SLIDING MODE VECTOR CONTROL OF THREE PHASE INDUCTION MOTOR

Transcription

1 SLIDING MODE VECTOR CONTROL OF THREE PHASE INDUCTION MOTOR A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Mat of Tchnology in Pow Contol and Div By SOBHA CHANDRA BARIK Dpatmnt of Elctical Engining National Intitut of Tchnology Roukla Oia May-2007

2 SLIDING MODE VECTOR CONTROL OF THREE PHASE INDUCTION MOTOR A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Mat of Tchnology in Pow Contol and Div By SOBHA CHANDRA BARIK Und th guidanc of D. K.B. MOHANTY Dpatmnt of Elctical Engining National Intitut of Tchnology Roukla Oia May-2007

3 CERTIFICATE Thi i to ctify that th wok in thi thi ntitld Sliding Mod Vcto Contol of th pha induction moto by Sobha Chanda Baik, ha bn caid out und my upviion in patial fulfillmnt of th quimnt fo th dg of Mat of Tchnology in Pow Contol and Div duing ion in th Dpatmnt of Elctical Engining, National Intitut of Tchnology, Roukla and thi wok ha not bn ubmittd lwh fo a dg. To th bt of my knowldg and blif, thi wok ha not bn ubmittd to any oth univity o intitution fo th awad of any dg o diploma. Plac: Dat: D. K.B.Mohanty At. Pofo Dpt. of Elctical Engining National Intitut of Tchnology, Roukla

4 ACKNOWLEDGEMENTS On th ubmiion of my Thi pot of Snol Sliding mod Vcto contol of th pha induction moto, I would lik to xtnd my gatitud & my inc thank to my upvio D. K. B. Mohanty, At. Pofo, Dpatmnt of Elctical Engining fo hi contant motivation and uppot duing th cou of my wok in th lat on ya. I tuly appciat and valu hi tmd guidanc and ncouagmnt fom th bginning to th nd of thi thi. Hi knowldg and company at th tim of cii would b mmbd liflong. I want to thank all my tach D A. K. Panda, D P.K. Nanda fo poviding a olid backgound fo my tudi and ach thaft. Thy hav bn gat ouc of inpiation to m and I thank thm fom th bottom of my hat. I will b failing in my duty if I do not mntion th laboatoy taff and adminitativ taff of thi dpatmnt fo thi timly hlp. I would lik to thank all who dict and indict uppot hlpd m complting my thi in tim. I would lik to thank all tho who mad my tay in Roukla an unfogttabl and wading xpinc. Lat but not lat I would lik to thank my pant, who taught m th valu of had wok by thi own xampl. I would lik to ha thi momnt of happin with my fath and moth. Thy ndd m nomou uppot duing th whol tnu of my tay in NIT Roukla. Sobha Chanda Baik M.Tch (Pow Contol and Div) i

5 ABSTRACT Sliding Mod Contol (SMC) i a obut contol chm bad on th concpt of changing th tuctu of th contoll in pon to th changing tat of th ytm in od to obtain a did pon. A high pd witching contol action i ud to witch btwn diffnt tuctu of th contoll and th tajctoy of th ytm i focd to mov along a chon witching manifold in th tat pac. Thi thi wok pnt a nw nol vcto contol chm coniting on th on hand of a pd timation algoithm which ovcom th ncity of th pd no and on th oth hand of a novl vaiabl tuctu contol law with an intgal liding ufac that compnat th unctainti that a pnt in th ytm. In thi wok, an indict fild-ointd induction moto div with a liding-mod contoll i pntd. Th dign includ oto pd timation fom maud tato tminal voltag and cunt. Th timatd pd i ud a fdback in an indict vcto contol ytm achiving th pd contol without th u of haft mountd tanduc. Stability analyi bad on Lyapunov thoy i alo pntd, to guaant th clod loop tability. Th high pfomanc of th contol chm und load ditubanc and paamt unctainti i alo dmontatd. ii

6 CONTENTS Acknowldgmnt Abtact Contnt Lgnd Abbviation and aconym Lit of figu i ii iii vi ix x CHAPTER 1 INTRODUCTION 1.1 Intoduction Motivation of wok Litatu ovviw Spd dtmination uing oto lot hamonic Paamt nitivity ffct Stady tat ffct Dynamic ffct Ma pd timation Vaiabl tuctu ytm: Spd timation uing voltag and cunt 14 iii

7 1.9 Sliding mod in v Thi outlin 18 CHAPTER 2 MODELLING AND FIELD ORIENTED CONTROL OF INDUCTION MOTOR 2.1 Intoduction Induction machin contol Scala contol Vcto o fild ointd contol Dc div analogy Pincipl of vcto contol Dynamic d-q modl dq-abc tanfomation Dict o fdback vcto contol Salint fatu of vcto contol Indict (fd fowad) vcto contol 31 CHAPTER 3 SENSORLESS SLIDING MODE VECTOR CONTROL 3.1 Intoduction Snl contol Sliding mod contol Block diagam of liding mod fild ointd contol 39 iv

8 3.5 Vaiabl tuctu obut pd contol Cunt contoll Etimation of moto pd Fild wakning contoll 47 CHAPTER- 4 RESULTS AND DISCUSSION 4.1 Opn loop imulation Simulation ult fo liding mod fild ointd contol Simulation ult und load toqu vaiation 57 CHAPTER 5 FUTURE WORK AND CONCLUSION 5.1 Summay and concluion Futu tudy 61 Appndix Bibliogaphy v

9 LEGENDS B Vicou fiction cofficint d q Synchonouly otating fnc fam (o otating fam) dict and quadatu ax d q f Stationay fnc fam dict and quadatu ax. Fquncy (Hz) I f Machin fild cunt. I Rm tato cunt. i d i d i q i q i q i d i d i q d - axi oto cunt. d - axi tato cunt q - axi oto cunt. q - axi tato cunt. q - axi oto cunt. d - axi oto cunt d - axi tato cunt q - axi tato cunt * i abc Command cunt i abc Actual cunt J K K T Momnt of intia. Contant gain. Toqu contant β Switching gain θ Angl of Synchonouly otating fam θ Roto angl vi

10 θ l Slip angl L m Magntizing inductanc L Roto inductanc L l Roto lakag inductanc L l Stato lakag inductanc P Numb of pol R Roto itanc R Stato itanc S Sliding vaiabl T Dvlopd toqu T L T m T V v d v q v d v q v q v d v q v d Ψ a Ψ f Load toqu Elcto magntic toqu Roto tim contant Lyapunov function d -axi oto voltag q - axi oto voltag d - axi tato voltag q - axi tato voltag q - axi oto voltag d - axi oto voltag q - axi tato voltag d - axi tato voltag Amatu action flux linkag Fild flux linkag vii

11 Ψ m Ψ Ψ d Ψ q Ψ d Ψ q Ψ q Ψ d Ψ q Ψ d ω ω m ω ω l σ Aigap flux linkag Roto flux linkag d - axi oto flux linkag q - axi oto flux linkag d - axi tato flux linkag q - axi tato flux linkag q - axi oto flux linkag d - axi oto flux linkag q - axi tato flux linkag d - axi tato flux linkag Stato fquncy Roto mchanical pd Roto lctical pd Slip fquncy Moto lakag cofficint viii

12 ABBREVIATION AND ACRONYMS AC Altnating Cunt CEMF Count Elctomotiv Foc DC Dict Cunt DSP Digital Signal Pocing EKF Extndd Kalman Filt FOP Fild Ointd Pincipl IGBT Inulatd Gat Bipola Tanito IM Induction Moto MRAC Modl Rfnc Adaptiv Contol MRAS Modl Rfnc Adaptiv Sytm PWM Pul Width Modulation SMC Sliding Mod Contol VR Vcto Rotation ix

13 LIST OF FIGURES Fig. no Nam of th Figu Pag no. Fig.2.1 Spaatly xcitd dc moto 22 Fig.2.2 Vcto contolld induction moto 23 Fig.2.3 Vcto contol implmntation pincipl with machin ( d q ) modl. 24 Fig.2.4 Fig.2.5 Dynamic Dynamic d d q quivalnt cicuit of machin ( q axi) 25 q quivalnt cicuit of machin ( d axi) 26 Fig.2.6 d q and d q phao with coct oto flux ointation 29 Fig.2.7 Plot of unit vcto ignal in coct pha poition 30 Fig.2.8 Phao diagam xplaining indict vcto contol 32 Fig.3.1 Block diagam of liding mod fild ointd contol 39 Fig.3.2 Hyti band cunt contol PWM 43 Fig.3.3 Pincipl of hyti band contol 44 Fig.3.4 Tanf function block diagam of vcto contol div 45 Fig.4.1 Toqu pd chaactitic 49 Fig.4.2 plot of i d vu tim 49 Fig.4.3 plot of i q vu tim 50 Fig.4.4 plot of ψ d vu tim 50 Fig.4.5 plot of ψ q vu tim 51 Fig.4.6 Rfnc and Ral oto pd ignal (ad/c) 52 Fig 4.7 Stato cunt i a 53 Fig 4.8 Moto toqu 54 Fig 4.9 Stato cunt i d 54 x

14 Contd. Fig. no Nam of th Figu Pag no. Fig 4.10 Stato cunt i q 55 Fig 4.11 Roto flux ψ d 56 Fig 4.12 Roto flux ψ q 56 Fig 4.13 Rfnc and al oto pd ignal 57 Fig 4.14 Stato cunt i a 58 Fig 4.15 Stato cunt i d 58 Fig 4.16 Stato cunt i q 59 Fig 4.17 Roto flux ψ d 59 Fig 4.18 Roto flux ψ q 60 xi

15 CHAPTER 1 INTRODUCTION

16 1.1 INTRODUCTION: Pow miconducto dvic contitut th hat of modn pow lctonic appaatu. Thy a ud in pow lctonic convt in th fom of a matix of on off witch, and hlp to convt pow fom ac to dc,dc to dc and ac to ac at th am o diffnt fqunci. Th witching mod pow convion giv high fficincy; th diadvantag i that du to th nonlinaity of th witch, hamonic a gnatd at both th upply and load id. Th witch a not idal, and thy hav conduction and tun on and tun off witching lo. Convt a widly ud in application uch a hating and lighting contol,ac and dc pow uppli, lctochmical poc, dc and ac moto div, tatic va gnation, activ hamonic filting,tc. Although th cot of th pow miconducto dvic in pow lctonic quipmnt may hadly xcd pcnt, th total quipmnt cot and pfomanc may b highly influncd by th chaactitic of th dvic. An ngin digning quipmnt mut undtand th dvic and thi chaactitic thooughly in od to dign fficint, liabl, and cot ffctiv ytm with optimum pfomanc. It i intting to not that th modn tchnology volution in pow lctonic ha gnally followd th volution of pow miconducto dvic. Th advancmnt of micolctonic ha gatly contibutd to th knowldg of pow dvic matial, pocing, fabication, packaging, modling, and imulation. In th pat, dc moto w ud xtnivly in aa wh vaiabl pd opation wa quid, inc thi flux and toqu could b contolld aily by th fild and amatu cunt. In paticula, th paatly xitd dc moto ha bn ud mainly fo application wh th wa a quimnt of fat pon and fou quadant opation with high pfomanc na zo pd. Howv th dc moto hav ctain diadvantag, which a du to th xitnc of th commutato and th buh. That i, thy qui piodic maintnanc; thy can not b ud in xploiv o cooiv nvionmnt and thy hav limitd commutato capability und high pd, high voltag opational condition. Th poblm can b ovcom by th application of altnating cunt moto, which can b impl and uggd tuctu, high maintainability and conomy; thy a alo obut and immun to havy ovloading

17 Thi mall dimnion compad with dc moto allow ac moto to b dignd with ubtantially high output ating fo low wight and low otating ma. Vaiabl pd ac div hav bn ud in th pat to pfom lativly undmanding ol in application which pclud th u of dc moto, ith bcau of th woking nvionmnt o commutato limit. Bcau of th high cot of fficint, fat witching fquncy tatic invt, th low cot of ac moto ha alo bn a dciiv conomic facto in multi moto ytm. Howv a a ult of th pog in th fild of pow lctonic, th continuing tnd i towad chap and mo ffctiv pow convt, and a ingl moto ac div complt favoably on a puly conomic bai with a dc div. Among th vaiou ac div ytm, tho which contain th cag induction moto hav a paticula cot advantag. Th cag moto i impl and uggd and i on of th chapt machin availabl at all pow ating. Owing to thi xcllnt contol capabiliti, th vaiabl pd div incopoating ac moto and mploying modn tatic convt and toqu contol can wll complt with high pfomanc fou quadant dc div. It i xpctd that with th apid dvlopmnt in th fild of micolctonic,toqu contol of vaiou typ of ac machin will bcom a commonly ud tchniqu whn, vn though high dynamic pfomanc i not quid, vo lik high pfomanc play a conday ol to liability and ngy aving. It i poibl to contibut to th ngy aving by th application of intllignt contol of th flux and toqu poducing componnt of th tato cunt. In th ca of dc div, th pow cicuit a lativly unifom and in mot ca contain a lin commutatd thyito convt o a tanitoizd chopp fo low pow application. Howv, fo ac div th i much gat vaity, du to th diffnt typ of convt voltag ouc, cunt ouc, natual commutation, focd commutation, dc link, cycloconvt, which can b combind with vaiou typ of ac machin. Adjutabl pd AC div hav bcom th pfd choic in many indutial application wh contolld pd i quid. At th am tim, th matuing of th - 2 -

18 tchnology and th availability of fat and fficint olid tat pow miconducto witch (IGBT) ha ultd in voltag ouc, PWM contolld invt bcoming a tandad configuation in th pow ang to 500kW. Whil high fquncy PWM contol pnt th mot advancd div concpt, whn inappopiatly applid, it alo gnat id ffct, om which hav bn cognizd only cntly. Thi cou pnt a comphniv covag of application iu of PWM invt contolld ac moto div which includ: damag to moto inulation du to flctd voltag caud by long moto lad; th mchanim of moto baing failu du to xciv common mod dv/dt and lakag cunt to gound. Th contol and timation of ac div in gnal a conidably mo complx than tho of dc div, and thi complxity inca ubtantially if high pfomanc a dmandd. Th main aon fo thi complxity a th nd of vaiabl fquncy hamonically optimum convt pow uppli, th complx dynamic of ac machin, machin paamt vaiation, and th difficulti of pocing fdback ignal in th pnc of hamonic. Whil coniding div application w nd to add following. On, two o fou quadant div Toqu, pd o poition contol in th pimay o out contol loop. Singl o multi moto div. Rang of pd contol. Accuacy and pon tim. Robutn with load toqu and paamt vaiation. Contol with pd no o no l contol. Typ of font nd convt. Efficincy, cot, liability, and maintainability conidation. Lin pow upply, hamonic, and pow facto conidation

19 In gnal an lctic moto can thought of a a contolld ouc of a toqu. Accuat contol of intantanou toqu poducd by a moto i quid in high pfomanc div ytm,.g. tho ud fo poition contol. Th toqu dvlopd in th moto i a ult of th intaction of btwn th cunt in th amatu winding and th magntic fild poducd in th fild ytm of th moto. Th fild hould b maintaind at a ctain optimal lvl, uffintly high to yild a high toqu p unit amp, but not too high to ult in xciv atuation of th magntic cicuit of th moto. With fixd fild, th toqu i popotional to th amatu cunt. Indpndnt contol of th fild and amatu cunt i faibl in paatly xitd dc moto wh th cunt in th tato fild winding dtmin th magntic fild of th moto, whil th cunt in th oto winding can b ud a a dict man of toqu contol. Th phyical dipoition of th buh with pct to th tato fild nu optimal condition fo toqu poduction und all condition. Evn today mot high pfomanc div pfomanc i till bad on dc moto. Vcto contol tchniqu incopoating fat micopoco and DSP hav mad poibl th application of th induction moto and ynchonou moto div fo high pfomanc application wh taditionally only dc div w applid. In th pat uch contol tchniqu would hav not bn poibl bcau of th complx hadwa and oftwa quid to olv th complx contol poblm. A fo dc machin, toqu contol in ac machin i achivd by contolling th moto cunt. Howv, in contat to a dc machin, in an ac machin, both th pha angl and th modulu of th cunt ha to b contolld, o in oth wod, th cunt vcto ha to b contolld. Thi i th aon fo th tminology vcto contol. Futhmo, in dc machin, th ointation of th fild flux and th amatu mmf i fixd by th commutato and th buh, whil in ac machin th fild flux and th patial angl of th amatu mmf qui xtnal contol. In th abnc of thi contol, th patial angl btwn th vaiou fild in ac machin vay with th load and yild unwantd ocillating dynamic pon. With vcto contol of ac machin, th toqu and flux poducing cunt componnt a dcoupld and th tanint pon chaactitic a imila to tho of a paatly - 4 -

20 xcitd dc machin, and th ytm will adapt to any load ditubanc o fnc valu vaiation a fat a a dc machin. Following th aly wok of Blachk and Ha and lagly du to th pioning wok of Pofo Lonhad, vcto contol of ac machin ha bcom a powful and fquntly adoptd tchniqu woldwid. In cant ya, numou impotant contibution hav bn mad in thi fild by contibuto fom many counti, including Canada, Gmany, Italy, Japan, th UK, and th USA. Many indutial compani hav maktd vaiou fom of induction moto and ynchonou moto div uing vcto contol. 1.2 Motivation of wok Th fild of ac div ha xpincd an xploiv gowth in cnt ya and it dmand ach at th pak a additional vic a bing addd to xiting infatuctu. Th contol and timation of induction moto div contitut a vat ubjct, and th tchnology ha futh advancd in cnt ya. Induction moto div with cag typ machin hav bn th wokho in induty fo vaiabl pd application in a wid pow ang that cov fom factional hopow to multimgawatt. Th application includ pump and fan, pap and txtil mill, ubway and locomotiv populion, lctic and hybid vhicl, machin tool and obotic, hom applianc, hat pump and ai condition, olling mill, wind gnation ytm, tc. In addition to poc contol, th ngy aving apct of vaiabl fquncy div i gtting a lot of attntion nowaday. In many book and uvy pap th autho mntiond that th ach in th aa of Vaiabl Stuctu Sytm and Sliding Mod Contol (SMC) wa initiatd in th fom Sovit Union about 40 ya ago and thn th dvlopd contol mthodology ha bn civing much mo attntion of th intnational contol community within th lat two dcad. So fit, th vnt happnd bfo th lat two dcad tating fom th lat fifti a uvyd to dmontat th initial ida and hop of th fit ach. Th topctiv viw will b hlpful to tablih th bidg btwn tho aly tp and th cintific anal accumulatd in th liding mod contol dign mthodology by now

21 1.3 LITERATURE OVERVIEW Th vcto contol tchniqu ha bn widly mployd in val lctic div application. By poviding dcoupling of toqu and flux contol command, th vcto contol can navigat an AC moto div imila to a paatly xcitd DC moto div without acificing th quality of th dynamic pfomanc. Within thi chm, a otational tanduc uch a a tachognato, an ncod o a olv, wa oftn mountd to tablih th pd fdback. In thi mann, th pd infomation can b obtaind. Th clo-loop contol paadigm i alo achd. Howv, thi pd no may low th ytm liability, inca dvic invtmnt and complicat th implmntation. Thfo, a pd no l div ha bn ud in modn indutial application. Th mthod of vcto contol allow high-pfomanc contol of toqu, pd, o poition to b achivd fom an induction machin. Thi mthod can povid at lat th am pfomanc fom an invt-divn induction machin a i obtainabl fom a paatly xcitd dc machin. Vcto contol povid dcoupld contol of th oto flux magnitud and th toqu-poducing cunt, with a fat, na-tp chang in toqu achivabl. Th fat toqu pon i achivd by timating, mauing, o calculating th magnitud and poition of th oto flux in th machin. In th indict mthod of vcto contol pntd h, th calculation of th oto flux poition i dpndnt on th oto itanc valu. A paamt idntification algoithm, uch a th xtndd Kalman filt (EKF), can b ud fo th timation of oto itanc. Th valuation of a vcto-contolld induction machin a ytm can b pfomd in two way. Th fit appoach u a al machin with an appopiat vcto contoll and a cunt-gulatd pul width modulation (PWM) invt. Th vcto contoll i uually implmntd on a micopoco o micocontoll and th algoithm codd in ambl o C if a compil i availabl. A digital ignal poco (DSP) i quid if oto itanc timation i alo to b implmntd. Th cond appoach u a imulation of th ytm. It i thfo ncay to b abl to modl th componnt of th ytm

22 Advantag of th fit appoach a that it natually includ facto uch a th actual noi pnt, th PWM wavfom and nonlina dvic, and no chaactitic that a difficult o impoibl to includ in a imulation. Advantag of uing a imulation nvionmnt a that all quantiti can b adily obvd and paamt altd to invtigat thi ffct and to hlp dbug timation and contol outin. Sno noi can b addd to imulat th pfomanc of al no in addition to tting th ability of paamt idntification tchniqu to cop with noiy maumnt. Poc noi can b addd to includ modl impfction in th machin modl. If tt on mo powful o high atd pd machin a quid, thi can b adily implmntd by changing only th paamt of th machin modl. Th ability to un th imulation lowly alo aid diagnotic. Thi div application allow vcto contol of th AC induction moto unning in a clod-pd loop with th pd / poition no coupld to th haft. Th application v a an xampl of AC induction vcto contol div dign uing a f cal hybid contoll with PE uppot. It alo illutat th u of ddicatd moto contol libai that a includd in PE. Thi application not includ a dciption of f cal hybid contoll fatu, baic AC induction moto thoy, th ytm dign concpt, hadwa implmntation and oftwa dign, including th PC mat oftwa viualization tool. Induction moto div a bcoming th tandad fo vaiabl pd application bcau of th obutn of quil cag induction moto, thi tiff toqu pd chaactitic and th dvlopmnt of high pfomanc contol algoithm and pow lctonic. Th oto pd i ud fo flux timation in high pfomanc div and fo pd fdback whn opn loop contol i ufficint. Howv oto pd maumnt i alway toublom, vy oftn not pactical and omtim impoibl. Fo th aon th i a gowing intt in timating th oto pd by uing only th tato voltag and cunt maumnt. Thi timato could b uful, not only fo pd fdback a pat of pd contol loop in vo div, but alo fo diagnoi of th div whn pd maumnt i availabl. Sinc all th ncay lctical vaiabl a availabl with in th pow lctonic contoll, pd timat - 7 -

23 and maumnt could b compad. Not that timation algoithm qui calculation of th vaiabl of intt, plu om avaging mthod to filt noi. Indict fild-ointd contol (vcto contol) of induction moto ha bn widly ud in high-pfomanc ac div. To oint th injctd tato cunt vcto and to tablih pd loop fdback, knowldg of oto pd i ncay in th application. Tachognato o digital haft-poition ncod a uually ud to dtct th oto pd of moto. Th pd no low th ytm liability and qui pcial attntion to noi. In addition, fo om pcial application uch a vy highpd moto div, th a difficulti in mounting th pd no. In cnt ya, val tachol vcto contol chm hav bn popod. Th taditional appoach to tachol vcto contol u th mthod of fild ointation of oto flux, which ha difficulty in dtmining th intantanou ointation of th flux vcto. Oth appoach a bad on th modl-fnc adaptiv ytm (MRAS), Th MRAS chm qui pu intgato in thi fnc modl, and a affctd by tato itanc thmal vaiation. Th poblm hav limitd th application of tachol vcto contol in high-pfomanc and low-pd div. Conquntly, tachol vcto contol ha an imag of poviding a low cla of ac div. In modn adjutabl-pd altnating cunt (ac) div an accuat and fat pd ning i highly diabl fo th optimum opation of th div. In mot div, an optolctical o lctomchanical pd tanduc i ud. Th convntional tanduc uff fom at lat on of th vaiou poblm uch a nonlinaity, dift, low olution and accuacy, and poo pfomanc at low pd. In addition to th poblm and th initial high cot, th tanduc qui mounting, wiing, calibation, and maintnanc. Th hotcoming poil th paid chaactitic of obutn and mchanical implicity of an ac div. Duing th lat two dcad, attmpt hav bn mad to plac th convntional pd tanduc in adjutabl- pd div, by ning th pd fom th lctical quantiti applid to th moto, i.., voltag and cunt which a alady availabl fo th div amnt and contol. An aly ffot wa mad by Abbondanti and Bnnn who dignd in 1975 an analog lip calculato bad on th pocing of th moto input quantiti, voltag, cunt, and pha [l]. In 1979, it wa followd by th wok - 8 -

24 of Ihida t al. [2], who ud oto lot hamonic voltag in lip fquncy contol. Thy potd ucc fo pd ov 300 /min. Ihida and Iwata ndod thi tchniqu in [3], [4], without any futh pog in impoving th pd ang. Hammli t al. [5] pntd a mthod, in 1987, bad on dtcting th pd in th ang % of nominal pd fom th oto lot hamonic and, in th ang und 30% of nominal pd, by injcting an additional ignal of contant fquncy (fom th invt) into th machin to poduc oto lot modulation and thfo nhanc th pd dtction at low fqunci. A diffnt appoach wa potd by Bck and Naunin in which thy dcibd a no l pd contol of a quil cag induction moto, bad on th calculation of th oto fquncy fom th pha angl btwn th tato voltag and cunt [6]. In 1990, William tal. [7] Ud oto lot hamonic in th tato cunt contuctd fom th dict cunt (dc) link cunt to dtct th pd of an invtfd induction moto uing witchd-capacito filt. In th publihd pap no pactical amnt wa hown to valuat th dtcto with pct to tatic and dynamic pfomanc. Rcntly, no l fild-ointd contol ytm w intoducd. In th div th pd i timatd digitally fom tminal voltag and cunt. Howv, th tchniqu ud ly havily on th timatd moto paamt which chang conidably with fquncy and tmpatu. Modn contol tchniqu fo ac moto div w dvlopd lagly a a ult of th ach fo low-cot altnativ to high-pfomanc fou-quadant dc vo div. In th application, th u of haft mountd tacho gnato and olv a tablihd pactic, and th digital haft-poition ncod ud in th mot ffctiv vcto-contol chm i conidd accptabl. Nvthl, th haft ncod do pnt poblm. Dlicat optical ncod with intnal ignal conditioning lctonic a widly ud. Th low th ytm liability, pcially in hotil nvionmnt, and qui caful cabling aangmnt with pcial attntion to lctical noi. Th a alo ituation wh th poitional fdback i xtmly difficult to obtain. Thi i paticulaly tu fo th ca of lina-moto div uch a fo tanpotation vhicl. Finally, th ncod i a cot facto inc th poviion of pcial moto-haft xtnion and ncod-mounting ufac lad to mo xpniv machin

25 ` Until cntly, th apid dvlopmnt in vcto contol tchnology hav had littl impact on adjutabl-pd ac div. Th a typically impl voltag-ouc invt with vaiabl output fquncy and a ud fo application quiing littl dynamic contol, uch a pump and fan. It ha now bcom cla that th div can bnfit fom th clod-loop cunt-contol tchniqu that hav volvd fo u in vcto contol ytm. Cunt contol i adily applicabl to xiting voltag-ouc invt, wh it duc th incidnc of ov cunt tipping and impov invt utilization. Onc th invt i cunt contolld, additional contol mut b povidd to pcify th magnitud and lip fquncy of th injctd cunt vcto and hnc gulat th flux and toqu of th moto. Moto pd fdback i typically quid fo out-loop pd contol a wll a in th flux and toqu contol algoithm. Thi pnt a poblm in low-pfomanc ytm wh moto pd tanduc a not uually availabl. Thi ha ld to a nwd intt in tachol vcto contol with th objctiv of poviding an intmdiat cla of ac div with nhancd pfomanc and a wid ang of application than adjutabl-pd div but about th am cot xcpt fo th mall additional cot of mo ophiticatd contol algoithm.. Th difficulty in ith ca li in dtmining th intantanou ointation of th lvant vcto. Tamai t al. hav dcibd an appoach in which th fild-ointd fnc fam i idntifid by man of a modl-fnc adaptiv ytm (MRAS). Thi pap pnt an altnativ tachol contol mthod that u an MRAS to dtmin th moto pd and thby tablih vcto contol of th moto a wll a ovall pd contol. Th nw MRAS chm i thought to b l complx and mo ffctiv than th pviou appoach. It ha bn implmntd in a 30-hp div, which ha povd it viability and obut natu. 1.4 SPEED DETERMINATION USING ROTOR SLOT HARMONICS: Fo a givn pol pitch and upply fquncy f 0 th pd of th tavling (otating) fild i contant and i known a th ynchonou pd. It i givn in volution p minut (/min) by th wll-known quation

26 n 60 f p 0 = (1.1) Th diffnc btwn th actual mchanical pd n of th oto and th ynchonou pd n i known a lip. Thi diffnc in pd dpnd upon th load on th moto and i oftn xpd a a faction of th ynchonou pd, a follow n Th lativ pd n givn by = n n (1.2) n = n n (1.3) And, known a lip pd. If at any lip pd, th fquncy of th oto cunt i f thn f will b xpd a f = f0 (1.4) And it i fd to a lip fquncy. Sinc th oto cunt i popotional to th lip fquncy, to tict th cunt dawn by th tato fom xcding it atd valu, th tady-tat lip fquncy in commonly ud induction moto div i alway kpt mall. In thi wok, in od to dfin a dtction ang fo lot hamonic, th maximum lip i aumd qual to 5%, which i uually th ca fo mot div ov 10 kw. Combining th two lat quation to oto otational fquncy f 0 will b givn by Wh, fh f = (1 ) f (1.5) n ( f f ) z = h ± 0 (1.6) i th lot hamonic fquncy. If Z i a numb oth than a multipl of th, only on lot hamonic componnt i dtctd [3], which i nomally th ca fo all quil-cag moto

27 1.5 PARAMETER SENSITIVITY EFFECT: Th indict vcto contoll i dpndnt on th oto itanc R th mutual inductanc L m and th lf inductanc of th oto L. Th inductanc chang with th atuation of th magntic matial whil th oto itanc i affctd by th vaiation in th tmpatu. Th inca in tmpatu inca th oto itanc. In ca of th cunt ouc invt ud in high pfomanc div ytm, if th tato cunt i maintaind contant thi ha th ffct of incaing th magntizing cunt and hnc atuating th machin. Co lo in th moto inca with th atuation of th magntic path and in th nd ncitat a conidabl dating of th machin. Th ffct of thi mimatch btwn th contoll and moto paamt both fo tadytat and dynamic condition a ummaizd STEADY STATE EFFECTS: In a toqu contolld induction moto div, i.., with th out pd loop opn, th oto flux linkag and th lctomagntic toqu a th xtnal command ignal whil th actual lip pd i maintaind qual to th command valu. Thi mimatch btwn th contoll and th moto paamt intoduc dviation in th flux and toqu poducing componnt of th tato cunt and hnc th toqu angl. Th paamt α i th tmpatu facto and dfind a th atio btwn th oto tim contant of th moto and it intumntd valu in th vcto contoll. Th paamt p i th atuation facto and dfind a th atio btwn th actual mutual inductanc and th intumntd valu in th vcto contoll. Fo α < I which ignifi an inca in th oto tmpatu, th lctomagntic toqu i gat than th commandd valu. An inca in α indicat an inca in moto atuation at ambint tmpatu and fo uch opating condition th toqu i l than th commandd valu. Thi ult in incad tato copp lo which ha a dtimntal ffct on th thmal ating of th machin. α can b gat than l du to any of th following facto: Fild wakning. Ambint l than th aumd valu. Wong intumntation of th contoll paamt

28 Und thi cicumtanc, th toqu command ha to b high than fo that quid with α = 1, and hnc th tato cunt and lip pd will b high than th nominal valu. Thi would ult in high copp lo in th machin having a dtimntal ffct on th ating of th moto div DYNAMIC EFFECTS: In th dynamic opation of th vcto contolld induction moto div it can b hown that th flux and toqu hav a tim contant qual to th oto tim contant and a natual fquncy of ocillation with a valu qual to th lip fquncy. In toqu contolld div, th dvlopd oto flux and toqu inca with iing tmpatu but th ocillatoy pon a undiabl and mak th induction moto div a nonidal toqu amplifi. In a pd contolld div, th ocillation in th toqu a not tanmittd to th oto haft du to th following aon. Th high bandwidth of th out pd loop foc th toqu command to match th load toqu in vy hot tim. Th momnt of intia of th induction moto div and th load intoduc filting. 1.6 MRAS SPEED ESTIMATION: Th pd timat ^ ω can b mad to tack th actual pd vy cloly and can b ud both fo pd loop fdback and fo ointing th injctd tato cunt vcto fo toqu and flux contol. An impotant fatu of thi ytm i that, povidd th am valu of T, i ud in th MRAS adjutabl modl, pfct ointation of th injctd cunt vcto i achivd, in thoy, vn if th valu of T2 ud i quit wong. If th MRAS uccfully maintain naly zo o, thn th adjutabl modl accuatly plicat th dynamic lationhip btwn th tato cunt vcto and th oto flux vcto that xit in th actual moto. Examination how that thi i only poibl if T T Thu, if T 2 ^ 2 2actual 2ω l = T2actualω lactual (1.8) ^ ( ω ω ) = T ( ω ω ) (1.7) T 2actual thn ω l ω lactual th poduct T 2 ω l i ud in tting up th injctd cunt vcto, thi i alway don coctly fo th actual lip, vn und

29 dynamic condition. Natually, th o in th valu of T 2 will flct a an o in th pd fdback, which will affct th accuacy of th pd contol lightly. 1.7 VARIABLE STRUCTURE SYSTEM: A high lvl of cintific and publication activity, an unmitting intt in vaiabl tuctu contol nhancd by ffctiv application to automation poblm mot div in thi phyical natu and functional pupo a a cognt agumnt to conid thi cla of nonlina ytm a a popctiv aa fo tudy and application. Th tm vaiabl tuctu ytm (VSS) fit mad it appaanc in th lat Sinc that tim, th fit xpctation of uch ytm hav natually bn valuatd, thi al potntial ha bn vald, nw ach diction hav bn oiginatd du to th appaanc of nw cla of contol poblm, nw mathmatical mthod, cnt advanc in witching cicuity, and (a a conqunc) nw contol pincipl. Th pap i ointd to ba-ton ida of VSS dign mthod and lctd t of application ath than th uvy infomation o a hitoical qunc of th vnt accompanying. Futhmo, it will b hown that th dominant ol in VSS thoy i playd by liding mod, and th co ida of digning VSS contol algoithm conit of nfocing thi typ of motion in om manifold in ytm tat pac. Implmntation of liding mod contol impli high-fquncy witching. It do not cau any difficulti whn lctic div a contolld inc th on-off opation mod i th only admiibl on fo pow convt. Thi aon pdtmind both th high fficincy of liding mod contol fo lctic div and th autho choic of th application lction topic in thi pap. 1.8 SPEED ESTIMATION USING VOLTAGE AND CURRENT: Th main typ of algoithm hav bn popod latd to thi pap, bad on th idal modl of th induction moto. Extndd timato fo joint tat and oto pd timation(coniding th latt a a paamt) (Kim t al,1994; Do t al., 1995) Lina gion modl. (Vlz Ry, 1992) and Modl fnc adaptiv ytm (Schaud, 1992; Png and Fukao, 1994) Algoithm of th fit typ qui a high ampling fquncy o that a impl modl dictization algoithm can b ud, and a computationally intniv, anyway

30 algoithm of typ two a vy impl and ay to implmnt in al tim. In addition thy a wll known and hav bn ud uccfully in many application, calculation of th intgal and divativ of ignal i quid. Howv it will b hown that a tat vaiabl filt can b ud fo thi pupo. Algoithm of typ th ha bn widly applid in thi fild. Thi main dawback a thi nitivity to inaccuacy in th fnc modl, and th difficulti of digning th adaptation block. In thi pap algoithm two i utilizd. Th popod algoithm timat oto pd togth with lip fquncy and oto flux fquncy. Thi mthod i imila to that popod by Va (1993), but includ modification that a th implmntation of a tat vaiabl filt to obtaind th divativ and intgal involvd duing calculation. Th pap intndd not only to dcib in dtail an altnativ fo oto pd timation, but alo to giv a good inid into th fatu and limitation of th moto modl ud which could b applicabl to oth timation algoithm dcibd. Typically, th oto pd vai lowly, and can b conidd a a paamt. In thi can th moto admittanc can b wittn a th fquncy pon tanf function btwn tato cunt and voltag Y ( ω, ω ) R i ( ω, ω R ) ( ω, ω ) = (1.9) v R Th idntifiably of oto pd by uing tato cunt and voltag ha to b invtigatd by coniding th nitivity of moto admittanc to oto pd. Th moto admittanc i a complx function, with al and imaginay pat fo ach hamonic in upply voltag; thfo, th pon of th induction moto fo ach fquncy componnt could b ud to calculat th paamt. Howv th aymptotic valu of th moto admittanc with incaing hamonic od i howing that th lakag inductanc σ L i th only moto paamt in thi limit, wh a th oto pd i abnt. Thfo, only fundamntal and low od hamonic can b ud to calculat th oto pd

31 Y lim 1 = lim Y = ω j σ L ω (1.10) 1.9 SLIDING MODES IN VSS: Vaiabl tuctu ytm conit of a t of continuou ubytm with a pop witching logic and, a a ult, contol action a dicontinuou function of ytm tat, ditubanc (if thy a accibl fo maumnt), and fnc input. In th cou of th nti hitoy of contol thoy, intnity of dicontinuou contol ytm invtigation ha bn maintaind at a high nough lvl. In paticula, at th fit tag, on-off o bang-bang gulato a ankd highly du to a of implmntation and fficincy of contol hadwa. Futhmo, w hall dal with th vaiabl tuctu ytm govnd by (,, ) n m x = f x t u ifx R, u R (1.11) u + u ( x, t) if( x) > 0 = u ( x, t) if( x) < 0 (1.12) ` T x ( ) ( ( x)..., ( x)) = 1 m (1.13) Th VSS (1.11) with continuou function f,, u +,u conit of 2 m ubytm and it tuctu vai on m ufac at th tat pac. Fom th point of viw of ou lat tatmnt, it i woth quoting th lmntay xampl of a cond-od ytm with bang-bang contol and liding mod: x + a x+ a x = u (1.14) u 2 1 = Mign (1.15) = cx+ x, M, c, a1, a2... cont (1.16)

32 . It follow fom analyi of th (X, x) tat plan that, in th nighbohood of gmnt on th witching lin = 0, th tajctoi un in oppoit diction, which lad to th appaanc of a liding mod along thi lin. Th witching lin quation S=0 may b tatd a a motion with olution dpnding only on th lop gain and invaiant to plant paamt and ditubanc. Indict fild-ointd tchniqu micopoco a now widly ud fo th contol of induction moto vo div in high-pfomanc application. With th fildointd tchniqu [9,13,22], th dcoupling of toqu and flux contol command of th induction moto i guaantd, and th induction moto can b contolld linaly a a paatd xcitd dc moto. Howv, th contol pfomanc of th ulting lina ytm i till influncd by th unctainti, which a uually compod of unpdictabl paamt vaiation, xtnal load ditubanc, unmodld and nonlina dynamic. Thfo, many tudi hav bn mad on th moto div in od to pv th pfomanc und th paamt vaiation and xtnal load ditubanc, uch a nonlina contol, optimal contol, vaiabl tuctu ytm contol, adaptiv contol and nual contol [14 16]. In th pat dcad, th vaiabl tuctu contol tatgy uing th liding-mod ha bn focud on many tudi and ach fo th contol of th ac vo div ytm [8, 10, 17, and 20]. Th liding-mod contol can off many good popti, uch a good pfomanc againt unmodlld dynamic, innitivity to paamt vaiation, xtnal ditubanc jction and fat dynamic pon [21]. Th advantag of th liding-mod contol may b mployd in th poition and pd contol of an ac vo ytm. On th oth hand, in indict fild-ointd contol of induction moto, knowldg of oto pd i quid in od to oint th injctd tato cunt vcto and to tablih pd loop fdback contol. Tachognato o digital haft-poition ncod a uually ud to dtct th oto pd of moto. Th pd no low th ytm liability and qui pcial attntion to noi. In addition, fo om pcial application uch a vy high-pd moto div, th xit difficulti in mounting th pd no

33 Rcntly, much ach ha bn caid on th dign of pd no l contol chm [11, 12, 20, 18, and 23]. In th chm th pd i obtaind bad on th maumnt of tato voltag and cunt. Howv, th timation i uually complx and havily dpndnt on machin paamt. Thfo, although no l vcto-contolld div a commcially availabl at thi tim, th paamt unctainti impo a challng in th contol pfomanc THESIS OUTLINE: Apat fom th intoduction chapt 1 contain th litatu uvy of th thi wok followd by by th paamt nitivity, tady tat and dynamic affct and alo MRAS pd timation. Contol. Chapt 2 contain th modling of th induction moto uch a cala contol, vcto contol and it pincipl, dynamic d-q modl of th machin and th dc div analogy to th induction machin contol Chapt 3 contain th liding mod contol and it pincipl and th thoy bhind it. In thi ction w wih to timat th pd with out any no o calld nol contol. Chapt 4 xplain th paamt valu takn following by ult and dicuion, and finally th achivmnt, futu wok, ach and concluion i dicud

34 CHAPTER 2 MODELLING AND FIELD ORIENTED CONTROL OF INDUCTION MOTOR

35 2.1 INTRODUCTION: Th Induction moto (IM) fo many ya hav bn gadd a th wokho in induty. Rcntly, th induction moto w volvd fom bing a contant pd moto to a vaiabl pd. In addition, th mot famou mthod fo contolling induction moto i by vaying th tato voltag o fquncy. To u thi mthod, th atio of th moto voltag and fquncy hould b appoximatly contant. With th invntion of Fild Ointatd Contol, th complx induction moto can b modld a a DC moto by pfoming impl tanfomation. In a imila mann to a dc machin in induction moto th amatu winding i alo on th oto, whil th fild i gnatd by cunt in th tato winding. Howv th oto cunt i not dictly divd fom an xtnal ouc but ult fom th mf inducd in th winding a a ult of th lativ motion of th oto conducto with pct to th tato fild. In oth wod, th tato cunt i th ouc of both th magntic fild and amatu cunt. In th mot commonly ud, quil cag moto, only th tato cunt can dictly b contolld, inc th oto winding i not accibl. Optimal toqu poduction condition a not inhnt du to th abnc of a fixd phyical dipoition btwn th tato and oto fild, and th toqu quation i non lina. In ffct, indpndnt and fficint contol of th fild and toqu i not a impl and taightfowad a in th dc moto. Th concpt of th tady tat toqu contol of an induction moto i xtndd to tanint tat of opation in th high pfomanc, vcto contol ac div ytm bad on th fild opation pincipl (FOP). Th FOP dfin condition fo dcoupling th fild contol fom th toqu contol. A fild ointd induction moto mulat a paatly xitd dc moto in two apct: Both th magntic fild and toqu dvlopd in th moto can b contolld indpndntly. Optimal condition fo th toqu poduction, ulting in th maximum toqu p unit amp, occu in th moto both in tady tat and in tanint condition of opation

36 2.2 INDUCTION MACHINE CONTROL: Squil cag induction machin a impl and uggd and a conidd to b th wokho of induty. At pnt induction moto div dominat th wold makt. Howv, th contol tuctu of an induction moto i complicatd inc th tato fild i volving, and futh complication ai du to th fact that th oto cunt o oto flux of a quil cag induction moto can not b dictly monitod Th mchanim of toqu poduction in an ac machin and in a dc machin i imila. Unfotunatly thi imilaity wa not mphaizd bfo th 1970, and thi i on of th aon why th tchniqu of vcto contol did not mg ali. Th fomula givn in many wll known txtbook of th machin thoy hav alo implid that, fo th monitoing of th intantanou lctomagntic toqu of an induction machin, it i alo ncay to monito th oto cunt and th oto poition. Evn in th 1980 om publication md to tngthn thi fal concption, which only ao bcau th complicatd fomula divd fo th xpion of th intantanou lctomagntic toqu hav not bn implifid. Howv by uing fundamntal phyical law o pac vcto thoy, it i ay to how that, imila to th xpion of th lctomagntic toqu of a paatly xitd dc machin, th intantanou lctomagntic toqu of an induction moto can b xpd a th poduct of a flux poducing cunt and a toqu poducing cunt, if a pcial flux ointd fnc i ud Scala contol: Scala contol, a th nam indicat, i du to magnitud vaiation of th contol vaiabl only, and digading th coupling ffct in th machin. Fo xampl, th voltag of th machin can b contolld to contol th flux, and th fquncy and lip can b contolld to contol th toqu. Howv, flux and toqu a alo function of fquncy and voltag, pctivly. Scala contol in contat to th vcto contol o fild ointd contol, wh both th magnitud and pha i contolld. Scala contolld div giv om what infio pfomanc, but thy a aily implmntd. Scala contolld div hav bn widly ud in induty. How v thi impotanc

37 ha diminihd cntly bcau of th upio pfomanc of vcto contolld div, which i dmandd in many application Vcto o fild ointd contol: Scala contol i omwhat impl to implmnt, but th inhnt coupling ffct i.. both toqu and flux a function of voltag o cunt and fquncy giv th luggih pon and th ytm i aily pon to intability bcau of high od ytm hamonic. Fo xampl, if th toqu i incad by incmnting th lip o lip th flux tnd to dca. Th flux vaiation i luggih. Th flux vaiation thn compnatd by th luggih flux contol loop fding additional voltag. Thi tmpoay dipping of flux duc th toqu nitivity with lip and lngthn th ytm pon tim. Th fogoing poblm can b olvd by vcto contol o fild ointd contol. Th invntion of vcto contol in th bginning of 1970, and th dmontation that an induction moto can b contolld lik a paatly xcitd dc moto, bought a naianc in th high pfomanc contol of ac div. Bcau of dc machin lik pfomanc, vcto contol i known a dcoupling, othogonal, o tanvcto contol. Vcto contol i applicabl to both induction and ynchonou moto div. Vcto contol and th coponding fdback ignal pocing, paticulaly fo modn no l vcto contol, a complx and th u of powful micocomput o DSP i mandatoy. It appa that vntually, vcto contol will out cala contol, and will b accptd a th induty tandad contol fo ac div. 2.3 DC DRIVE ANALOGY: Idally, a vcto contolld induction moto div opat lik a paatly xcitd dc moto div in fig 1.1. In a dc machin, nglcting th amatu action ffct and fild atuation, th dvlopd toqu i givn by T Wh I a = amatu cunt And I f = fild cunt = K Ψ Ψ = K I I (2.1) t f a ' t a f

38 I I f I f ψ a Dcoupld ψ f Fig 2.1-paatly xcitd dc moto Thi contuction of dc machin i uch that th fild flux Ψf poducd by th cunt I f i ppndicula to th amatu flux Ψ a, which i poducd by th amatu cunt. Th pac vcto, which a tationay in pac, a othogonal and dcoupld in natu. Thi man that whn toqu i contolld by contolling th cunt I a, th flux Ψf i not affctd and w gt th fat tanint pon and high toqu amp atio. Bcau of dcoupling, whn th fild cunt I f i contolld, it affct th fild flux Ψf only, but not th Ψ a flux. Bcau of th inhnt coupling poblm, an induction moto can not gnally giv uch fat pon. DC machin lik pfomanc can alo b xtndd to an induction moto if th machin i conidd in a ynchonouly otating fnc fam ( d q ), wh th inuoidal vaiabl appa a dc quantity in tady. In fig 1.2, th induction moto with th invt and vcto contol in th font nd i hown with two contol cunt input i * d and * i q.th cunt a th dict axi componnt and quadatu axi componnt of th tato cunt, pctivly, in a ynchonouly otating fnc fam

39 I q * I d * I q Vcto Contol Invt IM I d ω Fig 2.2 vcto contolld induction moto ψ With vcto contol, i d i analogou to fild cunt I f and i q i analogou to amatu cunt Ia of a dc machin. Thfo, th toqu can b xpd a ^ ' t q t q d T = K Ψ I = K I I (2.2) Wh Ψ ˆ = abolut pak valu of th inuoidal pac vcto. Thi dc machin lik pfomanc i only poibl if i d i ointd in th diction of Ψˆ and i q i tablihd ppndicula to it, a hown by th pac vcto diagam of fig 1.2. Thi man that whn * iq i contolld; it affct th actuali q cunt only, but do not affct th flux Ψ ˆ. Similaly, whn i * d i contolld, it contol th flux only and do not affct th i q componnt of cunt. Thi vcto o fild ointation of cunt i ntial und all opating condition in a vcto contol div. Whn compad to dc machin pac vcto, induction machin pac vcto otat ynchonouly at fquncy ω a indicatd in fig PRINCIPLE OF VECTOR CONTROL: Th fundamntal of vcto contol implmntation can b xplaind with th hlp of fig 1.3. Wh th machin modl i pntd in a ynchonouly otating fnc fam. Th invt i omittd fom th figu, auming that it ha unity cunt gain, that i, it gnat cunt i ab i andi c a dictatd by th coponding command cunt i *, * a i b and * i c fom th contoll. A machin modl with intnal

40 convion i hown on th ight. Th machin tminal pha cunt i ab i andi c a convtd to Id and Iq componnt by 3 2 ϕ ϕ tanfomation. Contol Machin * I d * I q d to d q q * I d * I q d q to a b c * I a * I b * I c I b I c I a a to I d b c d q I q d q to d q I d I q machin d q mod l I q I d coθ inθ coθ inθ ω ψ Inv tanfomation Machin modl Tanfomation Fig 2.3 vcto contol implmntation pincipl with machin ( d q ) modl. Th a thn convtd to ynchonouly otating fam by th unit vcto componnt coθ and inθ bfo applying thm to th d q machin modl a hown in th fig 1.3. Th contoll mak two tag of inv tanfomation, a hown, o that th contol cunt * id and * iq copond to th machin cunt i d andi q, pctivly. Th tanfomation and inv tanfomation including th invt idally do not incopoat any dynamic thfo, th pon to i d and i q i intantanou. 2.5 DYNAMIC d-q MODEL: Th p pha quivalnt cicuit of th machin, which i only valid in tady tat condition. In an adjutabl pd div, th machin nomally contitut an lmnt with in a fdback loop, and thfo it tanint bhavio ha to b takn into

41 conidation. Bid, high pfomanc div contol, uch a vcto o fild ointd contol i bad on th dynamic d-q modl of th machin. Baically, it can b lookd on a a tanfom with a moving conday, wh th coupling cofficint btwn tato and oto pha chang continuouly with th chang of oto poitionθ. Th machin modl can b dcibd by th diffntial quation with timing vaying mutual inductanc, but uch a modl tnd to b vaying complx. A th pha machin can b pntd by an quivalnt two pha machin, wh d q d q copond to tato dict and quadatu ax, and copond to oto dict and quadatu ax. Although it i omwhat impl, th poblm of tim vaying paamt till main. R. H Pak in th 1920, popod a nw thoy of lctic machin analyi to olv thi poblm. H fomulatd a chang of vaiabl which, in ffct, placd th vaiabl voltag, cunt and flux linkag aociatd with tato winding of a ynchonou machin with vaiabl aociatd with fictitiou winding otating with th oto at ynchonou pd h fd, th tato vaiabl to a ynchonouly otating fnc fam fixd in th oto. With uch tanfomation calld Pak tanfomation, howd that all th tim vaying inductanc that occu du to an lctic cicuit in lativ motion and lctic cicuit with vaying magntic luctanc i liminatd. i q R L = L L + l m Ll = L Lm ω ψ d i q + ( ω ) ω ψ R d v q ψ q L m ψ q v q Fig 2.4 dynamic d q quivalnt cicuit of machin ( q axi)

42 i d R L = L L + l m Ll = L Lm ω ψ q i d + ( ω ) ω ψ R q v d ψ d L m ψ d v d Fig 2.5 dynamic d q quivalnt cicuit of machin ( d axi) Th abov figu how th d q dynamic modl quivalnt cicuit. A pcial advantag of th d q dynamic modl of th machin i that all th inuoidal vaiabl in tationay fam appa a dc quantity in ynchonou fam. Fom th abov modl th lctical tanint modl in tm of voltag and cunt can b givn in matix fom, vq R + SL ωl SLm ωlm iq v ω d L R + SL ωlm SL m i d = v SL q m ( ω ω) Lm R + SL ( ω ω) L iq vd ( ω ω) Lm SLm ( ω ω) L R + SL id 2.3 Th a baically two diffnt typ of vcto contol tchniqu: dict and indict tchniqu. Th dict implmntation li on th dict maumnt o timation of oto-, tato-, o magntizing-flux-linkag vcto amplitud and poition. Th indict mthod u a machin modl,.g. fo oto flux ointd contol, it utiliz th inhnt lip lation. In contat to dict mthod, th indict mthod a highly dpndnt on machin paamt. Taditional dict vcto contol chm u ach coil, tappd tato winding o Hall Effct no fo flux ning. Thi intoduc limitation du to machin tuctual and thmal quimnt. Many application u indict chm, inc th hav lativly impl hadwa and btt ovall

43 pfomanc at low fqunci, but inc th contain vaiou machin paamt, which may vay with tmpatu, atuation lvl and fquncy, vaiou paamt adaptation chm, hav bn dvlopd. Th includ lf tuning contol application, modl fnc adaptiv ytm (MRAS) application, application of obv, application of intllignt contoll tc. to obtain a olution, in th dvlopmnt of thoy it i omtim aumd that th mchanical tim contant i much gat than th lctical tim contant, but thi bcom an invalid aumption if th machin intia i low. If incoct modulu and th angl of th flux linkag pac vcto a ud in a vcto contol chm, thn flux and toqu dcoupling i lot and th tanint and tady tat pon a dgadd. Low fquncy pon, pd ocillation, and lo of input output toqu linaity i majo conqunc of dtund opation, togth with dcad div fficincy. 2.6 Dq-abc TRANSFORMATION: Th lation btwn th ynchonouly otating fnc fam and th tationay fnc fam i pfomd by th o-calld v Pak tanfomation: ia co( θ) in( θ) id i b co( θ 2 π/3) in( θ 2 π/3) = i q i c co( θ+ 2 π/3) in( θ 2 π/3) (2.4) Wh θ i th angl poition btwn th d-axi of th ynchonouly otating fnc fam and th a-axi of th tationay fnc fam and it i aumd that th quantiti a balancd. Thi tat tanfomation off ctain advantag, among which, th fact that, in thi nw fnc fam, th lctomagntic toqu i dictly an imag of th quadatu ("q ) componnt of th tato cunt. 2.7 DIRECT OR FEEDBACK VECTOR CONTROL: Th pincipal vcto contol paamt, i * d and * i q, which a dc valu in ynchonouly otating fam, a convtd to tationay fam a vcto otation (VR)

44 with th hlp of unit vcto gnatd fom flux vcto ignal Ψ d and Ψ q. Th ulting tationay fam ignal a thn convtd into pha cunt command fo th invt. Th flux ignal Ψd and Ψ q.a gnatd fom th machin tminal voltag and cunt with th hlp of th voltag modl timato. A flux contol loop ha bn addd fo pciion contol of flux. Th toqu componnt of cunt i * q i gnatd fom th pd contol loop though a bipola limit. Th toqu popotional to i q,can b bipola. Th coct alignmnt of cunt i d in th diction of th flux Ψ ˆ and th cunt iq ppndicula to it a cucial in vcto contol. Thi alignmnt with th hlp of th tationay fam oto flux vcto d Ψd and q fam i otating with a ynchonou pd Ψ q i xplaind in fig 1.4. In thi figu, th ω with pct to tationay fam d q, and at any intant, th angula poition of th d q to d q axi iθ, whθ = ω t

45 i q q Ψ q q i q θ ^ Ψ i d Ψ d d d Fig 2.6 d q and d q phao with coct oto flux ointation Fom th fig 1.6 w can wit th following quation: ^ Ψ = Ψ coθ (2.5) d ^ Ψ = Ψ in θ (2.6) q co θ = Ψ Ψ d ^ (2.7) in θ = Ψ Ψ ^ q (2.8) 2 2 ˆ d q Ψ = Ψ + Ψ (2.9)

46 coθ Ψ d inθ Ψ q Fig 2.7 plot of unit vcto ignal in coct pha poition 2.8 SALIENT FEATURES OF VECTOR CONTROL: Th fquncy ω of th div i not dictly contolld a in cala contol. Th machin i ntially lf contolld wh th fquncy a wll a th pha a contolld indictly with th hlp of unit vcto. Th i no fa of an intability poblm by coing th opating point byond th bakdown toqu T m a in a cala contol. Limiting th total I ^ with in th af limit automatically limit opation with in th tabl gion. Th tanint pon will b fat and dc machin lik bcau toqu contol by i q do not affct th flux. Howv idal vcto contol i not poibl in pactic, bcau of dlay in convt and ignal pocing and th paamt vaiation ffct. Lik a dc machin, pd contol i poibl in fou quadant without any additional contol lmnt lik pha qunc ving. In fowad motoing condition, if th toqu T in ngativ, th div initially go into gnativ baking mod, which low down th pd. At zo pd, th pha qunc of th unit vcto automatically vu, giving v motoing opation

47 Th dict mthod of vcto contol i difficult to opat uccfully at vy low fquncy including zo pd bcau of th following poblm: At low fquncy, voltag ignal v d and v q a vy low. In addition, idal intgation bcom difficult bcau dc offt tnd to build up at th intgat output. Th paamt vaiation ffct of itanc R and inductanc L l, Ll and L m tnd to duc accuacy of th timatd ignal. Paticulaly tmpatu vaiation of R bcom mo dominant. Howv, compnation of R i omwhat ai, which will b dicud lat. At high voltag, th ffct of paamt can b nglctd. In indutial application, vcto div oftn quid opating fom zo pd (including zo pd tat up), hnc dict vcto contol with voltag modl ignal timation can not b ud. 2.9 INDIRECT (FEED FORWARD) VECTOR CONTROL: Th indict vcto contol mthod i ntially th am a dict vcto contol, xcpt th unit vcto ignal a gnatd in fd fowad mann. Indict vcto contol i vy popula in indutial application. Th xplanation of th fundamntal pincipl of th indict vcto contol with th hlp of phao diagam i givn by th fig

48 θ q i q ψ q = 0 i d ψ d d θ i d θ θ i I q θ l Roto Axi ψ q ψ d ω l d Fig 2.8 phao diagam xplaining indict vcto contol = ψ ω d ω q Th d q ax a fixd on th tato, but th d q ax, which a fixd on th oto, a moving at a pd ω a hown in th fig 1.6. Synchonouly otating ax d q a otating ahad of th d q ax by th poitiv lip angl l θ coponding to lip fquncyω. Sinc th oto pol i dictd on th l d ax and, W can wit ω = ω + ω l (2.10) (2.11) θ = ωdt = ( ω + ω ) dt = θ + θ l l Th oto pol poition i not abolut, but i lipping with pct to th oto at fquncyω. Th phao diagam uggt that fo dcoupling contol, th tato flux l componnt of cunt i d hould b alignd on th cunt i q hould b on th q ax a hown in th fig 1.8. d ax, and th toqu componnt of

49 Fom th voltag modl of th flux vcto timation, th machin tminal voltag and cunt a nd and flux a computd fom th tationay fam d q quivalnt cicuit. Th flux quation a: d d d (2.12) q q q (2.13) Ψ = ( v R i ) dt Ψ = ( v Ri ) dt Ψ = Ψ + Ψ (2.14) d q Ψ =Ψ Li = L ( i + i ) (2.15) dm d l d m d d Ψ =Ψ Li = L ( i + i ) (2.16) qm q l q m q q Ψ = L i + L i (2.17) d m d d Ψ = L i + L i (2.18) q m q q Eliminating i d and i q fom th quation 2.17and 2.18 with th hlp of th quation 2.15 and 2.16 pctivly, w gt, L Ψ = Ψ Li (2.19) d dm l d Lm L Ψ = Ψ L i (2.20) q qm l q Lm Fo dcoupling contol, w can now mak divation of contol quation of indict vcto contol with th hlp of quivalnt cicuit. Th oto cicuit quation can b wittn a

50 d Ψ d + Ri d ( ω ω) Ψ = q 0 dt (2.21) d Ψ q + Ri + q ( ω ω) Ψ = d 0 dt (2.22) Th oto flux linkag xpion can b givn a Ψ = L i + L i (2.23) d d m d Ψ = Li + L i (2.24) q q m q Fom th abov quation w can wit i i = Ψ L (2.25) 1 m d d id L L = Ψ L (2.26) 1 m q q iq L L Th oto cunt in quation2.21 and 2.22 which a in accibl can b liminatd with th hlp of quation 2.25 and 2.26 a, d Ψ d R L + Ψ m d Ri d ω Ψ = l q 0 dt L L (2.27) d Ψ q R L + Ψ m q Ri q ω Ψ = l d 0 dt L L (2.28) Wh ω l = ω ω ha bn ubtitutd. Fo dcupling contol, it i diabl that Ψ = 0 (2.29) q That i d Ψ q = 0 (2.30) dt So that, th total oto flux ^ Ψ i dictd on th d axi

51 Subtituting th abov condition in quation 2.29 and 2.30, w gt L R Ψ ^ ^ +Ψ = L mid (2.31) d dt ω l = L m ^ Ψ R L i q (2.32) Wh Ψ ^ = Ψ ha bn ubtitutd. d If oto flux Ψ ^ =contant, which i uually th ca, thn fom quation 1.30 ^ Ψ = L mid (2.33) In oth wod, th oto flux i dictly popotional to cunt i d in tady tat. To implmnt th indict vcto contol tatgy, it i ncay to tak 2.11, 2.31 and 2.32 into conidation. Th pd contol ang in indict vcto contol can aily b xtndd fom tand till o zo pd to th fild wakning gion how v in fild wakning gion, th flux i pogammd uch that th invt all way opatd in PWM mod. In both th dict and indict contol mthod intantanou cunt contol of invt i ncay. Hytii bnd PWM cunt contol can b ud but it hamonic contnt i not optimum. Bid at high pd th cunt contoll will tnt to atuat in pat th quai PWM bcau of high CEMF. In thi condition, th fundamntal cunt magnitud it pha lo tacking with th command cunt and thu, vcto contol will not b valid

52 CHAPTER 3 SENSORLESS SLIDING MODE VECTOR CONTROL

53 3.1 INTRODUCTION: Contol action of th ytm und tudy a aumd to b dicontinuou function of th ytm tat. Fo th pincipl opation mod th tat tajctoi a in th vicinity of dicontinuity point. Thi motion i fd to a liding mod. Th cop of liding mod contol tudi mbac - mathmatical mthod of dicontinuou diffntial quation, - dign of manifold in th tat pac and dicontinuou contol function nfocing motion along th manifold, - implmntation of liding mod contoll and thi application to contol of dynamic plant. Th fit poblm concn dvlopmnt of th tool to div th quation govning liding mod and th condition fo thi motion to xit. Fomally motion quation of SMC do not atify th convntional uniqun-xitnc thom of th odinay diffntial quation thoy. Th aon of ambiguity a dicud. Th gulaization appoach to div liding motion quation i dmontatd and compad with oth modl of liding mod. Th liding mod xitnc poblm i tudid in tm of th tability thoy. Enfocing liding mod nabl dcoupling of th dign pocdu, inc th motion pcding liding mod and motion in liding mod a of low dimnion and may b dignd indpndntly. On th oth hand, und o calld matching condition th liding mod quation dpnd nith plant paamt vaiation no xtnal ditubanc. Thfo liding mod contol algoithm a fficint whn contolling nonlina dynamic plant of high dimnion opating und unctainty condition. Th dign mthod a dmontatd mainly fo ytm in th gula fom. Componnt-wi and vcto dign vion of liding mod contol a dicud. Th dign mthodology i illutatd by liding mod contol in lina ytm. Th concpt "liding mod contol" i gnalizd fo dict-tim ytm to mak faibl it implmntation fo th ytm with digital contoll. Nw mathmatical and dign mthod a ndd fo liding mod contol in infinit-dimnional ytm including ytm govnd by PDE. Th cnt ult in thi aa a bifly uvyd. Th poblm of chatting caud by unmodld dynamic i dicud in th contxt of application. Th ytm with aymptotic obv a hown to b f of chatting. Sliding mod contol application i uful to lctic div, mobil obot, flxibl ba and plat

54 Sliding mod contol i a typ of vaiabl tuctu contol wh th dynamic of a nonlina ytm i altd via application of high fquncy witching contol. Thi i a tat fdback contol chm wh th fdback i not a continuou function of tim. Th pincipl of liding mod contol i to focibly contain th ytm, by uitabl contol tatgy, to tay on th liding ufac on which th ytm will xhibit diabl fatu. Whn th ytm i containd by th liding contol to tay on th liding ufac, th ytm dynamic a govnd by ducd od ytm. Sliding mod tchniqu a on appoach to olving contol poblm and a an aa of incaing intt. Thi txt povid th ad with an intoduction to th liding mod contol aa and thn go on to dvlop th thotical ult. Fully wokd dign xampl which can b ud a tutoial matial a includd. Indutial ca tudi, which pnt th ult of liding mod contoll implmntation, and a ud to illutat uccful pactical application of th thoy. In th fomulation of any contol poblm th will typically b dicpanci btwn th actual plant and th mathmatical modl dvlopd fo contoll dign. Thi mimatch may b du to any numb of facto and it i th ngin' ol to nu th quid pfomanc lvl xit dpit th xitnc of plant/modl mimatch. Thi ha ld to th dvlopmnt of o-calld obut contol mthod. 3.2 SENSOR LESS CONTROL: Snol vcto contol of an induction moto div ntially man vcto contol without any pd no. An incmntal haft mountd pd ncod uually an optical typ i quid fo clo loop pd o poition contol in both vcto and cala contol div. A pd ignal i alo quid in indict vcto contol in th whol pd ang, and in dict vcto contol fo th low pd ang, including th zo pd tat up opation. A pd ncod i undiabl in th div bcau it add cot and liability poblm, bid th nd fo a haft xtnion and mounting aangmnt. It i poibl to timat th pd ignal fom machin tminal voltag and cunt with th hlp of a dp. Howv th timation i nomally complx and havily dpnd on th machin paamt. Although th nol vcto contolld

55 div a commcially availabl thi tim, th paamt vaiation poblm, paticulaly na zo pd, impo a challng in th accuacy of pd timation. 3.3 SLIDING MODE CONTROL: A liding mod contol (SMC) with a vaiabl tuctu i baically an adaptiv contol that giv obut pfomanc of a div with paamt vaiation and load toqu ditubanc. Th contol i nonlina and can b applid to a lina o nonlina plant. In an SMC, th nam indicat th div pon i focd to tact o lid along a pdfind tajctoy o fnc modl in a pha plan by a witching contol algoithm, ipctiv of th plant paamt vaiation and load ditubanc. Th contoll dtct th dviation of th actual tajctoy and copondingly chang th witching tatgy to to th tacking. In pfomanc, it i omwhat imila to an MRAC, but th dign and implmntation of an SMC a omwhat impl. SMCS can b applid to vo div with dc moto, induction moto, and ynchonou moto fo application uch a obot div, machin tool contol, tc. On paticula appoach to obut contol contoll dign i th o-calld liding mod contol mthodology which i a paticula typ of Vaiabl Stuctu Contol Sytm (VSCS). Vaiabl Stuctu Contol Sytm a chaactid by a uit of fdback contol law and a dciion ul (tmd th witching function) and can b gadd a a combination of ubytm wh ach ubytm ha a fixd contol tuctu and i valid fo pcifid gion of ytm bhavio. Th advantag i it ability to combin uful popti of ach of th compoit tuctu of th ytm. Futhmo, th ytm may b dignd to po nw popti not pnt in any of th compoit tuctu alon. In liding mod contol, th VSCS i dignd to div and thn contain th ytm tat to li within a nighbohood of th witching function. It two main advantag a (1) th dynamic bhavio of th ytm may b tailod by th paticula choic of witching function, and (2) th clod-loop pon bcom totally innitiv to a paticula cla of unctainty. Alo, th ability to pcify pfomanc dictly mak liding mod contol attactiv fom th dign ppctiv

56 Sliding mod contol i an fficint tool to contol complx high-od dynamic plant opating und unctainty condition du to it od duction popty and it low nitivity to ditubanc and plant paamt vaiation. It obutn popty com with a pic, which i high contol activity. Th pincipl of liding mod contol i that; tat of th ytm to b contolld a fit takn to a ufac (liding ufac) in tat pac and thn kpt th with a hifting law bad on th ytm tat. Onc liding ufac i achd th clod loop ytm ha low nitivity to matchd and boundd ditubanc, plant paamt vaiation. Sliding mod contol can b convnintly ud fo both non-lina ytm and ytm with paamt unctainti du to it dicontinuou contoll tm. That dicontinuou contol tm i ud to ngat th ffct of non-linaiti and/o paamt unctainti. 3.4 BLOCK DIAGRAM OF SLIDING MODE FIELD ORIENTED CONTROL: * ω (t) VSC Contoll * i q Limit d q -abc Cunt contoll * i d * i q * i abc i abc ω Fild Wakning * Ψ d * i d Calculation θ 1 Pul PWM Invt ω ω ω ω & Etimato i abc v abc Fig 3.1 block diagam of liding mod fild ointd contol IM

57 3.5 VARIABLE STRUCTURE ROBUST SPEED CONTROL: In gnal, th mchanical quation of an induction moto can b wittn a: J wm + Bw m + TL = T (3.1) Wh J and B a th intia contant and th vicou fiction cofficint of th induction moto ytm, pctivly; T L i th xtnal load; w m th oto mchanical pd in angula fquncy, which i latd to th oto lctical pd by, ω m 2ω p = (3.2) Wh p i th pol numb and T dnot th gnatd toqu of an induction moto, dfind a, L 3 p m T ( = ψ diq ψ qid 4 L wh ψ and d ) (3.3) ψ q a th oto-flux linkag, with th ubcipt dnoting that th quantity i fd to th ynchonouly otating fnc fam; i q and tato cunt. Thn th mchanical quation bcom, ω m + a ω m + f = bi q (3.4) Wh th paamt a dfind a, B K a = b =, f J J T J T L, = (3.5) i d a th Now, w a going to conid th pviou mchanical Equation with unctainti a follow: ω m = ( a + a) ωm + ( f + f ) + ( b + b) iq (3.6)

58 Wh th tm a, b and f a th unctainty of th paamt a, b, and f pctivly. Lt u dfin th tacking pd o a follow: ( t) = ω m( t) ωm( t) (3.7) Wh, th ωm i th oto pd command. Taking th divativ of th pviou quation with pct to tim yild: * m m + Wh th following tm hav bn collctd in th ignal u (t), ( t) = ω ω = a( t) + u( t) d( t) (3.8) u( t) * m * = bi q ( t) aω m ( t) f ( t) ω ( t) (3.9) And, th unctainty tm hav bn collctd in th ignal d(t), d ( t) = aω ( t) f ( t) + bi q ( t) (3.10) m Now, w a going to dfin th liding vaiabl S (t) with an intgal componnt a: t ( t) = ( t) ( k a) ( τ ) dτ (3.11) 0 Wh, k i a contant gain. Thn th liding ufac i dfind a: t ( t) = ( t) ( k a) ( τ ) dτ = 0 0 Th vaiabl tuctu pd contoll i dignd a: (3.12) u( t) k βgn( ) = (3.13) In od to obtain th pd tajctoy tacking, th following aumption hould b fomulatd,

59 Th gain k mut b chon o that th tm (k k < 0. a) i tictly ngativ, thfo Th gain β mut b chon o that β d (t) fo all tim. If th aumption i vifid, th contol law 3.13 lad th oto mchanical pd o that * th pd tacking o ( t) = ωm( t) ω m( t) tnd to zo if th tim tnd to infinity. Th poof of thi thom will b caid out uing th Lyapunov tability thoy. 1 v ( t) = ( t) ( t) (3.14) 2 It tim divativ i calculatd a,. V ( t). = ( t) ( t) = [ ( k a) ]. = [( a + u + d ) ( k a)] = [ u + d k] = [ k β gn( ) + d k] = [ d β gn( )] [ β d ] 0 (3.15) Uing th Lyapunov dict mthod, inc V(t) i claly poitiv-dfinit, V (t) i ngativ dfinit and V(t) tnd to infinity a S(t) tnd to infinity, thn th quilibium at th oigin S(t) = 0 i globally aymptotically tabl. Thfo S (t) tnd to zo a th tim t tnd to infinity. Moov, all tajctoi tating off th liding ufac S = 0 mut ach it in finit tim and thn will main on thi ufac. Thi ytm bhavio onc on th liding ufac i uually calld liding mod. Whn th liding mod occu on th liding ufac thn S (t) = S (t) = 0, and thfo, th dynamic bhavio of th tacking poblm i quivalntly govnd by th following quation: ( t) = 0 ( t) = ( k a) ( t) (3.16) Thn, und aumption 1, th tacking o (t) convg to zo xponntially

60 It hould b notd that, a typical motion und liding mod contol conit of a aching pha duing which tajctoi tating off th liding ufac S = 0 mov towad it and ach it in finit tim, followd by liding pha duing which th motion will b confind to thi ufac and th ytm tacking o will b pntd by th ducd-od modl, wh th tacking o tnd to zo. * Finally, th toqu cunt command, i q ( t), can b obtaind dictly ubtituting u (t) in th pviou quation, * 1 * * i q( t) = [ k βgn( ) + aω m + ω m + f] (3.17) b Thfo, th vaiabl tuctu pd contol olv th pd tacking poblm fo th induction moto, with om unctainti in mchanical paamt and load toqu. 3.6 CURRENT CONTROLLER: Th block cunt contoll conit of th hyti band cunt PWM contol. it i baically an intantanou fdback cunt contol mthod of PWM wh th actual cunt continuouly tack th cunt command within a hyti band. SPWM * i i K K PWM φ Fig 3.2 hyti band cunt contol PWM

61 Th contol cicuit gnat th in fnc cunt wav of did magnitud and fquncy and it i compad with th actual pha cunt wav. A th cunt xcd th pcibd hyti band, th upp witch in th half bidg i tund off and low i tund on. Th output voltag tanition a fom +0.5Vd to -0.5Vd, and th cunt tat dcay. A th cunt co th low band limit, th low witch i tund off and th upp witch i tund on. A lock out tim i povidd at ach tanition to pvnt a hoot though fault. Th actual cunt wav i thu focd to tack th in fnc wav with in th hyti band by back and foth witching of th upp and low witch. Th invt thn ntially bcom a cunt ouc with pak to pak cunt ippl, which i contolld with in th hyti band ipctiv of Vd fluctuation. Hytii band 2HB Upp band HB Sin fnc wav Low band HB Actual cunt +0.5V d 0-0.5V d ω t Fig 3.3 pincipl of hyti band contol Whn th upp witch i clod, th poitiv lop of th cunt i givn a, di dt 0.5Vd Vcm inω t L = (3.18) Wh 0.5 V d i th applid voltag. V cm in ω t = intantanou valu of th oppoing load CEMF. L = ffctiv load inductanc

62 Th coponding quation whn th low witch i clod i givn a, di dt (0.5Vd Vcmin ωt) = L (3.19) Th pak to pak cunt ippl and witching fquncy a latd to th width of th hyti band. A mall band will inca witching fquncy and low th ippl. Th hyti band PWM can b moothly tanitiond to qua wav voltag mod though th quai PWM gion. Whn upp witch on * ( ) i i > HB Whn low witch on * ( ) i i < HB Th hyti band PWM ha bn vy popula bcau of it impl implmntation, fat tanint pon, dict limiting of dvic pak cunt and pactical innitivity of dc link voltag ippl that pmit a low filt capacito. 3.7 ESTIMATION OF MOTOR SPEED: i d LL mm L L S R S + 1 R ^ Ψ T l i q 3 p L 2 2 L m T + p 2 J 1 S ω Fig 3.4 tanf function block diagam of vcto contol div Fom th indict vcto contol th tato voltag quation in th tationay fam i givn a, L L d Ψ = v ( R + σl ) i L L dt d d d m m (3.20)

63 L L d Ψ = v ( R + σ L ) i L L dt q q q m m Th oto flux quation in th tationay fam a (3.21) Lm 1 Ψ d = i d ω Ψ q Ψ d (3.22) T T Lm 1 Ψ q = i q + ωψ d Ψ q (3.23) T T Wh T = L R And th angl btwn oto flux vcto in lation to th d axi of th tationay fam i, θ Ψ q = actan( ) Ψ Taking it divativ of th abov quation, w gt, d (3.24) Ψ Ψ Ψ Ψ θ = ω = Ψ +Ψ (3.25) Simplifying th abov quation, Wh L ω = ω T ω d q q d 2 2 d q Ψ i Ψ i ( ) m d q q d 2 2 Ψ d +Ψq 1 L [ ( )] m = Ψ 2 dψq ΨqΨ d + Ψdq i Ψqd i Ψ T (3.26) (3.27) Ψ =Ψ d +Ψ q (3.28) Thfo, givn a complt knowldg of th moto paamt, th intantanou pd ω can b calculatd fom th pviou quation, wh th tato maud cunt and voltag, and th oto flux timatd obtaind fom a oto flux obv bad on Equation 3.5 and 3.6 a mployd. Th gnatd toqu in th induction moto i givn a,

64 3 p Lm T = ( Ψ diq Ψ qid) 4 L (3.29) Uing th fild-ointation contol pincipl th cunt componnt Id i alignd in th diction of th oto flux vcto ψ, and th cunt componnt Iq i alignd in th diction ppndicula to it. Fo dcoupling contol, it i diabl that, Ψ q = 0, Ψ d = Ψ (3.30) Taking into account of th pviou ult th quation of toqu i givn a, 3 p Lm T = Ψ i = K i 4 L d q t q (3.31) Wh, K i th toqu contant and dfind a follow, t K t 3 p Lm = Ψ d (3.32) 4 L 3.8 FIELD WEAKENING CONTROLLER: Th block fild wakning giv th flux command bad on th oto pd, o that th PWM contoll do not atuat. If And ω < ω, Ψ =Ψ * b d dratd ω ω > Ψ = Ψ (3.33) * b ωb, d dratd ω With th pop mntiond fild ointation, th dynamic of th oto flux i givn a: d Ψ d R L + Ψ m d Ri d ω Ψ = l q 0 dt L L (3.34) Fo dcoupling,

65 dψ q Ψ q = 0, = 0 dt (3.35) d Ψ d R L + Ψ m d Ri = d 0 dt L L (3.36) Multiplying th quation by T = L/R calld oto tim contant and aanging w gt, L R d dt Ψ d +Ψ = d Lmid (3.37) If th oto flux Ψ i contant thn th abov quation i ducd a, Ψ d = Lmid (3.38) Ψ = Lmid (3.39) In oth wod th oto flux i dictly popotional to th cunt I d in tady tat. H in thi ction th analyi of th liding mod contol i givn. Th toqu i calculatd by toqu componnt of cunt. Th oto pd i timatd with out uing any pd no o any typ of tanduc. All th mathmatical fomulation of th nti contoll which i ud in th block diagam i givn in thi ction

66 CHAPTER 4 RESULTS AND DISCUSSION

67 4.1 OPEN LOOP SIMULATION: In th fit ction imulation fo th opn loop i givn. Fig 4.1 i th toqu pd chaactitic of th induction moto in opn loop contol. Toqu (Nm) Spd (N) pm Fig 4.1 Toqu pd chaactitic Tim () Tim () Fig4.2 plot of i d vu tim

68 Tim () Fig 4.3 plot of i q vu tim Tim () Tim () Fig4.4 plot of ψ d vu tim

69 Tim () Fig 4.5 plot of ψ q vu tim In thi ction fig 4.2 and 4.3 i th plot of i d and i q vu tim, h w hav n that a th tim inca fom i dca vy lowly but th lat i fit inca to a mall valu and thn dca apidly. Upto th tim 2.0 c it i th tanint piod of th ytm and it com to th tady tat valu. Fig 4.4 and 4.5 i th plot of th oto flux in d and q axi pctivly. H th oto flux in th d axi i inca at th tady tat wh a th flux in th q axi dca aft th tanint piod, and it com to ngligibl valu. Th paamt of th induction moto a found out by th no load tt and block oto tt, which i givn in th appndic. 4.2 SIMULATION RESULTS FOR SLIDING MODE FIELD ORIENTED CONTROL: Th block VSC Contoll pnt th popod liding mod contoll and it i implmntd by Equation. (3.11) and (3.17). Th block limit limit th cunt applid to th moto winding o that it main within th limit valu and it i implmntd by a atuation function. Th block dq abc mak th convion

70 btwn th ynchonouly otating and tationay fnc fam and i implmntd by Equation. (2.4). Th block Cunt Contoll conit of a th hyti-band cunt PWM contol, which i baically an intantanou fdback cunt contol mthod of PWM wh th actual cunt (i abc ) continually tack th command cunt (i * abc) within a hyti band. Th block PWM Invt i a ix IGBT-diod bidg invt with 780 V DC voltag ouc. Th block Fild Wakning contoll giv th flux command bad on oto pd, o that th PWM contoll do not atuat. Th block i * d Calculation povid th cunt fnc i * d fom th oto flux fnc though th Equation (3.38). Th block ω and ω Etimato pnt th popod oto pd and ynchonou pd timato, and i implmntd by quation (3.27) and (3.26) pctivly. Th block IM pnt th induction moto. All th lctical, mchanical and contoll paamt a givn in th appndic ω m * ω m Tim in c Fig 4.6 Rfnc and Ral oto pd ignal (ad/c) Th imulation ult a hown though vaiou figu. Figu.4.6 how th did oto pd (dahd lin) and th al oto pd (olid lin). Th moto i

71 allowd to tat fom a tandtill tat and th oto pd to follow th pd command that tat fom zo and acclat until th oto pd i 90ad/. Th ytm tat with an initial load toqu T L =50Nm, and at tim t=1 th load toqu tp to T L =100Nm. Fom th figu it i obvd that th oto pd tack th did pd in pit of ytm unctainti. Th pd tacking i not affctd by th load toqu chang at th tim t=1, bcau whn th liding ufac i achd (liding mod) th ytm bcom innitiv to th bounday xtnal ditubanc. Fig 4.7 Stato cunt i a (A) Th fig 4.7 how th cunt of on tato winding. Thi figu how that in th initial tat, th cunt ignal pnt a high valu bcau it i ncay a high toqu to incmnt th oto pd. In th contant pd gion, th moto toqu only ha to compnat th fiction and th load toqu and o, th cunt i low. Finally, at tim t = 1 th cunt inca bcau th load toqu ha bn incad

72 Fig 4.8 Moto toqu (Nm) Fig. 4.8 how th moto toqu. A in th ca of th cunt (Fig. 4.2), th moto toqu ha a high initial valu pd in th acclation zon, thn th valu dca in a contant gion and finally inca du to th load toqu incmnt. Fig 4.9 Stato cunt i d (A)

73 Fig 4.10 Stato cunt i q (A) In thi figu 4.8 it may b n that in th moto toqu appa th o-calld chatting phnomnon, howv, thi high fquncy chang in th toqu will b filtd by th mchanical ytm intia. Fig. 4.9 and 4.10 how th tato cunt in th otating fnc fam. A may b obvd in th figu, both cunt pnt an initial pak at th bginning, a it i uual in th tating of moto. Thn th cunt, i d, coponding to th fild componnt, main contant. On th oth hand, th cunt i q, coponding to th toqu componnt, vai with th toqu; that i, pnt a high initial valu in th acclation zon, thn th valu dca in a contant gion and finally inca du to th load toqu incmnt

74 Fig 4.11 Roto flux ψ d (Wb) Fig 4.12 Roto flux ψ q (Wb) Fig and 4.12 how th timatd oto flux in th tationay fnc fam. A may b obvd th oto flux tat fom zo and inca until th nominal valu

75 4.3 SIMULATION RESULTS UNDER LOAD TORQUE VARIATION: Thi figu no 4.13 i th al and fnc pd with a load toqu vaiation fom 50 Nm to 100 Nm thn at tim of 0.3 c th pd fnc chang fom 90 ad/ to 120 ad/. Thi how th did oto pd with dahd lin and th al oto pd with olid lin. Whn th pd fnc tp to 0.3 c th moto can not follow thi fnc intantanouly du to th phyical limitation of th ytm. Howv, aft a tanitoy tim in which th moto acclat until th final pd tajctoy tacking i obtaind. Fig 4.13 fnc and al oto pd ignal (ad/)

76 Fig 4.14 Stato cunt i a (A) Fig 4.15 Stato cunt i d (A)

77 Fig 4.16 Stato cunt i q (A) Fig 4.17 Roto flux ψ d (Wb)