgned n the decton of the oto fl ecto nd the stto cent component q s lgned n the decton pependcl to t The oto fl oentton n the sqel-cge oto IM cnnot be dectl mesed, bt t cn be obtned fom temnl bles Afte sng tnsfomton of coodntes d, q to the ottng sstem -, the electc toqe s popotonl to the component nd the elton beteen the oto fl nd component s gen b the fst ode lne tnsfe fncton th T L /R tme constnt
3 Act Poltechnc Hngc Vol 9, No, Fom ths fct nd fo the consdeed fl contol, the stto cent nd oltge components ee chosen s npt sgnls fo the econstcton of the ndcton moto speed The deeloped estmtos ee tned ccodng to selected tnng pttens fom the dect feld oented contol of the ndcton moto Bloc dgm of the contol scheme s pesented n Fge Fge Bsc feld oented contol scheme Indcton Moto FOC Smlton Desgn Feld oented contol smlton desgn hd been mde fo ndcton moto th the follong pmetes: P n,75 W; U n V/8V; I n,8 A/, A; n n 8 pm; p; s,8; J5, - gm In the desgn of stte contol b method of the poles detemne fo to npt bles nd one otpt bsed on the follong eqtons: d d σ ω m ( σ ) T σt m T T dt R dt () d σ ω ( σ ) T ω σt m m m T T dt R d m T m T J p dt m dω dt ω ω p m L h m σ m z () () () (5)
4 P Gosý et l Shft Senso-less FOC Contol of Indcton Moto Usng Nel Estmtos Defne the stte bles: m ; ; ω ; ; m z z; / T ; / T Then, tten cn be the stte eqton fo ndcton moto: c z e B z e b b f f (6) The constnts nd fnctons sed n the stte eqton (6): T ; T σ ; σ h L J p ; σ σ ; L h L σ σ ; L L L h σ ; L b T σ ; J p e f f Nonlne fncton f (), f () n the contol scheme shon n Fg compenstng fo ntodcton of contol, so s to smplf the stte eqton: f f b Cent Sb-Cct (R, R ) dt ;
5 Act Poltechnc Hngc Vol 9, No, 5 The chctestc polnoml of sstem P : det det A I P Fo cent contolle select the dmpng d85, eglton tme t 5s nd detemne the desed chctestc polnoml S P : 75 6 s s P S B compng the chctestc polnoml nd the desed chctestc polnoml e obtn contolle constnts, nd, hee nd Speo Cct of Mgnetzng Cent (R m ) d d ; The chctestc polnoml of sstem P : det d d d A I P Select the dmpng d85, eglton tme t s nd detemne the desed chctestc polnoml S P : s s s s P S B compng of the chctestc polnoml nd the desed chctestc polnoml e obtn contolle constnts,,, d Speo Cct of Speed (R ω ) d
6 P Gosý et l Shft Senso-less FOC Contol of Indcton Moto Usng Nel Estmtos ; d The chctestc polnoml of sstem P ( ) : P det I A d d Select the dmpng d85, eglton tme t s nd detemne the desed chctestc polnoml P ( S ): P S s s 79s 6 s 9797 B compng of the chctestc polnoml nd the desed chctestc polnoml obtned e contolle constnts,,, d Constnts clclted fo ll ccts of contolle e sed b the feld oented contol scheme shon n Fge Fge Smlton feld oented contol scheme Mgnetsng Cent Nel Estmto If fo ecto contol the -th component of the stto cent ecto s consdeed s bss of cent-cetng component, then the mgnetsng cent m estmto ll pocess cent-cetng component of the stto cent As mentoned boe, the mgnetsng cent m nel estmto bses ts estmton of the cent-cetng component of stto cent Dependence beteen cents m nd s lne, nd hence the estmto cn be mde p of feed-fod nel neto thot n hdden le Fo the cttng fncton, the peln lne fncton cn be sed The npt dt ecto conssts of les of the stto cent n step () nd step (-), espectel, nd lso the pecedng le of mgnetsng cent m n step (-) A bsc dgm of sch nel estmto s shon n Fge 6
7 Act Poltechnc Hngc Vol 9, No, Fge Bsc dgm of mgnetsng cent m nel estmto Hee, O stnds fo otpt les ecto, I s the npt dt ecto, nd pesents eghts of nddl connectons of neons O f I bs (7) Sbstttng the npt mt to eqton (7), e ll obtn the eqton fo the mgnetsng cent nel estmto n the follong fom: ( ) m peln bs m (8) hee cent m () s the otpt ble nd the npt bles e (), (- ) nd m (-) Speed Nel Estmto If fo the bss of toqe-cetng component e estblsh the -th component of the ecto, then the speed estmto ll estmte ths toqe cetng component fom the stto oltge nd cent As s led mentoned boe, the ngl speed ω nel estmto bses ts estmton on the toqe component of stto oltge nd cent The elton beteen the npt nd otpt qnttes s not epesented b smple lne dependenc, nd ths s the eson h fo the estmton cscde nel neto th one hdden le conssted of eght neons ll be sed As n cttng fncton fo the hdden le sed, thee s the tnsg nonlne fncton nd fo the otpt le sed s peln lne fncton The npt dt ecto s epesented b les of stto oltge nd stto cent n steps () nd (-), s ell s b le of mgnetsng cent m n steps () nd (-) Bsc dgm of sch nel estmto s shon n Fge 7
8 P Gosý et l Shft Senso-less FOC Contol of Indcton Moto Usng Nel Estmtos 8 Fge Bsc dgm of ω moto ngl speed nel estmto In the fge, O s the otpt les ecto, I pesents ecto of npt bles nd, j, e eghts of nddl connectons of neons bs I A f O bs I f A j (9) Post sbstttng the npt mt to eqton (9) the nel speed estmto cn be descbed b the follong eqton: bs bs tnsg peln m m j m m ω () hee the otpt qntt s ω() ngl speed le nd hee the npt e les (), (-), (), (-), m () nd m (-) Smlton Reslts In the follong, e sho the smlton eslts of senso-less ecto contol of n ndcton moto hen pplng nel estmtos of the speed nd mgnetsng cent, espectel The pncpl dgm of the ecto contol th connected nel estmtos of the mgnetsng cent nd speed s shon n Fge 5
9 Act Poltechnc Hngc Vol 9, No, Fge 5 Bsc dgm of ecto contol th nel estmtos Smlton, desgn nd tnng of nel estmtos ee pefomed fo the ndcton moto th pmetes: P n,75 W; U n V/8V; I n,8 A/, A; n n 8 pm; p; s,8; J5, - gm Fge 6 Compson of the estmted ess ctl mgnetsng cent Fges 6 nd 7 sho compson of el nd obseed les of the mgnetzng cent nd the ngl speed A dshed lne shos thee s the eqed ngl speed le dng sttng, eesng nd lodng tnsents In tme of s the moto s loded b the ted lod toqe 9
10 P Gosý et l Shft Senso-less FOC Contol of Indcton Moto Usng Nel Estmtos Fge 7 Compson of the estmted ess ctl speed of the IM The efoms shon n Fges 6 nd 7 e ld fo the cse of no feedbc to contol fom the nel obsees bt led dectl fom the moto mthemtcl model Fge 8 Tnsents of desed ess el ngl speed nd the moto lod toqe Shon n Fge 8 s smlted esponse of the ndcton moto ngl speed (n sold lne) t condtons dentcl th the peos one, shon n Fge 7 In ths cse, nd the sme s n n follong ones, the feedbc to contol s ntodced fom nel obsees of the mgnetsng cent nd ngl speed
11 Act Poltechnc Hngc Vol 9, No, Epementl Vefcton Fo efcton of smlton eslts, n epementl Rel-Tme sstem bsed on RT-LAB sstem s sed The pncpl scheme of the hole sstem s sho n Fge 9 The epementl sstem conssts of the SIMOVERT MASTERDRIVES Vecto Contol nd n ndcton moto th the sme pmetes s those of the moto sed fo smlton Used s the lod thee s dnmo th essto nd the bse of ths epementl sstem conssts of Rel-tme sstem th NI PCI-65E Fge 9 Pncpl scheme of Rel-Tme sstem Nel Estmton fo Epementl Vefcton Regdng dffeent s of ecto contol n SIMOVERT MASTERDRIVES, Vecto Contol (sstem n ot coodntes d-q), sed fo desgn of speed nel estmto, s the npt stto oltge n step () (), n the step (-) - (-) nd le of cent components d,q n step () d (), q () nd n step (-) - d (-), q (-) Fo off-lne tnng sng the Leenbeg-Mqdt lgothm 6 smples n ggegte ee sed The otpt ecto fo tnng s epesented b le of the oto speed ȏ() n step () Fo the speed nel estmto e sed cscde nel neto th one hdden le hng s npt neons nd s hdden neons Fo the hdden le cttng fncton sed s the tnsg nonlne fncton nd fo the otpt le e sed peln lne fncton Usng them e obtned n eqton fo nel estmto of speed n the follong fom: oˆ ( ) ( ) ( ) d ( ) ( ) q ( ) ( ) ( ) ( ) d bs bs ( ) q peln j tnsg d d q q ()
12 P Gosý et l Shft Senso-less FOC Contol of Indcton Moto Usng Nel Estmtos Epementl Reslts Pesented n the follong e the smlton eslts of senso-less ecto contol of n ndcton moto hen sng nel estmtos of speed The pncpl dgm of ecto contol effected th the se of nel estmto of speed s shon n Fge Fge Pncpl scheme of Rel-Tme sstem th nel estmto ) speed b) oltge c) cent d, q Fge Tme coses of desed ess ctl oto speed thot lod nd elent oltge nd cent
13 Act Poltechnc Hngc Vol 9, No, In Fges nd e shon coses of desed (dsh lne) nd ctl oto speeds of ndcton moto n the ecto contol sng the scheme ccodng to Fge At tme second, the eqed le of oto speed chnged fom % to 5% of nomnl speed, t tme seconds, fom 5% to 5%; t tme seconds, fom 5% to % of nomnl oto speed nd t tme seconds, the ndcton moto eesed Fo efcton e sed n epementl el tme sstem The eslts obtned, llstted b especte efoms, ldte the possblt of tlsng tfcl nel netos n senso-less ecto contol of the ndcton moto The de fetes bette dptblt nd obstness n compson th de thot estmto ) speed b) oltge c) cent d, q Fge Tme coses of desed ess ctl oto speed th lod nd elent oltge nd cent Conclsons The ppe s concened th desgnng ndcton moto nel estmtos Bsed on esl mesble qnttes, sch s components of stto cent nd oltge, e desgned estmtos of the moto speed nd mgnetsng cent, tlzng feedfod nd cscde nel netos Both these netos ee tned off-lne
14 P Gosý et l Shft Senso-less FOC Contol of Indcton Moto Usng Nel Estmtos sng the Leenbeg-Mqdt lgothm, hch s modfcton of the tdtonl bc-popgton tnng lgothm The eslts ed t, llstted b especte efoms, ldte the possblt of tlsng tfcl nel netos n the senso-less ecto contollng of n ndcton moto, hle lso tng dntge of the dntgeos popetes, sch s dptblt nd obstness At the end of ths ppe pesented e esech eslts Fo ppled efcton sed s epementl Rel-Tme sstem Acnoledgement The thos sh to thn fo the sppot to the R&D opetonl pogm Cente of ecellence of poe electoncs sstems nd mtels fo the components II No OPVV-9//-SORO, ITMS 66 fnded b Eopen egonl deelopment fnd (ERDF) Refeences [] Vs P, Atfcl-Intellgence-bsed Electcl Mchnes nd Des, Ofod Unest Pess, Ofod, 999 [] Vtte J, Dodds S J, Mš P, Lehocý P, An Obsee Desgn fo Foced Dnmcs Contol of AC Des, Tnscom 7, Žln, Sloenso, pp 7-, 7 [] Vtte J, Bs P, Štljte M, Pách M, Chtteng Fee Sldng Mode Contol L fo Poston Contol of the De Emplong Indcton Moto, Poe Engneeng Confeence 8, AUPEC '8, Astlsn Unestes, pp -6, -7 Dec, 8 [] ch M, Bndštette P, dch M, Senso-less Indcton Moto De th Nel Neto IEEE, Ann Poe Elec Speclsts Confm pp -5, [5] Jonoč J, Žlmn M, Applcton of the Vtl Sensos Bsed on the Atfcl Nel Netos, EDPE, Intentonl confeence, Slo,, pp 86-9 [6] Benslem Y, Abbod W, Sbt L, Abdelm M N, A Senso-less Nel Neto Speed Contol of Indcton Moto De, Int Jonl of Sgnl Sstem Contol nd Engneeng Applcton (): pp 5-58, 8 [7] Jdlosá A, bo N, Snosý J, Pedcte Contol Desgn Bsed on Nel Model of Non-lne Sstem, Act Poltechnc Hngc, Vol 5, No, pp 9-8, 8 [8] Jmn V, Redd S R, Modelng nd Speed Contol of Indcton Moto Des Usng Nel Neto, Annls of De de Jos Unest of Glt, III, Vol, No, pp -9,
15 Act Poltechnc Hngc Vol 9, No, [9] Hsse, Z Dnm Dehzhlgeegelte Antebe mt stomchtegespesten Asnchon-schlsslüfe Mschnen, Techn Hochsch: Dmstdt, Dssetton, 969, pp 7-78 [] Blsche F, The Pncple of Feld Oentton s Appled to the Ne Tnseto Closed Loop Contol Sstem fo Rottng-Feld Mchnes, Semens Re 9 (5): 97, pp 7- [] Mezne S, Tofot R, Benll H, Nonlne Contol of Indcton Mchnes Usng n Etended lmn Flte, Act Poltechnc Hngc, Vol 5, No, pp -58, 8 [] Žloá J, Tmo J, Beo J, Speed Senso-less Contol of n Indcton Moto De Usng Etended lmn Flte, In: Act Technc ČSAV 5, No, Pge, 5, pp [] Tmo J, Žloá J, Bl D, Atfcl Nel Netos Applcton n Electcl Des, (n Slo), Clpso so, ošce,, p 9, ISBN [] Tmo J, Žloá J, Gosý P, Shft Senso-less Vecto Contol of n Indcton Moto, In: Act Technc CSAV, Vol 5, No (7), pp 8-9, ISSN -7 [5] Tmo J, Žloá J, Gosý P, Modelng nd Contol of Electcl Des Usng Nel Netos, (n Slo), C-Pess, ošce, 9, p, ISBN [6] Žloá J, Tmo J, Gosý P, Nonlne Sstem Contol Usng Nel Netos, Act Poltechnc Hngc, Vol, No, pp 85-9, 6 5
The Shape of the Pair Distribution Function.
The Shpe of the P Dstbuton Functon. Vlentn Levshov nd.f. Thope Deptment of Phscs & stonom nd Cente fo Fundmentl tels Resech chgn Stte Unvest Sgnfcnt pogess n hgh-esoluton dffcton epements on powde smples
Torque generation with Electrical Machines. Industrial Electrical Engineering and Automation Lund University, Sweden
Toqe geneton wth Electcl Mchne Indtl Electcl Engneeng nd Atoton nd Unvet, Sweden Toqe genetng phenoen Indtl Electcl Engneeng nd Atoton Condcto n gnetc feld Ion hpe n gnetc feld 3 Electottc 4 Pezotcton
Uniform Circular Motion
Unfom Ccul Moton Unfom ccul Moton An object mong t constnt sped n ccle The ntude of the eloct emns constnt The decton of the eloct chnges contnuousl!!!! Snce cceleton s te of chnge of eloct:!! Δ Δt The
3. A Review of Some Existing AW (BT, CT) Algorithms
3. A Revew of Some Exstng AW (BT, CT) Algothms In ths secton, some typcal ant-wndp algothms wll be descbed. As the soltons fo bmpless and condtoned tansfe ae smla to those fo ant-wndp, the pesented algothms
Chapter I Vector Analysis
. Chpte I Vecto nlss . Vecto lgeb j It s well-nown tht n vecto cn be wtten s Vectos obe the followng lgebc ules: scl s ) ( j v v cos ) ( e Commuttv ) ( ssoctve C C ) ( ) ( v j ) ( ) ( ) ( ) ( (v) he lw
Scalars and Vectors Scalar
Scalas and ectos Scala A phscal quantt that s completel chaacteed b a eal numbe (o b ts numecal value) s called a scala. In othe wods a scala possesses onl a magntude. Mass denst volume tempeatue tme eneg
Neural Network Introduction. Hung-yi Lee
Neu Neto Intoducton Hung- ee Reve: Supevsed enng Mode Hpothess Functon Set f, f : : (e) Tnng: Pc the est Functon f * Best Functon f * Testng: f Tnng Dt : functon nput : functon output, ˆ,, ˆ, Neu Neto
Lecture 5 Single factor design and analysis
Lectue 5 Sngle fcto desgn nd nlss Completel ndomzed desgn (CRD Completel ndomzed desgn In the desgn of expements, completel ndomzed desgns e fo studng the effects of one pm fcto wthout the need to tke
VEKTORANALYS FLUX INTEGRAL LINE INTEGRAL. and. Kursvecka 2. Kapitel 4 5. Sidor 29 50
VEKTORANAYS Ksecka INE INTEGRA and UX INTEGRA Kaptel 4 5 Sdo 9 5 A wnd TARGET PROBEM We want to psh a mne cat along a path fom A to B. Bt the wnd s blowng. How mch enegy s needed? (.e. how mch s the wok?
An Analytical Time Domain Solution for the Forced Vibration Analysis of Thick-Walled Cylinders
1741 An Anlytcl Tme Domn Soluton fo the Foced Vbton Anlyss of Thck-Wlled Cylndes Abstct n ths ppe, we popose tme domn nlytcl soluton fo the foced vbton nlyss of thck-wlled hollow cylndes n pesence of pol
Unit_III Complex Numbers: Some Basic Results: 1. If z = x +iy is a complex number, then the complex number z = x iy is
Unt_III Comple Nmbes: In the sstem o eal nmbes R we can sole all qadatc eqatons o the om a b c, a, and the dscmnant b 4ac. When the dscmnant b 4ac
A New Fuzzy Control Model for Kidney Patients
Appled Mathematcs, 0, 3, 097-0 http://dx.do.og/0.436/am.0.396 Pblshed Onlne Septembe 0 (http://www.scrp.og/onal/am) A ew Fzzy Contol Model fo Kdney Patents Mna Lagzan, Mohammad Shazan, Al Vahdan Kamyad,
Absolutely no collaboration allowed in any form
Toy Fnl Exm poste toy, ue n one week Tke home, open notes exm Absolutely no collboton llowe n ny fom Instuctos wll not nswe ny uestons elte to exm solutons o soluton ppoches Questons fo clfcton shoul be
Using DP for hierarchical discretization of continuous attributes. Amit Goyal (31 st March 2008)
Usng DP fo heachcal dscetzaton of contnos attbtes Amt Goyal 31 st Mach 2008 Refeence Chng-Cheng Shen and Yen-Lang Chen. A dynamc-pogammng algothm fo heachcal dscetzaton of contnos attbtes. In Eopean Jonal
Spinor Geometry Based Robots Spatial Rotations Terminal Control
Mthemtcl Models nd Methods n Moden Scence Spno Geomet Bsed Robots Sptl Rottons Temnl Contol A Mlnkov T. Ntshvl Deptment o Robotcs Insttute o Mechncs o Mchnes Mndel st. Tbls 86 Geog lende.mlnkov@gm.com
Rigid Body Dynamics. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018
Rg Bo Dnmcs CSE169: Compute Anmton nstucto: Steve Roteneg UCSD, Wnte 2018 Coss Pouct k j Popetes of the Coss Pouct Coss Pouct c c c 0 0 0 c Coss Pouct c c c c c c 0 0 0 0 0 0 Coss Pouct 0 0 0 ˆ ˆ 0 0 0
CHAPTER 4 EVALUATION OF FORCE-CONSTANT MATRIX
CHAPTER 4 EVALUATION OF FORCE-CONSTANT MATRIX 4.- AIM OF THE WORK As antcpated n the ntodcton the am of the pesent ok s to obtan the nmecal vale of the foce-constant matx fo tantalm. In a fst step expesson
COMPLEMENTARY ENERGY METHOD FOR CURVED COMPOSITE BEAMS
ultscence - XXX. mcocd Intenatonal ultdscplnay Scentfc Confeence Unvesty of skolc Hungay - pl 06 ISBN 978-963-358-3- COPLEENTRY ENERGY ETHOD FOR CURVED COPOSITE BES Ákos József Lengyel István Ecsed ssstant
Suggested t-z and q-z functions for load-movement responsef
40 Rtio (Exponent = 0.5 80 % Fnction (.5 times 0 Hypeolic ( = 0 % SHAFT SHEAR (% of lt 00 80 60 ULT Zhng = 0.0083 / = 50 % Exponentil (e = 0.45 80 % (stin-softening 40 0 0 0 5 0 5 0 5 RELATIVE MOVEMENT
Lecture 9-3/8/10-14 Spatial Description and Transformation
Letue 9-8- tl Deton nd nfomton Homewo No. Due 9. Fme ngement onl. Do not lulte...8..7.8 Otonl et edt hot oof tht = - Homewo No. egned due 9 tud eton.-.. olve oblem:.....7.8. ee lde 6 7. e Mtlb on. f oble.
A Heuristic Algorithm for the Scheduling Problem of Parallel Machines with Mold Constraints
A Heustc Algothm fo the Schedulng Poblem of Pllel Mchnes wth Mold Constnts TZUNG-PEI HONG 1, PEI-CHEN SUN 2, nd SHIN-DAI LI 2 1 Deptment of Compute Scence nd Infomton Engneeng Ntonl Unvesty of Kohsung
Advanced image processing Lab
L. Yoslvsy Advnced mge pocessng Lb A Ttol Eopen Sgnl Pocessng Confeence EUSIPCO, Tmpee, Fnlnd Sept. 4, Leond Yoslvsy, Pofesso, Dept. of Intedscplny Stdes, Fclty of Engneeng, Tel Avv Unvesty, Tel Avv 69978
Physics 11b Lecture #2. Electric Field Electric Flux Gauss s Law
Physcs 11b Lectue # Electc Feld Electc Flux Gauss s Law What We Dd Last Tme Electc chage = How object esponds to electc foce Comes n postve and negatve flavos Conseved Electc foce Coulomb s Law F Same
Rigid Bodies: Equivalent Systems of Forces
Engneeng Statcs, ENGR 2301 Chapte 3 Rgd Bodes: Equvalent Sstems of oces Intoducton Teatment of a bod as a sngle patcle s not alwas possble. In geneal, the se of the bod and the specfc ponts of applcaton
The Schur-Cohn Algorithm
Modelng, Estmton nd Otml Flterng n Sgnl Processng Mohmed Njm Coyrght 8, ISTE Ltd. Aendx F The Schur-Cohn Algorthm In ths endx, our m s to resent the Schur-Cohn lgorthm [] whch s often used s crteron for
6.6 The Marquardt Algorithm
6.6 The Mqudt Algothm lmttons of the gdent nd Tylo expnson methods ecstng the Tylo expnson n tems of ch-sque devtves ecstng the gdent sech nto n tetve mtx fomlsm Mqudt's lgothm utomtclly combnes the gdent
Newton-Raphson Based Computation of i d in the Field Weakening Region of IPM Motor Incorporating the Stator Resistance to Improve the Performance
Pge 1 o 6 Newton-Rphson Bse Computton o n the Fel Wekenng Regon o IPM Moto Incopotng the Stto Resstnce to Impove the Peomnce Shh Pevn 1, Z. S 1, n M. Ns Un, Seno Membe IEEE 1. Insttute o Mthemtcl Scences
Chapter 21: Electric Charge and Electric Field
Chpte : lectc Chge nd lectc Feld lectc Chge Known b ncent Geeks s el s 600 BC Sttc electct: electc chge v fcton (see lso fg.) (Attempted) pth bll demo nd/o scotch tpe demo: knds of popetes objects wth
Section 35 SHM and Circular Motion
Section 35 SHM nd Cicul Motion Phsics 204A Clss Notes Wht do objects do? nd Wh do the do it? Objects sometimes oscillte in simple hmonic motion. In the lst section we looed t mss ibting t the end of sping.
(8) Gain Stage and Simple Output Stage
EEEB23 Electoncs Analyss & Desgn (8) Gan Stage and Smple Output Stage Leanng Outcome Able to: Analyze an example of a gan stage and output stage of a multstage amplfe. efeence: Neamen, Chapte 11 8.0) ntoducton
Physics Exam II Chapters 25-29
Physcs 114 1 Exam II Chaptes 5-9 Answe 8 of the followng 9 questons o poblems. Each one s weghted equally. Clealy mak on you blue book whch numbe you do not want gaded. If you ae not sue whch one you do
Mechanical design of IM. Torque Control of. Induction Machines... Slip ring rotor. Mathematical model. r r. Stator same as PMSM Rotor:
Toqe ontol of Incton Machne... a copae to PMSM Intal Electcal Engneeng an Atoaton Mechancal egn of IM Stato ae a PMSM oto: at aln Won coppe /Slp ng Intal Electcal Engneeng an Atoaton n Unvety, Sween Nan
Engineering Tensors. Friday November 16, h30 -Muddy Charles. A BEH430 review session by Thomas Gervais.
ngneerng Tensors References: BH4 reew sesson b Thoms Gers tgers@mt.ed Long, RR, Mechncs of Solds nd lds, Prentce-Hll, 96, pp - Deen, WD, nlss of trnsport phenomen, Oford, 998, p. 55-56 Goodbod, M, Crtesn
Discrete Model Parametrization
Poceedings of Intentionl cientific Confeence of FME ession 4: Automtion Contol nd Applied Infomtics Ppe 9 Discete Model Pmetition NOKIEVIČ, Pet Doc,Ing,Cc Deptment of Contol ystems nd Instumenttion, Fculty
A simple embedded atom potential for palladiumhydride
Mshll Unvesty Mshll Dgtl Schol Theses Dssettons nd Cpstones 07 A smple embedded tom potentl fo plldmhydde Yng Zhng 44034800@qq.com ollow ths nd ddtonl woks t: http://mds.mshll.ed/etd Pt of the Mechncl
Linear Algebra Math 221
Linea Algeba Math Open Book Eam Open Notes Sept Calculatos Pemitted Sho all ok (ecept #). ( pts) Gien the sstem of equations a) ( pts) Epess this sstem as an augmented mati. b) ( pts) Bing this mati to
Averaging Level Control of Multiple Tanks: A Passivity Based Approach
Avergng Level Control of Mltple Tnks: A Pssvty Bse Approch Dnel Sbrbro Deprtment of Electrcl Engneerng, Unvers e Concepcón, Concepcón,, Chle. In collborton wth Romeo Orteg Lbortore es Sgn et Systèmes mes,
UNIVERSITÀ DI PISA. Math thbackground
UNIVERSITÀ DI ISA Electomagnetc Radatons and Bologcal l Inteactons Lauea Magstale n Bomedcal Engneeng Fst semeste (6 cedts), academc ea 2011/12 of. aolo Nepa p.nepa@et.unp.t Math thbackgound Edted b D.
Complex Numbers Practice 0708 & SP 1. The complex number z is defined by
IB Math Hgh Leel: Complex Nmbers Practce 0708 & SP Complex Nmbers Practce 0708 & SP. The complex nmber z s defned by π π π π z = sn sn. 6 6 Ale - Desert Academy (a) Express z n the form re, where r and
Rotary motion
ectue 8 RTARY TN F THE RGD BDY Notes: ectue 8 - Rgd bod Rgd bod: j const numbe of degees of feedom 6 3 tanslatonal + 3 ota motons m j m j Constants educe numbe of degees of feedom non-fee object: 6-p
Definition of Tracking
Trckng Defnton of Trckng Trckng: Generte some conclusons bout the moton of the scene, objects, or the cmer, gven sequence of mges. Knowng ths moton, predct where thngs re gong to project n the net mge,
KINEMATICS OF THE 3-RRR PLANAR PARALLEL ROBOT
U.P.. Sc. ll. Sees D Vol. 7 No. 8 ISSN 454-58 KINEMIS OF HE -RRR PLNR PRLLEL ROO Ştefn SIU Lce stbleşte elţ mtcele ecente pent cnemtc obotl pln plel cnosct -RRR c cţone evoltă. ele te pcoe dentce le obotl
Solutions to selected problems from homework 1.
Jan Hagemejer 1 Soltons to selected problems from homeork 1. Qeston 1 Let be a tlty fncton hch generates demand fncton xp, ) and ndrect tlty fncton vp, ). Let F : R R be a strctly ncreasng fncton. If the
Review of Vector Algebra and Vector Calculus Operations
Revew of Vecto Algeba and Vecto Calculus Opeatons Tpes of vaables n Flud Mechancs Repesentaton of vectos Dffeent coodnate sstems Base vecto elatons Scala and vecto poducts Stess Newton s law of vscost
Capítulo. Three Dimensions
Capítulo Knematcs of Rgd Bodes n Thee Dmensons Mecánca Contents ntoducton Rgd Bod Angula Momentum n Thee Dmensons Pncple of mpulse and Momentum Knetc Eneg Sample Poblem 8. Sample Poblem 8. Moton of a Rgd
PHYS 2421 Fields and Waves
PHYS 242 Felds nd Wves Instucto: Joge A. López Offce: PSCI 29 A, Phone: 747-7528 Textook: Unvesty Physcs e, Young nd Feedmn 23. Electc potentl enegy 23.2 Electc potentl 23.3 Clcultng electc potentl 23.4
ME 3600 Control Systems Frequency Domain Analysis
ME 3600 Contol Systems Fequency Domain Analysis The fequency esponse of a system is defined as the steady-state esponse of the system to a sinusoidal (hamonic) input. Fo linea systems, the esulting steady-state
? plate in A G in
Proble (0 ponts): The plstc block shon s bonded to rgd support nd to vertcl plte to hch 0 kp lod P s ppled. Knong tht for the plstc used G = 50 ks, deterne the deflecton of the plte. Gven: G 50 ks, P 0
9.4 The response of equilibrium to temperature (continued)
9.4 The esponse of equilibium to tempetue (continued) In the lst lectue, we studied how the chemicl equilibium esponds to the vition of pessue nd tempetue. At the end, we deived the vn t off eqution: d
Available online Journal of Scientific and Engineering Research, 2017, 4(2): Research Article
Avlble onlne www.jse.com Jonl of Scenfc nd Engneeng Resech, 7, 4():5- Resech Acle SSN: 394-63 CODEN(USA): JSERBR Exc Solons of Qselsc Poblems of Lne Theoy of Vscoelscy nd Nonlne Theoy Vscoelscy fo echnclly
An Analytical Approach to Turbulent Flow Through Smooth Pipes
An Analytcal Appoach to Tblent Flow Thogh Smooth Ppes AMIN MOOSAIE and GHOLAMALI ATEFI Depatment of Mechancal Engneeng Ian nesty of Scence and Technology P.O. Box 6844, Namak, Tehan IAN amnmoosae@mal.st.ac.
( ) α is determined to be a solution of the one-dimensional minimization problem: = 2. min = 2
Homewo (Patal Solton) Posted on Mach, 999 MEAM 5 Deental Eqaton Methods n Mechancs. Sole the ollowng mat eqaton A b by () Steepest Descent Method and/o Pecondtoned SD Method Snce the coecent mat A s symmetc,
Rotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1
Rotatonal Knematcs Rgd Object about a Fxed Axs Westen HS AP Physcs 1 Leanng Objectes What we know Unfom Ccula Moton q s Centpetal Acceleaton : Centpetal Foce: Non-unfom a F c c m F F F t m ma t What we
V. Principles of Irreversible Thermodynamics. s = S - S 0 (7.3) s = = - g i, k. "Flux": = da i. "Force": = -Â g a ik k = X i. Â J i X i (7.
Themodynamcs and Knetcs of Solds 71 V. Pncples of Ievesble Themodynamcs 5. Onsage s Teatment s = S - S 0 = s( a 1, a 2,...) a n = A g - A n (7.6) Equlbum themodynamcs detemnes the paametes of an equlbum
School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 3 Due on Sep. 14, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
A. Thicknesses and Densities
10 Lab0 The Eath s Shells A. Thcknesses and Denstes Any theoy of the nteo of the Eath must be consstent wth the fact that ts aggegate densty s 5.5 g/cm (ecall we calculated ths densty last tme). In othe
Hyperbolic Heat Equation as Mathematical Model for Steel Quenching of L-shape and T-shape Samples, Direct and Inverse Problems
SEAS RANSACIONS o HEA MASS RANSER Bos M Be As Bs Hpeo He Eo s Me Moe o See Qe o L-spe -spe Spes De Iese Poes ABIA BOBINSKA o Pss Mes es o L Ze See 8 L R LAIA e@o MARARIA BIKE ANDRIS BIKIS Ise o Mes Cope
Solution of fuzzy multi-objective nonlinear programming problem using interval arithmetic based alpha-cut
Intentionl Jounl of Sttistics nd Applied Mthemtics 016; 1(3): 1-5 ISSN: 456-145 Mths 016; 1(3): 1-5 016 Stts & Mths www.mthsounl.com Received: 05-07-016 Accepted: 06-08-016 C Lognthn Dept of Mthemtics
Data Structures Week #10. Graphs & Graph Algorithms
Data Stctes Week #0 Gaphs & Gaph Algoithms Otline Motiation fo Gaphs Definitions Repesentation of Gaphs Topological Sot Beadth-Fist Seach (BFS) Depth-Fist Seach (DFS) Single-Soce Shotest Path Poblem (SSSP)
The analysis of dynamic response of rock mass around tunnel under dynamic unloading. Xian Li1, a
4th Intentonl Confeence on Sustnble Enegy nd Envonmentl Engneeng (ICSEEE 5) The nlyss of dynmc esponse of ock mss ound tunnel unde dynmc unlodng Xn L, Fculty of Cvl Engneeng nd Mechncs, Kunmng Unvesty
VECTORS VECTORS VECTORS VECTORS. 2. Vector Representation. 1. Definition. 3. Types of Vectors. 5. Vector Operations I. 4. Equal and Opposite Vectors
1. Defnton A vetor s n entt tht m represent phsl quntt tht hs mgntude nd dreton s opposed to slr tht ls dreton.. Vetor Representton A vetor n e represented grphll n rrow. The length of the rrow s the mgntude
Set of square-integrable function 2 L : function space F
Set of squae-ntegable functon L : functon space F Motvaton: In ou pevous dscussons we have seen that fo fee patcles wave equatons (Helmholt o Schödnge) can be expessed n tems of egenvalue equatons. H E,
Solution of Tutorial 5 Drive dynamics & control
ELEC463 Unversty of New South Wles School of Electrcl Engneerng & elecommunctons ELEC463 Electrc Drve Systems Queston Motor Soluton of utorl 5 Drve dynmcs & control 500 rev/mn = 5.3 rd/s 750 rted 4.3 Nm
UNIT10 PLANE OF REGRESSION
UIT0 PLAE OF REGRESSIO Plane of Regesson Stuctue 0. Intoducton Ojectves 0. Yule s otaton 0. Plane of Regesson fo thee Vaales 0.4 Popetes of Resduals 0.5 Vaance of the Resduals 0.6 Summay 0.7 Solutons /
Angular Momentum in Spherical Symmetry
Angu Moentu n Sphec Set Angu Moentu n Sphec Set 6 Quntu Mechncs Pof. Y. F. Chen Angu Moentu n Sphec Set The concept of ngu oentu ps cuc oe n the theedenson 3D Schödnge we equton. The ethod of septon w
4. Eccentric axial loading, cross-section core
. Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we
Nonquadratic Lyapunov Functions for Nonlinear Takagi-Sugeno Discrete Time Uncertain Systems Analysis and Control
(JACSA) ntentonl Jounl of Advnced Compute Scence nd Applctons, Vol. 7, No., 6 Nonqudtc Lypunov unctons fo Nonlne g-sugeno Dscete me Uncetn Systems Anlyss nd Contol Al Bouyhy Unvesty of uns El Mn, Ntonl
Design of a Controller for Load Frequency Control in a Power System
4 NAIONAL POWER YEM CONFERENCE, NPC Desgn of Contolle fo Lod Fequency Contol n Powe ystem V..Ru A. ke Abstct: hs e descbes the desgn of contolle fo lod fequency contol n owe system. hs contolle s n ddtonl
Chapter #2 EEE State Space Analysis and Controller Design
Chpte EEE8- Chpte # EEE8- Stte Spce Al d Cotolle Deg Itodcto to tte pce Obevblt/Cotollblt Modle ede: D D Go - d.go@cl.c.k /4 Chpte EEE8-. Itodcto Ae tht we hve th ode te: f, ', '',.... Ve dffclt to td
Variable time amplitude amplification and quantum algorithms for linear algebra. Andris Ambainis University of Latvia
Vrble tme mpltude mplfcton nd quntum lgorthms for lner lgebr Andrs Ambns Unversty of Ltv Tlk outlne. ew verson of mpltude mplfcton;. Quntum lgorthm for testng f A s sngulr; 3. Quntum lgorthm for solvng
DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Kinematics of Rigid Bodies in Three Dimensions. Seventh Edition CHAPTER
Edton CAPTER 8 VECTOR MECANCS FOR ENGNEERS: DYNAMCS Fednand P. Bee E. Russell Johnston, J. Lectue Notes: J. Walt Ole Teas Tech Unvest Knematcs of Rgd Bodes n Thee Dmensons 003 The McGaw-ll Companes, nc.
Collision Avoidance of Moving Obstacles for Underwater Robots
Collson Avodnce of Movng Obstcles fo Undewte Robots Kyoung-Youb Kwon Technologcl Deptment, Dewon Mechtoncs Co., #2- hnchon-dong Chngwon, Kyungnm, 64-37, Koe nd Jeongmok Cho, *Joongseon Joh * Coespondng
3D Analytical Calculation of Forces between Linear Halbach-Type Permanent Magnet Arrays
D Anltcl Clculton of s etween Lne Hlch-Tpe Pemnent Mgnet As Hchm Allg, Jen-Pul onnet, Mohmed E. H. Lteche To cte ths veson: Hchm Allg, Jen-Pul onnet, Mohmed E. H. Lteche. D Anltcl Clculton of s etween
Chapter Linear Regression
Chpte 6.3 Le Regesso Afte edg ths chpte, ou should be ble to. defe egesso,. use sevel mmzg of esdul cte to choose the ght cteo, 3. deve the costts of le egesso model bsed o lest sques method cteo,. use
SOME REMARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOMIAL ASYMPTOTE
D I D A C T I C S O F A T H E A T I C S No (4) 3 SOE REARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOIAL ASYPTOTE Tdeusz Jszk Abstct I the techg o clculus, we cosde hozotl d slt symptote I ths ppe the
ESCI 342 Atmospheric Dynamics I Lesson 1 Vectors and Vector Calculus
ESI 34 tmospherc Dnmcs I Lesson 1 Vectors nd Vector lculus Reference: Schum s Outlne Seres: Mthemtcl Hndbook of Formuls nd Tbles Suggested Redng: Mrtn Secton 1 OORDINTE SYSTEMS n orthonorml coordnte sstem
Semi-empirical Evaluation of the Plasma Internal Inductance in Tokamaks
Jounl of Nucle nd Ptcle Physcs 14 4(3): 94-99 DO: 1.593/j.jn.1443. Sem-emcl Evluton of the Plsm ntenl nductnce n Tokmks A. Pknezhd 1* A. Sl Elh M. Ghonnevss 1 Physcs Detment Shest nch-slmc Azd Unvesty
1. A body will remain in a state of rest, or of uniform motion in a straight line unless it
Pncples of Dnamcs: Newton's Laws of moton. : Foce Analss 1. A bod wll eman n a state of est, o of unfom moton n a staght lne unless t s acted b etenal foces to change ts state.. The ate of change of momentum
Per-unitization and Equivalent Circuits
Pe-untzton n Eulent Ccuts 1. Nomlzton of oltge eutons We ese to nomlze the oltge eutons, tht s, we ese to expess them n pe-unt. The ntges of ong so e: The pe-unt system offes computtonl smplcty by elmntng
Multivariate Ratio Estimation With Known Population Proportion Of Two Auxiliary Characters For Finite Population
Multvarate Rato Estmaton Wth Knon Populaton Proporton Of To Auxlar haracters For Fnte Populaton *Raesh Sngh, *Sachn Mal, **A. A. Adeara, ***Florentn Smarandache *Department of Statstcs, Banaras Hndu Unverst,Varanas-5,
f(y) signal norms system gain bounded input bounded output (BIBO) stability For what G(s) and f( ) is the closed-loop system stable?
Lecte 5 Inpt otpt stabilit Cose Otline o How to make a cicle ot of the point + i, and diffeent was to sta awa fom it... Lecte -3 Lecte 4-6 Modelling and basic phenomena (lineaization, phase plane, limit
Effects of polarization on the reflected wave
Lecture Notes. L Ros PPLIED OPTICS Effects of polrzton on the reflected wve Ref: The Feynmn Lectures on Physcs, Vol-I, Secton 33-6 Plne of ncdence Z Plne of nterfce Fg. 1 Y Y r 1 Glss r 1 Glss Fg. Reflecton
CSJM University Class: B.Sc.-II Sub:Physics Paper-II Title: Electromagnetics Unit-1: Electrostatics Lecture: 1 to 4
CSJM Unvesty Class: B.Sc.-II Sub:Physcs Pape-II Ttle: Electomagnetcs Unt-: Electostatcs Lectue: to 4 Electostatcs: It deals the study of behavo of statc o statonay Chages. Electc Chage: It s popety by
Rotating Disk Electrode -a hydrodynamic method
Rotatng Dsk Electode -a hdodnamc method Fe Lu Ma 3, 0 ente fo Electochemcal Engneeng Reseach Depatment of hemcal and Bomolecula Engneeng Rotatng Dsk Electode A otatng dsk electode RDE s a hdodnamc wokng
Algebra Based Physics. Gravitational Force. PSI Honors universal gravitation presentation Update Fall 2016.notebookNovember 10, 2016
Newton's Lw of Univesl Gvittion Gvittionl Foce lick on the topic to go to tht section Gvittionl Field lgeb sed Physics Newton's Lw of Univesl Gvittion Sufce Gvity Gvittionl Field in Spce Keple's Thid Lw
Dynamically Equivalent Systems. Dynamically Equivalent Systems. Dynamically Equivalent Systems. ME 201 Mechanics of Machines
ME 0 Mechnics of Mchines 8//006 Dynmicy Equivent Systems Ex: Connecting od G Dynmicy Equivent Systems. If the mss of the connecting od m G m m B m m m. Moment out cente of gvity shoud e zeo m G m B Theefoe;
Chapter I Matrices, Vectors, & Vector Calculus 1-1, 1-9, 1-10, 1-11, 1-17, 1-18, 1-25, 1-27, 1-36, 1-37, 1-41.
Chapte I Matces, Vectos, & Vecto Calculus -, -9, -0, -, -7, -8, -5, -7, -36, -37, -4. . Concept of a Scala Consde the aa of patcles shown n the fgue. he mass of the patcle at (,) can be epessed as. M (,
A Non-parametric Regression Model for Consumption of Urban Residents and Foreign Exchange Reserve
ode Aed Scece Novembe 009 A No-metc Regesso ode fo Cosmto of Ub Resdets d Foeg Echge Reseve Ng & gdog Sog Detmet of obbty Theoy d themtc Sttstcs sh Uvesty Qhgdo 066004 Ch E-m: mddt3@6.com Abstct The cosmto
( ) ( )()4 x 10-6 C) ( ) = 3.6 N ( ) = "0.9 N. ( )ˆ i ' ( ) 2 ( ) 2. q 1 = 4 µc q 2 = -4 µc q 3 = 4 µc. q 1 q 2 q 3
3 Emple : Three chrges re fed long strght lne s shown n the fgure boe wth 4 µc, -4 µc, nd 3 4 µc. The dstnce between nd s. m nd the dstnce between nd 3 s lso. m. Fnd the net force on ech chrge due to the
Chapter 21: Electric Charge and Electric Field
Chpte 1: Electic Chge nd Electic Field Electic Chge Ancient Gees ~ 600 BC Sttic electicit: electic chge vi fiction (see lso fig 1.1) (Attempted) pith bll demonsttion: inds of popeties objects with sme
Class Summary. be functions and f( D) , we define the composition of f with g, denoted g f by
Clss Summy.5 Eponentil Functions.6 Invese Functions nd Logithms A function f is ule tht ssigns to ech element D ectly one element, clled f( ), in. Fo emple : function not function Given functions f, g:
Sensorless A.C. Drive with Vector Controlled Synchronous Motor
Seole A.C. Dve wth Vecto Cotolle Sychoo Moto Ořej Fše VŠB-echcal Uvety of Otava, Faclty of Electcal Egeeg a Ifomatc, Deatmet of Powe Electoc a Electcal Dve, 17.ltoa 15, 78 33 Otava-Poba, Czech eblc oej.fe@vb.cz
Chapter 28 Sources of Magnetic Field
Chpte 8 Souces of Mgnetic Field - Mgnetic Field of Moving Chge - Mgnetic Field of Cuent Element - Mgnetic Field of Stight Cuent-Cying Conducto - Foce Between Pllel Conductos - Mgnetic Field of Cicul Cuent
Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration
Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse
Lecture 10. Solution of Nonlinear Equations - II
Fied point Poblems Lectue Solution o Nonline Equtions - II Given unction g : R R, vlue such tht gis clled ied point o the unction g, since is unchnged when g is pplied to it. Whees with nonline eqution
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3
DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl
Physics 11b Lecture #11
Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge
Instantaneous velocity field of a round jet
Fee shea flows Instantaneos velocty feld of a ond et 3 Aveage velocty feld of a ond et 4 Vtal ogn nozzle coe Developng egon elf smla egon 5 elf smlaty caled vaables: ~ Q ξ ( ξ, ) y δ ( ) Q Q (, y) ( )
1. Viscosities: μ = ρν. 2. Newton s viscosity law: 3. Infinitesimal surface force df. 4. Moment about the point o, dm
3- Fluid Mecnics Clss Emple 3: Newton s Viscosit Lw nd Se Stess 3- Fluid Mecnics Clss Emple 3: Newton s Viscosit Lw nd Se Stess Motition Gien elocit field o ppoimted elocit field, we wnt to be ble to estimte