STATE ESTIMATION TECHNIQUES FOR SPEED SENSORLESS FIELD ORIENTED CONTROL OF INDUCTION MOTORS

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1 SAE ESIMAION ECHNIQUES FOR SPEED SENSORESS FIED ORIENED CONRO OF INDUCION MOORS A HESIS SUBMIED O HE GRADUAE SCHOO OF NAURA AND APPIED SCIENCES OF HE MIDDE EAS ECHNICA UNIVERSIY BY BİA AKIN IN PARIA FUFIMEN OF HE REQUIREMENS FOR HE DEGREE OF MASER OF SCIENCE IN HE DEPARMEN OF EECRICA AND EECRONICS ENGINEERING AUGUS-3

2 ABSRAC SAE ESIMAION ECHNIQUES FOR SPEED SENSORESS FIED ORIENED CONRO OF INDUCION MOORS Akın, Bilal M.Sc. Depatent of Electical and Electonic Engineeing Supevio: Pof. D. Aydin Eak Augut, 3 hi thei peent diffeent tate etiation technique fo peed enolee field oiented contol of induction oto. he theoetical bai of each algoith i explained in detail and it pefoance i teted with iulation and expeient individually. Fit, a tochatical nonlinea tate etiato, Extended Kalan Filte (EKF) i peented. he oto odel deigned fo EKF application involve oto peed, dq-axi oto fluxe and dq-axi tato cuent. hu, uing thi obeve the oto peed and oto fluxe ae etiated iultaneouly. Diffeent fo the widely accepted ue of EKF, in which it i optiized fo eithe teady-tate o tanient opeation, hee uing adjutable noie level poce algoith the optiization of EKF ha been done fo both tate; the teady-tate and the tanient-tate of opeation. Additionally, the eaueent noie iunity of EKF i alo invetigated. Second, Uncented Kalan Filte (UKF), which i an updated veion of EKF, i popoed a a tate etiato fo peed enole field oiented contol of iii

3 induction oto. UKF tate update coputation, diffeent fo EKF, ae deivative fee and they do not involve cotly calculation of Jacobian atice. Moeove, vaiance of each tate i not aued Gauian, theefoe a oe ealitic appoach i povided by UKF. In thi wok, the upeioity of UKF i hown in the tate etiation of induction oto. hid, Model Refeence Adaptive Syte i tudied a a tate etiato. wo diffeent ethod, back ef chee and eactive powe chee, ae applied to MRAS algoith to etiate oto peed. Finally, a flux etiato and an open-loop peed etiato cobination i eployed to obeve tato-oto fluxe, oto-flux angle and oto peed. In flux etiato, voltage odel i aited by cuent odel via a cloed-loop to copenate voltage odel diadvantage. Keywod: Induction oto dive, enole field-oiented contol, tate etiation, EKF, UKF, MRAS iv

4 ÖZ HIZ DUYAÇSIZ AAN YÖNENDİRMEİ ENDÜKSİYON MOOR DENEİMİNDE DURUM AHMİN EKNİKERİ Akın, Bilal Yükek ian, Elektik ve Elektonik Mühendiliği Bölüü ez Danışanı : Pof. D. Aydın Eak Ağuto,3 Bu çalışada hız duyaçız alan yönlendieli endükiyon oto denetiinde uygulaaya yönelik duu tahin yöntelei geliştiilişti. Sunulan tü yöntelein kuaal içeiği ayıntılı olaak aaştıılış ve bu yöntelein başaılaı benzeti yoluyla ve deneyel olaak tet edilişti. İlk olaak, doğual olayan itelede duu tahini için geliştiiliş olan EKF yöntei ele alınıştı. Bu yöntee uyalanan oto odeli, oto hızı, oto akılaı ve oto akılaı aynı anda bilikte tahin edileye yönelik olaak taalanıştı. Genellikle EKF başaıı ya kaalı-duu ya da geçici-duu için ayı ayı olaak en iyilendiileye çalışılı. Buada kullanılan ANP yönteiyle detekleneek EKF nin başaıı he kaalı-duuda he geçici-duuda bilikte en iyileştiilişti. Ek olaak EKF yönteinin ölçü hatalaına olan duyalılığıda tet edilişti. EKF ye ek olaak EKF nin geliştiiliş bi veiyonu olan UKF yöntei, endükiyon otolaında bi duu tahin tekniği olaak unuluştu. UKF yönteinde itei doğual yapak için uygulanan tüev ala yöntelei ve bu yöntele için geekli olan ve heaplaalaı zolaştıan bazı baaakla v

5 kullanılaıştı. Ayıca UKF odeli beliizliklei geçeğe daha yakın bi tazda heapla. UKF nin bu ütün özellikleinin oto duu tahinine naıl olulu yanıdığı göteilişti. Bunlaa ek olaak MRAS yöntei de oto hız tahini için endükiyon akinei odeline uyalanıştı. Bunun için MRAS odeli gei belee ve eaktif güç yöntelei şeklinde iilendiilen iki faklı algoita ile deneniş ve hız tahini bu algoitalala yapılıştı. Son olaakta, geliştiiliş bi akı tahin yöntei ve bi açık döngülü hız tahin yöntei duu tahini için uygulanıştı. Bu yöntelele, tato-oto akılaını, oto hızını ve oto açıını heaplaak ükündü. Buada kullanılan akı tahin yönteinde geili yöntei olaak bilinen akı tahin yöntei akı odeli ile kapalı bi döngü ayeinde deteklenişti. Anahta Keliele : Endükiyon oto üücüü, enöüz alan yönlendieli kontol, duu tahini, EKF, UKF, MRAS vi

6 ACKNOWEDGMENS I would like to expe y incee gatitude to y upevio Pof. D. Aydin Eak fo hi encouageent and guidance thoughout the tudy. I alo thank hi not only fo hi technical ait but fo hi fiendhip in due coue of developent of the thei. Alo, I thank M. Uut Ogune and D. Ahet Hava fo thei technical advice and continuou uppot duing y tudie. Finally, y pecial thank go to M. Günay Şiek, M. Eay Özçelik, M. Etan Muat and übitak Bilten PEG Goup fo thei help duing the expeiental tage of thi wok. vii

7 ABE OF CONENS ABSRAC...iii ÖZ... v ACKNOWEDGEMENS... vii ABE OF CONENS...viii IS OF ABES... xii IS OF FIGURES...xiii IS OF SYMBOS... xii CHAPER.INRODUCION.... OVERVIEW of HE CHAPERS....IERARURE REVIEW INDUCION MACHINE CONRO FOC OF INDUCION MACHINE IFOC DFO....3 VARIABE SPEED CONRO USING ADVANCED CONRO AGORIHMS....4 CONCUSIONS INDUCION MACHINE MODEING AND FOC SIMUAION HE INDUCION MOOR PHYSICA AYOU MAHEMAICA MODE OF INDUCION MOOR HREE-PHASE RANSFORMAIONS CARK RANSFORMAION CIRCUI MODE OF A HREE-PHASE INDUCION... MOOR... 3 viii

8 3.4 MACHINE MODE IN ARBIRARY dq REFERENCE FRAME dq VOAGE EQUAIONS dq FUX INKAGE REAIONS dq ORQUE EQUAIONS dq SAIONARY and SYNCHRONOUS REFERENCE FRAMES SIMUAION OF IND. MOOR IN SAIONARY FRAME SIMUAION OF FOC DEVEOPED IN SAIONARY REFERENCE FRAME PUSEWIDH MODUAION with SPACE VECOR HEORY 4. INVERERS VOAGE SOURCE INVERER VOAGE SPACE VECORS SPACE VECOR MODUAIONS SVPWM APPICAION O HE SAIC POWER BRIDGE and IMPEMENAION USING DSP PAFORM EVEN MANAGER CONFIGURAION OF DSP FOR SVPWM SIMUAION and EXPERIMENA RESUS of SVPWM KAMAN FIER SENSORESS CONRO OBSERVERS GENERA HEORY ON OBSERVERS KAMAN FIER EXENDED KAMAN FIER APPICAION OF HE EXENDED KAMAN FIER MOOR MODE FOR EKF DISCREIZED AUGMENED MACH. MODE IMPEMENAION OF HE DISCREIZED EKF AGORIHM SAE ESIMAION SIMUAION with EKF UNCENED KAMAN FIER SIMUAION RESUS ix

9 5.6. EXPERIMENA RESUS MODE REFERENCE ADAPIVE SYSEMS ADAPIVE CONRO MODE REFERENCE ADAPIVE SYSEMS INRODUCION O MRAS PRACICE in MOOR CONRO APPICAIONS APPICAION of POPOV HYPERSABIIY HEOREM and INEGRA INEQUAIY BACK EMF MRAS SCHEME ADAPAION MECHANISMS and SABIIY of MRAS REACIVE POWER MRAS SCHEME REFERENCE MODE CONINUOUS IME REPRESENAION ADAPIVE MODE CONINUOUS IME REPRESENAION DICREE IME REPRESENAION fo MICROCONROER IMPEMENAION REFERENCE MODE ADAPIVE MODE PU DICREE IME REPRESENAION REFERENCE MODE ADAPIVE MODE SIMUAION OF HE MRAS SCHEME EXPERIMENA RESUS FUX and SPEED OBSERVERS FOR SENSORESS DFO FUX OBSERVER OPEN OOP SPEED OBSERVER EXPERIMENA RESUS HE HARDWARE & SOFWARE HARDWARE OVERVIEW HE MOOR HE MOOR DRIVE... 5 x

10 8..3 HE DSP HE INERFACE CARD SOFWARE OVERVIEW SOFWARE ORGANIZAION BASE VAUES and PU MODE FIXED POIN ARIHMEIC FOC SOFWWARE MODUES CONCUSION and FUURE WORK FUURE WORK REFERENCES... 7 APPENDICES A S FUNCION M FIE B HYPERSABIIY HEORY C INERFACE CARD SCHEMAICS... 8 D OBSERVER PERFORMANCE ES CODE xi

11 IS OF ABES ABE 3. Induction Machine Equation in Abitay Refeence Fae Induction Machine Equation in Stationay Refeence Fae Induction Machine Equation in Synchonouly Rotating Refeence Fae Powe Bidge Output Voltage Stato Voltage in (α-β) fae and elated Voltage Vecto Aigned duty cycle to the PWM output Dicete Kalan Filte Moto Paaete... 5 xii

12 IS OF FIGURES FIGURE. Phao Diaga of the Field Oiented Dive Syte Field Oiented induction Moto Dive Syte Indiect Field Oiented Dive Syte Diect Field Oiented Dive Syte Relationhip between the αβ abc quantitie Relationhip between the dq and the abc quantitie Relationhip between the qd and the abc quantitie Relationhip between abc and abitay dq Equivalent cicuit epeentation of an induction achine in the abitay efeence fae Equivalent cicuit of an induction achine in the tationay fae Equivalent cct. of an induction ach. in the ynchonouly otating fae A iulation of 3-phae AC quantitie conveted to both tationay fae (iq,id) and ynchonouly otating fae(iqe,ide) No-oad Repone of Stationay Fae Induction Moto Model Open-loop toque-peed cuve of the induction oto odel at no-load Pole path of ( w/ ech) fo no-load to twice the ated toque Root locu of ( w/ vqe) fo vaying gain Root locu of ( e/ vqe) fo vaying gain Step epone of w (pu) to one volt change in vqe Step epone of w (pu) to unit change in load Applied echanical toque, oto peed and poduced electoagnetic toque Synchonou fae dq axi cuent... 4 xiii

13 3.8 Phae-A tato voltage and cuent dq axi oto fluxe and oto flux Refeed oto cuent Fou quadant peed eveal and phae voltage Fou quadant peed eveal and phae voltage Fou-quadant peed eveal and poduced toque due to inetia Fou-quadant peed eveal and oto flux wave-fo Cicuit diaga of thee phae VSI hee phae invete with witching tate Eight witching tate topologie of a voltage ouce invete Fit witching tate V (pnn) Repeentation of topology in (α-β) plane Non-zeo voltage vecto in (α-β) plane Repeentation of the zeo voltage vecto in (α-β) plane Output voltage vecto (V) in (α-β) plane Output line voltage in the tie doain Synthei o the equied output voltage vecto in ecto Phae gating ignal in Sy. Seq. SVM Powe Bidge Voltage Vecto Pojection of the efeence Voltage Vecto Secto 3 PWM Patten and Duty Cycle Dead tie band SVPWM Algoith Siulation Siulated wavefo of duty cycle, ( taon, tbon,tcon ) Secto nube of voltage vecto Duation of two ecto bounday vecto (t,t) he pojection of the Va, Vb and Vc of the efeence voltage vecto in the (a b c) plane -(X, Y, Z) A typical line to line voltage output of SVPWM SVPWM output with the ignal apled (=.4) SVPWM output with the ignal apled (=.6)-Zooed Duty cycle of PWM xiv

14 4.6 ow-pa filteed fo of PWM pule Secto nube of the efeence voltage Duation of two bounday vecto (t,t) Pojection vecto in abc plain (X,Y in tie doain) ypical phae cuent of an induction oto diven by SVPWM unde heavy load condition Block diaga of an obeve Block Diaga of Kalan Filte High Speed, No-oad, Fou Quadant Speed Etiation with EKF High Speed, No-oad, Fou Quadant Speed Etiation with EKF at Steady State High Speed, No-oad, Speed Etiation with EKF Steady State Pefoance Optiized ow Speed, No-oad, Fou Quadant Speed Etiation with EKF ow Speed, No-oad, Speed Etiation with EKF at Steady State to anient State High Speed, Full-oad, Speed Etiation with EKF High Speed, No-oad, Speed Etiation uing EKF with Adjutable Noie evel Etiated State in (5.8) Repectively at No oad State I & II (dq-axi Stato Cuent) State III & IV (dq-axi Roto Fluxe with thei agnitude) Injected noie to the tato cuent in pu Etiated oto peed with eaued noiy cuent Induction oto actual tate at no load fou quadant high peed eveal Induction oto etiated tate with UKF at no load fou quadant high peed eveal Induction oto etiated peed at no-load fou quadant high peed eveal Induction oto etiated peed at no-load fou quadant low peed eveal Induction oto etiated tate at % ated toque and peed Induction oto etiated peed at % ated toque and peed Induction oto etiated peed at % ated toque and peed Induction oto etiated peed optiized fo teady tate pefoance at xv

15 % ated toque and peed uing EKF and UKF Induction oto etiated peed optiized fo tanient pefoance at % ated toque and peed uing EKF and UKF he etiated tate I&II by EKF and the eaued tate I&II he etiated tate II&III by EKF and the agnitude of the oto flux Roto peed tacking pefoance of EKF obtained expeientally he etiated tate I&II by EKF and the eaued tate I&II he etiated tate II&III by UKF and the agnitude of the oto flux Roto peed wavefo obtained expeientally by UKF and EKF unde the ae expeiental condition Geneal paallel MRAS chee Genealized Model Refeence Adaptive Syte MRAS baed peed etiato chee uing pace vecto Equivalent non-linea feedback yte Coodinate in tationay efeence fae Stuctue of the MRAS yte fo peed etiation Equivalent nonlinea feedback yte of MRAS Syte tuctue of oto peed obeve uing the tuning ignal I he Siulink odel of back ef MRAS chee he Siulink odel of eactive powe MRAS chee Fou-quadant peed eveal of 5 hp induction oto uing eactive powe MRAS chee at no_load up to ated peed Fou-quadant peed eveal of hp induction oto uing eactive powe MRAS chee at no_load up to ated peed hp induction oto peed etiation hp induction oto etiated peed peed uing eactive powe MRAS chee, applied toque and tato q-axi cuent hp induction oto etiated peed uing eactive powe MRAS chee, applied toque and tato q-axi cuent A typical etiated peed uing back ef MRAS chee Roto peed etiated by MRAS expeientally at no-load by back ef chee Speed tacking of the back ef MRAS chee xvi

16 7. (a) tato phae cuent unde heavy load condition (b) tato phae cuent unde no-load condition (c) tato phae voltage dq-axi oto fluxe in tationay fae obtained fo cuent odel dq-axi tato fluxe in tationay fae obtained fo the cuent odel he dq-axi tato fluxe in tationay fae obtained fo the voltage odel Back ef with added copenating voltage dq-axi tationay fae oto fluxe econtucted by voltage odel q-axi tationay fae oto flux econtucted by voltage odel with oto flux agnitude Roto flux angle baed on voltage odel Refeence peed and etiated peed Refeence peed and etiated peed Oveall hadwae configuation of the thei Appoxiate pe Phae Equivalent Cicuit fo an Induction Machine Diaga of dc eaueent Dc_link Cicuit Oveall Diaga of the Invete Expeiental etup (Inteface cad, DSP and invete) Inteface cad Softwae Flowchat Oveall FOC Algoith iing Speed Senole FOC of Induction Moto Syte Block Diaga Showing Softwae Module xvii

17 IS OF SYMBOS SYMBO e d e q i e d i e q i d i q i a i b i c i a i b i c l l R R q d q q e V a V b V c back ef d axi coponent back ef q axi coponent d axi tato cuent in ynchonou fae q axi tato cuent in ynchonou fae d axi tato cuent in tationay fae q axi tato cuent in tationay fae Phae-a oto cuent Phae-b oto cuent Phae-c oto cuent Phae-a tato cuent Phae-b tato cuent Phae-c tato cuent Magnetizing inductance Stato leakage inductance Roto leakage inductance Stato elf inductance Roto elf inductance Stato eitance Refeed oto eitance eactive powe d axi coponent eactive powe q axi coponent Electoechanical toque Roto tie contant Phae-a tato voltage Phae-b tato voltage Phae-c tato voltage xviii

18 V a V b V c V d V q V e d V e q V dc X X l X l X X w e w w l θ e θ d θ q θ ψ ψ d ψ q ψ e d ψ e q ψ a ψ b ψ c ψ a ψ b ψ c Phae-a oto voltage Phae-b oto voltage Phae-c oto voltage d axi tato voltage in tationay fae q axi tato voltage in tationay fae d axi tato voltage in ynchonou fae q axi tato voltage in ynchonou fae Dc-link voltage Stato agnetizing eactance Stato leakage eactance Roto leakage eactance Stato elf eactance Roto elf eactance Angula ynchonou peed Angula oto peed Angula lip peed Angle between the ynchonou fae and the tationay fae Angle between the ynchonou fae and the tationay fae when d axi i leading Angle between the ynchonou fae and the tationay fae when q axi i leading Roto flux angle d axi tato flux in tationay fae q axi tato flux in tationay fae d axi tato flux in ynchonou fae q axi tato flux in ynchonou fae Phae-a tato flux Phae-b tato flux Phae-c tato flux Phae-a oto flux Phae-b oto flux Phae-c oto flux xix

19 CHAPER INRODUCION Induction oto ae elatively ugged and inexpenive achine. heefoe uch attention i given to thei contol fo vaiou application with diffeent contol equieent. An induction achine, epecially quiel cage induction achine, ha any advantage when copaed with DC achine. Fit of all, it i vey cheap. Next, it ha vey copact tuctue and inenitive to envionent. Futheoe, it doe not equie peiodic aintenance like DC oto. Howeve, becaue of it highly non-linea and coupled dynaic tuctue, an induction achine equie oe coplex contol chee than DC oto. aditional open-loop contol of the induction achine with vaiable fequency ay povide a atifactoy olution unde liited condition. Howeve, when high pefoance dynaic opeation i equied, thee ethod ae unatifactoy. heefoe, oe ophiticated contol ethod ae needed to ake the pefoance of the induction oto copaable with DC oto. Recent developent in the aea of dive contol technique, fat eiconducto powe witche, poweful and cheap icocontolle ade induction oto altenative of DC oto in induty. he ot popula induction oto dive contol ethod ha been the field oiented contol (FOC) in the pat two decade. Futheoe, the ecent tend in FOC i towad the ue of enole technique that avoid the ue of peed eno and flux eno. he eno in the hadwae of the dive ae eplaced with tate obeve to iniize the cot and inceae the eliability.

20 hi wok i ainly focued on the tate obeve to etiate the tate that ae ued in the FOC algoith fequently. Fo thi pupoe, two diffeent Kalan Filteing technique, EKF and UKF, ae eployed to etiate oto peed and dq-axi oto fluxe. Uing thee technique, one can obtain vey pecie flux and peed infoation a hown in the iulation and expeiental eult. Futheoe, odel efeence adaptive yte (MRAS) i ued to etiate the oto peed. he back ef and the eactive powe chee ae applied to MRAS which ae upeio to the peviou MRAS chee popoed in the liteatue. In thi wok, it i alo hown that the oto peed etiation pefoance of thee chee i quite atifactoy in the iulation and expeiental eult. Finally, a cobination of well-known open loop obeve, voltage odel and cuent odel, i ued to etiate the oto flux and oto flux angle which ae eployed in diect field oientation.. Oveview of the Chapte hi thei i oganized a follow: he liteatue eview i given in Chapte. he eview ainly focued on field oiented contol, enole contol and tate obeve uch a EKF, UKF and MRAS. he peviou wok ae dicued biefly and copaed with each othe. Chapte 3 peent a genealized dynaic atheatical odel of the induction oto which can be ued to contuct vaiou equivalent cicuit odel in diffeent efeence fae. A toque-peed contol of induction achine with indiect field oientation i iulated to be failia with the FOC. Chapte 4 peent the theoetical backgound of pace vecto pule width odulation (SVPWM) in detail. DSP ipleentation of SVPWM i alo given in thi pat. Moeove, the iulation and the expeiental eult of SVPWM ae illutated. Chapte 5 i devoted to Kalan filteing technique. Fit the theoetical bae of EKF i given in detail. he dicetized odel of the oto, which i applied to EKF, i tudied fo icocontolle ipleentation. Aftewad, deivative fee, non-linea tate etiato technique, UKF, i peented and copaed with EKF. he pefoance of each technique i confied by iulation and expeiental eult.

21 In Chapte 6, MRAS ethod i intoduced to etiate the oto peed. wo diffeent chee ae applied to MRAS fo thi tak. he tability analyi and dicetized fo of both chee ae given fo icocontolle ipleentation. he pefoance of thee chee i exained unde vaying condition in iulation. he iulation ae uppoted with the expeiental eult. Chapte 7 uaize the developent of a flux etiato with a well known peed etiato. he oiginality of the flux etiato i ephaized and expeiental eult ae added fo both etiato. Chapte 8 intoduce the expeiental etup and the oftwae of thi thei biefly. Chapte 9 uaize the thei and conclude with the contibution aociated with the obevation technique eployed in FOC. 3

22 CHAPER IERAURE REVIEW An induction achine, a powe convete and a contolle ae the thee ajo coponent of an induction oto dive yte. Soe of the dicipline elated to thee coponent ae electic achine deign, electic achine odeling, ening and eaueent technique, ignal poceing, powe electonic deign and electic achine contol. It i beyond the cope of thi eeach to adde all of thee aea: it will piaily focu on the iue elated to the induction achine contol. A conventional low cot volt pe hetz o a high pefoance field oiented contolle can be ued to contol the achine. hi chapte eview the pinciple of the field oientation contol of the induction achine and outline ajo poble in it deign and ipleentation.. Induction Machine Contol he contolle equied fo induction oto dive can be divided into two ajo type: a conventional low cot volt pe hetz v/f contolle and toque contolle []-[4]. In v/f contol, the agnitude of the voltage and fequency ae kept in popotion. he pefoance of the v/f contol i not atifactoy, becaue the ate of change of voltage and fequency ha to be low. A udden acceleation o deceleation of the voltage and fequency can caue a tanient change in the cuent, which can eult in datic poble. Soe effot wee ade to ipove v/f contol pefoance, but none of thee ipoveent could yield a v/f toque contolled dive yte and thi ade DC oto a poinent choice fo vaiable peed application. hi began to change when the theoy of field oientation wa intoduced by Hae 4

23 and Blachke. Field oientation contol i conideably oe coplicated than DC oto contol. he ot popula cla of the ucceful contolle ue the vecto contol technique becaue it contol both the aplitude and phae of AC excitation. hi technique eult in an othogonal patial oientation of the electoagnetic field and toque, coonly known a Field Oiented Contol (FOC).. Field Oientation Contol of Induction Machine he concept of field oientation contol i ued to accoplih a decoupled contol of flux and toque. hi concept i copied fo dc achine diect toque contol that ha thee equieent [4]: An independent contol of aatue cuent to ovecoe the effect of aatue winding eitance, leakage inductance and induced voltage; An independent contol of contant value of flux; If all of thee thee equieent ae et at evey intant of tie, the toque will follow the cuent, allowing an iediate toque contol and decoupled flux and toque egulation. Next, a two phae d-q odel of an induction achine otating at the ynchonou peed i intoduced which will help to cay out thi decoupled contol concept to the induction achine. hi odel can be uaized by the following equation (ee chapte 3 fo detail): v e q = pψ 3P e q + w ψ e e d + i e q e e e e ( ψ' i ψ' i ) 5 (.) e e e e v d = pψ d w eψ q + i d (.) ψ ψ ψ e = p e q + (w e e w ) d + i q (.3) ψ ψ e = p e d (w e e w ) q + i d (.4) e e e q = iq + i' q e d e d e d (.5) ψ = i + i' (.6) e e e ψ q = iq + i' q (.7) e e e ψ d = id + i' d (.8) e = (.9) d q q d = Jpw + Bw + (.) e and it i quite ignificant to yntheize the concept of field-oiented contol. In thi odel it can be een fo the toque expeion (.9) that, if the flux along the q-axi can be ade zeo then all the flux i aligned along the d-axi and, theefoe, the

24 toque can be intantaneouly contolled by contolling the cuent along q-axi. hen the quetion will be how it can be guaanteed that all the flux i aligned along the d- axi of the achine. When thee-phae voltage ae applied to the achine, they poduce thee-phae fluxe both in the tato and the oto. he thee-phae fluxe can be epeented in a two-phae tationay (α-β) fae. If thee two phae fluxe along (α-β) axe ae epeented by a ingle-vecto then all the achine flux will be aligned along that vecto. hi vecto i coonly pecified a d-axi which ake an angle θ e with the tationay fae α-axi, a hown in Fig... he q-axi i et pependicula to the d-axi. he flux along the q-axi in thi cae will be obviouly zeo. he phao diaga Fig.. peent thee axe. When the achine input cuent change inuoidally in tie, the angle θ e keep changing. hu the poble i to know the angle the flux vecto. θ e accuately, o that the d-axi of the d-q fae i locked with β b q ψq ψβ ψ ψd d θ e ψα a,α Fig..- Phao Diaga of the Field Oiented Dive Syte he contol input can be pecified in two phae ynchonouly otating d-q fae a i e d and i e q uch that i e d being aligned with the d-axi o the flux vecto. hee twophae ynchonou contol input ae conveted into two-phae tationay quantitie and then to thee-phae tationay contol input. o accoplih thi the flux angle θ e 6

25 ut be known peciely. he angle θ e can be found eithe by Indiect Field Oientation contol (IFO) o by Diect Field Oientation contol (DFO). he contolle ipleented in thi fahion that can achieve a decoupled contol of the flux and the toque i known a field oiented contolle. he block diaga i hown in the Fig.. In the field-oiented contolle the flux can be egulated in the tato, ai-gap o oto flux oientation []-[4]. i e d + - i e q + - PI U dq - (θ) V abc PWM VSI IFO/DFO θ e IM i *e q i a i *e d (θ) i b Fig..- Field Oiented induction Moto Dive Syte he contol algoith fo calculation of the oto flux angle θe uing IFO contol i hown in the Fig.3. hi algoith i baed on the auption that, the flux along the q-axi i zeo, which foce the coand lip velocity to be w l = i e q /(.i e d ) a a neceay and ufficient condition to guaantee that all the flux i aligned with d-axi and the flux along q-axi i zeo. he angle θe can then be deteined a the u of the lip and the oto angle afte integating the epective velocitie. hi lip angle include the neceay and ufficient condition fo decoupled contol of flux and toque. he oto peed can be eaued diectly by uing an encode o can be etiated. In cae the oto peed i etiated, the contol technique i known a enole contol. hi concept will be tudied in detail in the following chapte. Fig.4. how the contol algoith block diaga fo DFO contol. In thi technique the flux angle θ e i claically calculated by ening the ai-gap flux though the ue of 7

26 flux ening coil, o can be calculated by etiating the flux along the α-β axe uing the voltage and cuent ignal. i e q i e d / /(-p ) w l + w + w e /p θ e Fig..3- Indiect Field Oiented Dive Syte i α β Flux Obeve ψ αβ / ψ αβ tan - (ψβψα) θ e v αβ Fig..4- Diect Field Oiented Dive Syte.. Indiect Field Oientation Contol In indiect field oientation, the ynchonou peed w e i the ae a the intantaneou peed of the oto flux vecto e ψ d and the d-axi of the d-q coodinate yte i exactly locked on the oto flux vecto (oto flux vecto oientation). hi facilitie the flux contol though the agnetizing cuent e i d by aligning all the flux with the d-axi while aligning the toque-poducing coponent of the cuent with the q-axi. Afte decoupling the oto flux and toque-poducing coponent of the cuent coponent, the toque can be intantaneouly contolled by contolling the cuent e i q. he equieent to align the oto flux with the d-axi of the d-q coodinate yte ean that the flux along the q-axi ut be zeo. hi ean that (.7) becoe i = ( i e q e q ) / and the cuent though the q-axi of the utual inductance i zeo. 8

27 Baed on thi etiction w l i : w i e q l = (.) e i d p hee elation ugget that flux and toque can be contolled independently by pecifying d-q axi cuent povided the lip fequency i atified (.) at all intant. he concept of indiect field oiented contol developed in the pat ha been widely tudied by eeache duing the lat two decade. he oto flux oientation i both the oiginal and uual choice fo the indiect oientation contol. Alo the IFO contol can be ipleented in the tato and ai-gap flux oientation a well. De Doncke [5] intoduced thi concept in hi univeal field oiented contolle. In the ai-gap flux the lip and flux elation ae coupled equation and the d-axi cuent doe not independently contol the flux a it doe in the oto flux oientation. Fo the contant ai-gap flux oientation, the axiu of the poduced toque i % le than that of the othe two ethod [3]. In the tato flux oientation, the tanient eactance i a coupling facto and it vaie with the opeating condition of the achine. In addition, Naa [3] how that aong thee ethod, oto flux oiented contol ha linea toque cuve. heefoe, the ot coonly ued choice fo IFO i the oto flux oientation. he IFOC i an open loop, feed-fowad contol in which the lip fequency i fed-fowad guaanteeing the field oientation. hi feed-fowad contol i vey enitive to the oto open cicuit tie contant, τ. heefoe, τ ut be known in ode to achieve a decoupled contol of toque and flux coponent by contolling i e q andi e d, epectively. When τ i not et coectly, the achine i aid to be detuned and the pefoance will becoe luggih due to lo of decoupled contol of toque and flux. he eaueent of the oto tie contant, it effect on the yte pefoance and it adaptive tuning to the vaiation eulting duing the opeation of the achine have been tudied extenively in the liteatue [6-8]. oenz, Kihnan and Novotny [6-8] tudied the effect of tepeatue and atuation level on the oto tie contant and concluded that it can educe the toque capability of the achine and toque/ap of the achine. he detuning effect becoe oe evee in the field-weakening egion. Alo, it eult in a teady-tate eo and, tanient 9

28 ocillation in the oto flux and toque. Soe of the advanced contol technique uch a etiation theoy tool and adaptive contol tool ae alo tudied to etiate oto tie contant and othe oto paaete [5, 6, 9, 3, 3, 5, 6-63].. Diect Field Oientation he DFO contol and enole contol ely heavily on accuate flux etiation. DFOC i ot often ued fo enole contol, becaue the flux obeve ued to etiate the ynchonou peed o angle can alo be ued to etiate the achine peed. Invetigation of way to etiate the flux and peed of the induction achine ha alo been extenively tudied in the pat two decade. Claically, the oto flux wa eaued by uing a pecial ening eleent, uch a Hall effect eno placed in the ai-gap. An advantage of thi ethod i that additional equied paaete, l,, and ae not ignificantly affected by change in tepeatue and flux level. Howeve, the diadvantage of thi ethod i that a flux eno i expenive and need pecial intallation and aintenance. Anothe flux and peed etiation technique i aliency baed with fundaental o high fequency ignal injection. One advantage of aliency technique i that the aliency i not enitive to actual oto paaete, but thi ethod fail at low and zeo peed level. When applied with high fequency ignal injection [9], the ethod ay caue toque ipple, and echanical poble. Gabiel [] avoided the pecial flux eno and coil by etiating the oto flux fo the teinal quantitie (tato voltage and cuent). hi technique equie the knowledge of the tato eitance along with the tato, oto leakage inductance and agnetizing inductance. hi ethod i coonly known a the Voltage Model Flux Obeve (VMFO). he tato flux in the tationay fae can be etiated by the equation: ψ& ψ& d q = v i d q ψ d = ( ψ d σi d ) (.5) ψ q = ( ψ q σi q ) (.6) d = v i q hen the oto flux can be expeed a: (.3) (.4)

29 whee σ = ( / ) i the tanient leakage inductance. In thi odel, integation of the low fequency ignal, doinance of tato eitance voltage dop at low peed and leakage inductance vaiation eult in a le pecie flux etiation. Integation at low fequency i tudied by [] and thee diffeent altenative ae given. Etiation of oto flux fo the teinal quantitie depend on paaete uch a tato eitance and leakage inductance. he tudy of paaete enitivity how that the leakage inductance can ignificantly affect the yte pefoance uch a tability, dynaic epone, and utilization of the achine and the invete. he Cuent Model Flux Obeve (CMFO) i an altenative appoach to ovecoe the poble of leakage inductance and tato eitance at low peed. In thi odel flux can be etiated a: ψ& ψ& d q = = ψ ψ d q w ψ w ψ q d + + i i d q (.7) (.8) Howeve, it doe not wok well at high peed due to it enitivity to the oto eitance. Janen [] did an extenive tudy on VMFO and CMFO baed diect field oientation contol, dicued the deign and accuacy aeent of vaiou flux obeve, copaed the, and analyzed the altenative flux obeve. o futhe ipove the obeve pefoance, cloed-loop oto flux obeve ae popoed which ue the etiated tato cuent eo [-3] o the etiated tato voltage eo [3] to etiate the oto flux. Futheoe, ennat [4] popoed educed ode obeve fo thi tak..3 Vaiable Speed Contol Uing Advanced Contol Algoith hee ae two iue in otion contol uing field-oiented contolled (FOC) induction achine dive. One i to ake the eulting dive yte and the contolle obut againt paaete deviation and ditubance. he othe i to ake the yte intelligent e.g. to adjut the contol yte itelf to envionent change and tak equieent. If the peed egulation loop fail to poduce the coand cuent

30 coectly, than the deied toque epone will not be poduced by the induction achine. In addition, uch a failue ay caue the degadation of lip coand a well. A a eult, a atifactoy peed egulation i exteely ipotant not only to poduce deied toque pefoance fo the induction achine but alo to guaantee the decoupling between contol of toque and flux. Conventionally, a PI contolle ha been ued fo the peed egulation to geneate a coand cuent fo lat two decade, and accepted by induty becaue of it iplicity. Even though, a well-tuned PI contolle pefo atifactoily fo a field-oiented induction achine duing teady tate. he peed epone of the achine at tanient, epecially fo the vaiable peed tacking, ay oetie be pobleatic. In lat two decade, altenative contol algoith fo the peed egulation wee invetigated. Aong thee, fuzzy logic, liding ode, and adaptive nonlinea contol algoith gained uch attention, howeve thee contolle ae not in the cope of thi thei. A taditional oto flux-oiented induction achine dive offe a bette contol pefoance but it often equie additional eno on the achine. hi add to the cot and coplexity of the dive yte. o avoid thee eno on the achine, any diffeent algoith ae popoed fo the lat thee decade to etiate the oto flux vecto and o/ oto haft peed. he ecent tend in field-oiented contol i to ue uch algoith baed on the teinal quantitie of the achine fo the etiation of the fluxe and peed. hey can eaily be applied to any induction achine. heefoe, ou focu in thi tudy i alo on thee algoith. Befoe looking into individual appoache, the coon poble of the peed and flux etiation ae dicued biefly fo geneal field-oientation and tate etiation algoith. Paaete enitivity: One of the ipotant poble of the enole contol algoith fo the field-oiented induction achine dive i the inufficient infoation about the achine paaete which yield the etiation of oe achine paaete along with the enole tuctue. Aong thee paaete tato eitance, oto eitance and oto tie-contant play oe ipotant ole than the othe paaete ince thee value ae oe enitive to tepeatue change. he knowledge of the coect tato eitance, i ipotant to widen the opeation egion towad the lowe peed ange. Since at low peed the

31 induced voltage i low and tato eitance voltage dop becoe doinant, a iatching tato eitance induce intability in the yte. On the othe hand, eo ade in deteining the actual value of the oto eitance, ay caue both intability of the yte and peed etiation eo popotional to [5]. Alo, coect τ value i vital decoupling facto in IFOC. Pue Integation: he othe ipotant iue egading any of the topologie i the integation poce inheited fo the induction achine dynaic whee an integation poce i needed to calculate the tate vaiable of the yte. Howeve, it i difficult both to decide on the initial value, and pevent the dift of the output of a pue integato. Uually, to ovecoe thi poble a low-pa filte eplace the integato. Ovelapping-loop Poble: In a enole contol yte, the contol loop and the peed etiation loop ay ovelap and thee loop influence each othe. A a eult, output of both of thee loop ay not be deigned independently; in oe bad cae thi dependency ay influence the tability o pefoance of the oveall yte. he algoith, whee teinal quantitie of the achine ae ued to etiate the fluxe and peed of the achine, ae categoized in two baic goup. Fit one i "the open-loop obeve," in a ene that the on-line odel of the achine doe not ue the feedback coection. Second one i "the cloed-loop obeve" whee the feedback coection i ued along with the achine odel itelf to ipove the etiation accuacy. hee two baic goup can alo be divided futhe into ubgoup baed on the contol ethod ued. hee can be uaized a: Open-loop obeve baed on; - Cuent odel, - Voltage odel, - Full-ode obeve, 3

32 Cloed loop obeve baed on; - Model Refeence Adaptive Syte (MRAS), - Kalan filte technique, - Adaptive obeve baed on both voltage and cuent odel, - Neual netwok flux and peed etiato, - Sliding ode flux and peed etiato. Open-loop obeve, in geneal, ue diffeent fo of the induction achine diffeential equation. Cuent odel baed open-loop obeve []-[4] ue the eaued tato cuent and oto velocity. he velocity dependency of the cuent odel i vey ipotant ince thi ean that although uing the etiated flux eliinate the flux eno, the poition eno i till equied. On the othe hand, voltage odel baed open-loop obeve []-[4] ue the eaued tato voltage and cuent a input. hee type of etiato equie a pue integation that i difficult to ipleent fo low excitation fequencie due to the offet and initial condition poble. Cancellation ethod open-loop obeve can be foed by uing eaued tato voltage, tato cuent and oto velocity a input, and ue the diffeentiation to cancel the effect of the integation. Howeve, it uffe fo two ain dawback. One i the need fo the deivation which ake the ethod oe uceptible to noie than the othe ethod. he othe dawback i the need fo the oto velocity iila to cuent odel. A full-ode open-loop obeve, on the othe hand, can be foed uing only the eaued tato voltage and oto velocity a input whee the tato cuent appea a an etiated quantity. Becaue of it dependency on the tato cuent etiation, the full ode obeve will not exhibit bette pefoance than the cuent odel. Futheoe, paaete enitivity and obeve gain ae the poble to be tuned in a full ode obeve deign [6]. hee open-loop obeve tuctue ae all baed on the induction achine odel, and they do not eploy any feedback. heefoe, they ae quite enitive to paaete vaiation, which yield the etiation of oe achine paaete along with the enole tuctue. On the othe hand, oe kind of feedback ay be helpful to poduce oe obut tuctue to paaete vaiation. Fo thi pupoe any cloed-loop topologie ae popoed uing diffeent induction achine odel and contol ethod. Aong thee MRAS attact attention and eveal diffeent algoith ae 4

33 poduced. In MRAS, in geneal, a copaion i ade between the output of two etiato. he etiato which doe not contain the quantity to be etiated can be conideed a a efeence odel of the induction achine. he othe one which contain the etiated quantity, i conideed a an adjutable odel. he eo between thee two etiato i ued a an input to an adaptation echani. Fo enole contol algoith ot of the tie the quantity which diffe the efeence odel fo the adjutable odel i the oto peed. he etiated oto peed in the adjutable odel i changed in uch a way that the diffeence between two etiato convege to zeo ayptotically, and the etiated oto peed will be equal to actual oto peed. he baic of the analyi and deign of MRAS ae dicued in [, 7]. In [5, 8, 9] voltage odel i aued a efeence odel, cuent odel i aued a the adjutable odel and etiated oto flux i aued a the efeence paaete to be copaed. In [] iila peed etiato ae popoed baed on the MRAS, and a econday vaiable i intoduced a the efeence quantity by letting the oto flux though a fit-ode delay intead of a pue integation to nullify the offet. Howeve, thei algoith poduce inaccuate etiated peed if the excitation fequency goe below cetain level. In addition thee algoith uffe fo the achine paaete uncetaintie ince the paaete vaiation in the efeence odel cannot be coected. [9, ] ugget an altenative MRAS baed on the electootive foce athe than the oto-flux a efeence quantity fo peed etiation whee the integation poble ha been ovecoe. Futhe in [], anothe new auxiliay vaiable i intoduced which epeent the intantaneou eactive powe fo aintaining the agnetizing cuent. In thi MRAS algoith tato eitance diappea fo the equation aking the algoith obut to that paaete. Zhen [] popoed an inteeting MRAS tuctue that i built with two utual MRAS chee. In thi tuctue, the efeence odel and the adjutable odel ae intechangeable. Fo oto peed etiation, one odel i ued a efeence odel and othe odel i ued a adjutable odel. he pue integation i eoved fo efeence odel. Fo tato eitance etiation the odel witch thei ole. [3-4] uppoted the MRAS chee with ANN uing it taining and odeling of non-linea yte. MRAS chee i alo ued fo the on-line adaptation of the oto paaete in field oiented contol technique [5-6]. Kalan filte (KF) i anothe ethod eployed to identify the peed and oto-flux of an induction achine baed on the eaued quantitie uch a tato 5

34 cuent and voltage [7,8]. Kalan filte appoach i baed on the yte odel and a atheatical odel decibing the induction oto dynaic fo the ue of Kalan filte application. Paaete deviation and eaueent ditubance ae taken into conideation in KF. Fo thi pupoe covaiance atice of the KF ut be popely initialized. KF itelf wok fo linea yte, o fo non-linea induction oto odel extended Kalan filte (EKF) i ued. Howeve, KF appoach i coputationally intenive and depend on the accuacy of the odel of the oto. In the EKF odel popoed by [8], one can etiate oto fluxe and oto peed which ake the field oientation. EKF i alo ued fo online paaete etiation of induction oto [9-3]. Reduced ode odel ae alo popoed to hoten and peed up the coplex EKF algoith [3]. A new KF technique fo non-linea yte, Uncented Kalan Filte (UKF), i applied to induction achine tate etiation in thi thei [33]. UKF i a deivative fee KF technique which avoid cotly calculation of Jacobian atix, lineaization and biaedne of the etiate [34-36]. Anothe ethod ued fo the enole contol of induction oto i the neual netwok technique, which i baed on a leaning poce. It ha the advantage of toleating achine paaete uncetaintie. Fo peed etiation, a two-layeed neual netwok, baed on back popagation technique, i ued and the neual netwok output ae copaed with the actual eaueent value and eo then backpopagated to adjut the weight uch that the etiated peed convege to actual one. he neual netwok baed enole contol algoith have the advantage of fault-toleant chaacteitic. Howeve, becaue of the neual netwok leaning poce thee algoith ay uffe fo the coputational intenity. Anothe appoach i liding ode contol fo FOC of induction achine. In the liding ode technique, the contol action i vey tong and being witched into eithe on o off at high fequency. he coand ignal contol diectly the powe device. hi type of contol i alo favoable becaue on-off i the only adiible ode of opeation fo the powe convete. heefoe, it ee oe natual to eploy the algoith towad dicontinuou contol. In addition to the algoith entioned above, oe of the popoed wok i had to claify becaue of thei cobined tuctue. Fo intance, [37-38] popoe open-loop obeve tuctue baed on voltage odel of the induction achine and attept to avoid integation poble by uing diffeent low-pa filte tuctue. On 6

35 the othe hand, oe wok ue both voltage and cuent odel of the induction achine to contuct an open-loop obeve tuctue and clai that oto-flux etiation i inenitive to oto tie-contant vaiation. In [39], a nonlinea highgain obeve tuctue i popoed, and it i claied that with the exact knowledge of tato eitance, flux and peed etiation convegence i guaanteed..4 CONCUSIONS he liteatue eview of DFOC, IFOC, flux, poition and velocity etiation and peed contol can be uaized a: he DFOC and IFOC ae the ethod fo intantaneou toque and peed contol of an induction oto dive yte. hee ethod can be ipleented with o without a peed eno. An IFOC i yntheized by popely contolled lipfequency which i neceay fo the field-oientation. he ain poble of an IFO dive yte i the oto tie-contant deviation. he dive yte toque contol pefoance deceae if the oto tie-contant i not et peciely. heefoe, on-line etiation i neceay and i one of the ain challenge fo bette pefoance of an IFOC. Mot of the technique popoed o fa eithe need oe pecial hadwae o ae vey coplex with epect to the oftwae and equie intenive calculation which put exta buden on the poceo. he ain poble in DFO contol i pecie oto flux o poition obevation. hi obevation fo teinal quantitie i oe deiable than the one including additional hadwae. Voltage odel and cuent odel flux obeve ae the two ot coon way to etiate the flux uing the teinal quantitie. he voltage odel flux obeve i doinated by tato IR dop at low peed, wheea the cuent odel flux obeve ha poble of oto tie contant vaiation. Alo the cuent odel flux obeve equie the oto peed. heefoe, if the flux obeve i being ued fo the enole contol, an eo in the etiated peed will be fed back in to the yte. hu will affect the obeve accuacy. he popoed open-loop obeve can be iple in the tuctue but they ae uceptible to vaiety of eo that becoe pecially detiental at low tato 7

36 fequencie, including eaueent, noie digital appoxiation eo, paaete detuning and DC offet in eaueent, which ultiately ay dive the obeve intability. Fo the tie-vaying yte odel poble, cloed-loop obeve ae popoed hee feedback coection i ued along with the achine odel itelf to ipove the etiation accuacy. he algoithic coplexity and calculation intenity look highe when copaed with foe olution but the ecent poceo ae fat enough to olve thee algoith in eal-tie application. hey alo equie a tong atheatical backgound to deal with. hei tate etiation pefoance i tudied in any application and they ae poved to be good altenative fo high pefoance ac dive aea. 8

37 CHAPER 3 INDUCION MACHINE MODEING AND FOC SIMUAION 3. he Induction Moto he two nae fo the ae type of oto, Induction oto and Aynchonou oto, decibe the two chaacteitic in which thi type of oto diffe fo DC oto and ynchonou oto. Induction efe to the fact that the field in the oto i induced by the tato cuent, and aynchonou efe to the fact that the oto peed i not equal to the tato fequency. No liding contact and peanent agnet ae needed to ake an induction oto wok, which ake it vey iple and cheap to anufactue. A oto, they ugged and equie vey little aintenance. Howeve, thei peed ae not a eaily contolled a with DC oto. hey daw lage tating cuent, and opeate with a poo lagging facto when lightly loaded. 3.. Contuction of the hee Phae Induction Moto (Phyical ayout) Mot induction oto ae of the otay type with baically a tationay tato and a otating oto. he tato ha a cylindical agnetic coe that i houed inide a etal fae. he tato agnetic coe i foed by tacking thin electical teel laination with unifoly paced lot taped in the inne cicufeence to accoodate the thee ditibuted tato winding. he tato winding ae foed by connecting coil of coppe o aluinu conducto that ae inulated fo the lot wall. he oto conit of a cylindical lainated ion coe with unifoly paced peipheal lot to accoodate the oto winding. In thi thei a quiel cage oto 9

38 induction oto i ued. It ha unifoly paced axial ba that ae oldeed onto end ing at both end. Afte the oto coe laination ae tacked in a old, the old i filled with olten aluinu. hee i no inulation between the ba and all of the oto lot. 3. Matheatical Model of Induction Moto Duing the entie epot, a coplex vecto notation and oe efeence fae conveion ae ued. Since thi i quite eential to the undetanding of the et of the theoy, it will hotly be decibed in the next ubection. 3.. hee-phae anfoation In the tudy of genealized achine theoy, atheatical tanfoation ae often ued to decouple vaiable, to facilitate the olution of difficult equation with tie vaying coefficient, o to efe all vaiable to a coon efeence fae [39]. he ot coonly ued tanfoation i the polyphae to othogonal twophae (o two-axi) tanfoation. Fo the n-phae to two-phae cae, it can be expeed in the fo: whee [ f xy ] = [( θ)][f,,... n ] (3.) p p p co θ co θ α...co θ (n ) α n [ ( θ)] = (3.) n p p p in θ in θ α...in θ (n ) α n and α i the electical angle between the two adjacent agnetic axe of a unifoly ditibuted n-phae winding. he coefficient tanfoation powe invaiant. / n, i intoduced to ake the Ipotant ubet of the geneal n-phae to two-phae tanfoation, though not neceaily powe invaiant, ae biefly dicued in the following pat.

39 β-axi b-axi w= a-axi α-axi c-axi 3.. Clak anfoation Fig.3.- Relationhip between the αβ abc quantitie he Clak tanfoation i baically eployed to tanfo thee-phae to two-phae quantitie. he two-phae vaiable in tationay efeence fae ae oetie denoted a α and β. A hown in Fig.3. the α-axi coincide with the phae-a axi and the β-axi lag the α-axi by 9. [ abc f αβ ] = [αβ ][f ] (3.3) whee the tanfoation atix, [ αβ ], i given by: 3 3 [ = αβ ] (3.4) 3 he invee tanfoation i: [ αβ 3 ] = (3.5) Pak anfoation he Pak tanfoation i a well-known tanfoation that convet the quantitie to to-phae ynchonouly otating fae. he tanfoation i in the fo of: [ f dq ] = [dq ( θd )][f abc ] (3.6)

40 whee the dq tanfoation atix i defined a : π + θ π θ θ π + θ π θ θ = θ 3 in 3 in in 3 co 3 co co 3 )] ( [ d d d d d d d dq (3.7) and the invee i given by: π + θ π + θ π θ π θ θ θ = θ 3 in 3 co 3 in 3 co in co )] ( [ d d d d d d d dq (3.8) whee the i the tanfoation angle. θ d he poitive q-axi i defined a leading the poitive d-axi by 9 in the oiginal Pak tanfoation. Soe autho define the q-axi a lagging the d-axi by 9.he tanfoation with q-axi lagging d-axi i given by: π + θ π θ θ π + θ π θ θ = θ 3 in 3 in in 3 co 3 co co 3 )] ( [ q q q q q q d qd (3.9) with an invee given by: π + θ π + θ π θ π θ θ θ = θ 3 in 3 co 3 in 3 co in co q)] ( [ q q q q q q qd (3.) whee i the tanfoation angle when q-axi i leading. θ q

41 he elationhip between the θ d and θq i: π θ q = θd + (3.) One can how that [ dq ]and[qd ], ae baically the ae, except fo the odeing of the d and q vaiable. Both of the altenative ae hown in Fig.3. & Fig.3.3. β-axi d-axi β-axi q-axi b-axi w=w b-axi w=w θ d a-axi θ q a-axi c-axi c-axi q-axi d-axi Fig.3.- Relationhip between the dq and the abc quantitie Fig Relationhip between the qd and the abc quantitie 3.3 Cicuit Model of a hee Phae Induction Moto Uing the coupled cicuit appoach and oto notation, the voltage equation of the agnetically coupled tato a oto cicuit can be witten a follow: Stato Voltage Equation: dψ a Va = i a + dt V dψ b Vb = i b + dt V (3.) dψ c Vc = i c + dt V Roto Voltage Equation: dψ a Va = i a + dt V dψ b Vb = i b + dt V (3.3) dψ c Vc = i c + dt V 3

42 In atix notation, the flux linkage of the tato and oto winding, in te of the winding inductance and cuent, ay be witten copactly a whee ψ ψ ψ ψ i i abc abc abc abc abc abc = = = abc abc abc abc i i t ( ψ a, ψ b, ψ c ) t ( ψ a, ψ b, ψ c ) t ( i a,i b,i c ) ( i,i,i ) t = = a b c abc abc Wb.tun (3.4) (3.5) and the upecipt denote the tanpoe of the aay. he ub-atice of the tato-to-oto and oto-to-oto winding inductance ae of the fo: abc abc l + = + = l + + l + + H (3.6) H hoe of the tato-to-oto utual inductance ae dependent on the oto angle, that i: abc π π coθ co θ + co θ 3 3 abc t [ ] π π = = co co co H θ θ θ + (3.7) 3 3 π π co θ + co θ coθ 3 3 whee l i the pe phae tato winding leakage inductance, l i the pe phae oto winding leakage inductance, i the elf inductance of the tato winding, i the elf inductance of the oto winding, i the utual inductance between tato winding, i the utual inductance between oto winding, and i the peak value of the tato to oto utual inductance. Note that the idealized achine i decibed by ix fit-ode diffeential equation, one fo each winding. hee diffeential equation ae coupled to one 4

43 anothe though the utual inductance between the winding. In paticula, the tatoto-oto coupling te vay with tie. anfoation like the dq o αβ can facilitate the coputation of the tanient olution of the above induction oto odel by tanfoing the diffeential equation with tie-vaying inductance to diffeential equation with contant inductance. 3.4 Machine Model in Abitay dq Refeence Fae he idealized thee-phae induction achine i aued to have yetical aigap. he dq efeence fae ae uually elected on the bai of convenience o coputational eduction. he two coonly ued efeence fae in the analyi of induction achine ae the tationay and ynchonouly otating fae. Each ha an advantage fo oe pupoe. In the tationay otating efeence, the dq vaiable of the achine ae in the ae fae a thoe noally ued fo the upply netwok. In the ynchonouly otating fae, the dq vaiable ae teady in teady-tate. Hee, fitly the equation of the induction achine in an abitay efeence fae which i otating at a peed of (w) in the diection of the oto otation will be deived. hoe if the induction achine in the tationay fae can then be obtained by etting w=, and thoe fo the ynchonouly otating fae ae obtained by etting w = w e. he elationhip between the abc quantitie and dq quantitie of a efeence fae otating at an angula peed, w, i hown in Fig.3.4. β-axi d-axi w b b a w=w θ a θ c c q-axi Fig.3.4- Relationhip between abc and abitay dq 5

44 he tanfoation equation fo abc to thi dq efeence fae i given by: f f f q d = [ ( θ) ] qd f f f a b c (3.8) whee the vaiable f can be the phae voltage, cuent, o flux linkage of the achine. he tanfoation angle, θ(t), between the q-axi of the efeence fae otating at a peed of w and the a-axi of the tationay tato winding ay be expeed a : t θ( t) = w(t)dt + θ() elec.ad. (3.9) ikewie, the oto angle, θ (t), between the axe of the tato and oto a-phae fo a oto otating with peed w (t) ay be expeed a: t θ ( t) = w (t)dt + θ () elec.ad. (3.) 3.4. dq Voltage Equation a: In atix notation, the tato winding abc voltage equation can be expeed v = pψ + i (3.) abc abc abc abc Applying the tanfoation given in (3.7) and (3.8), to the voltage, cuent and flux linkage eqn. (3.) becoe v qd qd qd [ ( θ) ] p[ ( θ) ] [ ψ ] + [ ( θ) ] [ ( θ) ] [ i ] = (3.) qd qd olving the equation above it becoe: qd qd qd qd qd v = w ψ + pψ + i (3.3) whee dθ qd w = and = (3.4) dt qd qd 6

45 ikewie, the oto voltage equation becoe: qd qd qd qd qd v = (w w ) ψ + pψ + i (3.5) 3.4. qd Flux inkage Relation he tato qd flux linkage ae obtained by applying qd (θ) to the tato abc flux linkage in (3.4). qd abc abc abc abc ψ = [ ( θ)] ( i i ) (3.6) qd + kipping the tanfoation tep the tato and the oto flux linkage elationhip can be expeed copactly: ψ ψ ψ ψ ψ ψ q d q d (3.7) l + = l + l + l + l i i i i i i q d q d Subtituting the (3.7) into voltage equation and then gouping q, d,, and θ te in the eulting voltage equation, we obtain the voltage equation that ugget the equivalent cicuit hown in Fig.3.5. q-axi iq ψ w ψ (w w ) d l l d iq + Vq - + E q E q + + Vq - Fig.3.5- (continued) Equivalent cicuit epeentation of an induction achine in the abitay efeence fae 7

46 id q l d-axi ψ w ψ (w w ) l q id + Vd - + E d E d + + Vd - Fig.3.5- Equivalent cicuit epeentation of an induction achine in the abitay efeence fae qd oque Equation he u of the intantaneou input powe to all ix winding of the tato and oto i given by : p = v i + v i + v i + v i + v i + v i W (3.8) in a a b b c c a a b b c c in te of dq quantitie p 3 = (v qi q + v di d + v i + v i q qa + v di d + v i ) W (3.9) in Uing tato and oto voltage to ubtitute fo the voltage on the ight hand ide of (3.9), we obtain thee kind of te: i, i pψ, and w ψ i. ( i ) te ae the coppe loe. he (i.pψ) te epeent the ate of exchange of agnetic field enegy between winding. he electoechanical toque developed by the achine i given by the u of the (w.ψi ) te divided by echanical peed, that i: [ w( ψ i ψ i ) + (w w )( ψ i ψ i )] N 3 p = d q q d d q q d (3.3) w e uing the flux linkage elationhip, e can alo be expeed a follow: [ w( ψ i ψ i ) + (w w )( ψ i ψ i )] N 3 p = d q q d d q q d (3.3) w e 8

47 Uing the flux linkage elationhip, one can how that e 3 P = ( ψ i q d ψ i d q ) 3 P = ( ψ di q ψ qi d ) 3 P = (i di q i qi d ) N N N (3.3) One can eaange the toque equation by ineting the peed voltage te given below: E q E q = wψ d = (w w ) ψ d E d E d = wψ q = (w w ) ψ q (3.33) able 3.- Induction Machine Equation in Abitay Refeence Fae Stato qd voltage equation: v v v q d = pψ = pψ = pψ q d + wψ wψ + i d q + i + i q d (3.34) Roto qd voltage equation: v q v d v = pψ q = pψ d = pψ + (w w ) ψ + i d (w w ) ψ q + i q + i d (3.35) whee ψ ψ ψ ψ ψ ψ l + = q d q d l + l + l + l i i i i i i q d q d (3.36) 9

48 able 3.- (continued) Ind. Machine Equation in Abitay Refeence Fae oque Equation: [ w( ψ i ψ i ) + (w w )( ψ i ψ i )] N 3 p = d q q d d q q d (3.37) w e e 3 P = ( ψ i q d ψ i d q ) 3 P = ( ψ di q ψ qi d ) 3 P = (i di q i qi d ) N N N (3.38) 3.5 qd Stationay and Synchonou Refeence Fae hee i eldo a need to iulate an induction achine in the abitay otating efeence fae. But it i ueful to convet a unified odel to othe fae. he ot coonly ued one ae, two aginal cae of the abitay otating fae, tationay efeence fae and ynchonouly otating fae. Fo tanient tudie of adjutable peed dive, it i uually oe convenient to iulate an induction achine and it convete on a tationay efeence fae. Moeove, calculation with tationay efeence fae i le coplex due to zeo fae peed (oe te cancelled). Fo all ignal tability analyi about oe opeating condition, a ynchonouly otating fae which yield teady value of teady-tate voltage and cuent unde balanced condition i ued. Since we have deived the equation of the induction achine fo the geneal cae, that i in the abitay otating efeence fae, the equation of the achine in the tationay and ynchonouly otating efeence fae, w to zeo and w e, epectively. o ditinguih thee two fae fo each othe, an additional upecipt will be ued, fo tationay fae vaiable and e fo ynchonouly otating fae vaiable. 3

49 i q q-axi l l ψ d ( w ) iq + E q + + V q Vq - - d-axi l l ψ q ( w ) i d id + V d E d + + Vd - - Fig3.6- Equivalent cicuit of an induction achine in the tationay fae able 3.-Induction Machine Equation in Stationay Refeence Fae Stato qd voltage equation: v v v q d = pψ = pψ = pψ q d + i + i + i q d (3.39) Roto qd voltage equation: v v v q d = pψ = pψ = pψ q d + ( w ) ψ + (w ) ψ + i q d + i + i d q (3.4) 3

50 able 3.- (continued) Induction Machine Equation in Stationay Refeence Fae whee ψ ψ ψ ψ ψ ψ q d q d l + = l + l + l + l i i i i i i q d q d (3.4) oque Equation: e 3 P = ( ψ qi 3 P = ( ψ di q 3 P = (i di d ψ q ψ i i d i i ) q d q ) ) q d N N N (3.4) he equivalent induction achine cicuit and induction achine equation in the tationay efeence fae ae given above in able 3. and Fig.3.6. In Fig3.7, 3- phae AC quantitie ae iulated in both tationay fae and ynchonouly otating fae. q-axi i e q e e ψ dw e l l ψ d (w e w ) iq e + V e q - e + E e q E q + + Vq e - Fig.3.7- (continued) Equivalent cicuit of an induction achine in the ynchonouly otating fae 3

51 d-axi 33 id e + Vd e - i e d + V e d - e q e l l e q e ) w (w w ψ ψ + + d e d e E E Fig.3.7 Equivalent cct of an induction achine in the ynchonouly otating fae able3.3- Induction Machine Equation in Synchonouly Rotating Refeence Fae Stato qd voltage equation: (4.43) d e q e e d e d e q e d e e q e q e i p v i w p v i w p v + ψ = + ψ ψ = + ψ + ψ = Roto qd voltage equation: d e q e e d e d e q e d e e q e q e i p v i ) w (w p v i ) w (w p v + ψ = + ψ ψ = + ψ + ψ = (4.44) whee = ψ ψ ψ ψ ψ ψ d e q e d e q e l l l l l d e q e d e q e i i i i i i (3.45)

52 able3.3-(continued) Induction Machine Equation in Synchonouly Rotating Refeence Fae oque Equation: e 3 P e e = ( ψ qi 3 P e e = ( ψ di q 3 P e = (i di d e q ψ ψ i e d i i i ) e e q d e q ) ) e e q d N N N (3.46) Fig.3.8- A iulation of 3-phae AC quantitie conveted to both tationay fae (i q,i d ) and ynchonouly otating fae(i qe,i de ) 34

53 3.6 Siulation of the Induction Moto in Stationay Fae Uing the tationay fae equation (3.39)-(3.4) induction oto i iulated in a tationay efeence fae and ued in the developent of field oientation contol technique and tate etiation technique. Applying the appopiate voltage to the oto odel eithe thoe obtained by uing feedback infoation o diect open-loop voltage, one can obeve the toque-peed epone and cuent-flux wavefo. Uing thi infoation, diffeent altenative contol technique ay be teted and developed. In thi odel, thee-phae voltage applied to the input ae conveted into two-phae tationay efeence fae voltage. Once d-q phae voltage obtained, uing the equation in able 3. aociated flux and cuent ae calculated and then applied to electoechanical and echanical toque equation to obtain toque-peed epone. Baed on the tationay efeence fae odel Fig.3.9 how the tato voltage, the tato cuent, the toque and the peed wavefo at no-load fo a -hp oto. oque v peed cuve obtained fo the ae odel i hown in Fig.3. fo no-load condition. Fig.3.9- No-oad Repone of Stationay Fae Induction Moto Model 35

54 Fig.3.- Open-loop toque-peed cuve of the induction oto odel at no-load Induction achine odel being non-linea it i needed fo oe cae to be lineaized at any diffeent opeating point to ake ue of linea contol technique. Epecially, the linea coputation technique baed on the tate-pace odel need the ue of lineaized odel of the induction achine at intantaneou opeating point to define A,B,C,D atice. Deied opeating point ay be found by uing ti function in MAAB. Afte that, linod function i ued to deteine the A,B,C,D atice of the all-ignal odel of the non-linea yte about the choen teadytate opeating point. Futheoe, tf coand i ued to deteine the tanfe function of the yte at the choen opeating point whoe intantaneou tate-pace atice ae calculated [39]. Afte calculating thee tep one ay conduct tudy on the tability analyi of the odel. Fo the induction achine odel tability analyi, two-phae tationay fae voltage and applied echanical load ae conideed a input. wo-phae tationay fae cuent, electoechanical toque and oto peed ae conideed a output of the yte in tate pace epeentation of the odel. In Fig.3. changing input3 (applied load) fo zeo to twice the ated toque, hift of the pole i obeved. It i confied that pole of the tanfe function of ( w / ech ) ae all on the left hand ide of the eal-axi. Fo a detailed tability analyi othe tanfe function of the diffeent output-input cobination ay be invetigated in the opeational ange. In addition to pole path, the tability analyi ay be eniched uing locu coand to aange the gain of the yte; thoe do not exceed the tability liit uing eal achine paaete. Fig.3. and Fig.3.3 ae the oot locu exaple of two diffeent tate tanfe function of the oto. 36

55 Fig.3.-Pole path of ( w / ech ) fo no-load to twice the ated toque Fig.3. Root locu of ( w / v qe ) fo vaying gain 37

56 Fig.3.3-Root locu of ( e / v qe ) fo vaying gain In addition to uch a tability analyi, one ay alo invetigate the tep epone of the deied (output-input) tanfe function (ee Fig ). Fig.3.4-Step epone of w (pu) to one volt change in v qe 38

57 Fig.3.5-Step epone of w (pu) to unit change in load Uing the thee diffeent peed fae (abitay, tationay, ynchonou) dicued in ection above oiented equivalent cicuit odel fo ai-gap flux, tato flux and oto flux ay alo be deived. hee odel, howeve, ae not conideed hee but left fo futue wok. 3.7 Siulation of FOC developed in Stationay Refeence Fae State obeve ued in thi thei ue tationay fae odel fo the ake of iplicity of the oveall algoith. Alo in the field-oiented contol iulation tationay axi dq odel of a -hp induction oto i ued. he iulation i ipleented uing MAAB/Siulink. hi iulation i ipleented to be failia with indiect field-oiented contol and obeve the vaiable at evey tage of the contol. Alo one can obeve how well the flux aplitude eain contant when the oto i loaded and the electoechanical toque i ooth. Related dq cuent in the iulation ay give ignificant clue about the field oiented contol pinciple to a beginne. In thi iulation, efeence dq cuent ae obtained accoding to the efeence load toque and peed wavefo. hey ae copaed with the actual oto cuent and the eo ae input to PI contolle to obtain efeence voltage. Afte thi point iulation of Space Vecto PWM and FOC ae ipleented epaately due to vey long iulation tie of PWM pat. Intead, the oto i fed with the fit 39

58 haonic of the PWM voltage to ave tie and iplify the iulation. he iulation eult ae given below: Fig 3.6- Applied echanical toque, oto peed and poduced electoagnetic toque Fig. 3.6 how the load toque, the oto peed and the poduced electoechanical toque. In the fit.5 ec., the oto poduce electoechanical toque to ovecoe the effect of the inetia. In the no-load tie inteval, e i cloe to zeo. A can be een fo F.g.3.6 vey ooth toque i obtained with field-oiented contol. Fig.3.7- Synchonou fae dq axi cuent 4

59 In Fig.3.7 ynchonou fae cuent; toque poducing cuent coponent, i q and contant flux poducing cuent ae hown. Note fo Fig.3.7 that i q i popotional to the toque poduced by the achine both duing acceleation (ee Fig 3.6) and at loaded egion. Fo contant flux opeation, d-axi cuent, i d eain contant yielding a ooth flux in ode to pevent toque ocillation. Fig.3.8 how the tato phae voltage and the cuent. Note that the phae cuent inceae popotionally to the load equieent. In Fig.3.9 dq tationay axi fluxe ae hown. he agnitude of each flux coponent eain the ae afte the tanient tate. he oto-flux i obtained a the quae oot of the u of the quae of dq axi fluxe. Contant oto-flux i vital fo field-oiented contol in contolling the toque pefectly. A in the cae of DC oto, once contant flux i obtained, one can contol the poduced toque eaily by contolling the toque poducing cuent coponent, i q which i independent of the flux. Fig Phae-A tato voltage and cuent 4

60 Fig dq axi oto fluxe and oto flux (load applied at.75 ec) Fig.3.- Refeed oto cuent (dq-axi) 4

61 Fig.3.- Fou quadant peed eveal and phae voltage Fig.3.- Fou quadant peed eveal and phae cuent Fig.3. how efeed oto cuent. At no load cae the oto cuent convege to zeo due to unity lip. In Fig.3. and 3. fou-quadant peed eveal i given with phae voltage and cuent vaiation. he fequency and the agnitude of both the tato voltage and the tato cuent ae contolled by FOC duing the peed eveal opeation. 43

62 Fig.3.3- Fou-quadant peed eveal and poduced toque due to inetia Fig.3.4- Fou-quadant peed eveal and oto flux wave-fo In Fig.3.3 fou-quadant peed eveal wavefo i given with poduced toque. Since the opeation i iulated at no-load, the toque poduced due to the deand by the oto inetia i quite ooth becaue of the contant flux hown in Fig3.4. In Fig.3.4 we obeve that the peed change doe not affect the contant flux condition and thi illutate the atifactoy eult of oto field oientation. 44

63 CHAPER 4 PUSEWIDH MODUAION with SPACE VECOR HEORY 4. Invete hee phae invete, upplying voltage and cuent of adjutable fequency and agnitude to the tato, ae an ipotant eleent of adjutable peed dive yte eploying induction oto. Invete with eiconducto powe witche ae d.c. to a.c. tatic powe convete. Depending on the type of d.c. ouce upplying the invete, they can be claified a voltage ouce invete (VSI) o cuent ouce invete (CSI). In pactice, the d.c. ouce i uually a ectifie, typically of the thee phae bidge configuation, with d.c. link connected between the ectifie and the invete. he d.c. link i a iple inductive, capacitive, o inductive-capacitive low-pa filte. Since neithe the voltage aco a capacito no the cuent though an inducto can change intantaneouly. A capacitive-output d.c. link i ued fo a VSI and an inductive-output link i eployed in CSI. VSI can be eithe voltage o cuent contolled. In a voltage-contolled invete, it i the fequency and agnitude of the fundaental of the output voltage that i adjuted. Feed-fowad voltage contol i eployed, ince the invete voltage i dependent only on the upply voltage and the tate of the invete witche, and, theefoe, accuately pedictable. Cuent contolled VSI equie eno of the output cuent which povide the neceay contol feedback. he type of eiconducto powe witch ued in an invete depend on the volt-apee ating of the invete, a well a on othe opeating and econoic conideation, uch a witching fequency o cot of the yte. aking into account the tanient- and teady-tate equieent, we have ued V, 4A IGB witche. With appopiate heat ink, we can ie to KHz, howeve at 45

64 KHz, witching loe and conduction loe becoe equal [4], oeove, coplex atheatical algoith equie uch tie. hu KHz i elected a the witching fequency in ou algoith. 4.. Voltage Souce Invete (VSI) A diaga of the powe cicuit of a thee phae VSI i hown in the Fig.4.. he cicuit ha bidge topology with thee banche (phae), each coniting of two powe witche and two feewheeling diode. In the cae illutated and ipleented in thi thei, the invete i upplied fo an uncontolled, diode-baed ectifie, via d.c. link which contain an C filte in the inveted configuation. While thi cicuit epeent a tandad aangeent, it allow only poitive powe flow fo the upply yte to the load via typically thee-phae powe line. Negative powe flow, which occu when the load feed the ecoveed powe back to the upply, i not poible ince the eulting negative d.c. coponent of the cuent in the d.c. link can not pa though the ectifie diode. heefoe, in dive yte whee the VSI-fed oto ay not opeate a a geneato, oe coplex upply yte ut be ued. hee involve eithe a baking eitance connected aco the d.c. link o eplaceent of the uncontolled ectifie by a dual convete. A a futue wok, the invete ay be uppoted with baking eitance connected aco the d.c. link via fee wheeling diode and a tanito. When the powe i etuned by the oto, it i diipated in the baking eito which i called dynaic baking. he cicuit diaga of thee-phae VSI ued in thi poject i hown in Fig.4.. A B C RECIFIER INVERER Fig.4.- Cicuit diaga of thee phae VSI Becaue of the containt that the input line ut neve be hoted and the output cuent ut alway be continuou, a voltage ouce invete can aue only 46

65 eight ditinct opeational topologie. hey ae hown in Fig.4. and Fig.4.3. Six out of thee eight topologie poduce a non-zeo output voltage and ae known a nonzeo witching tate and the eaining two topologie poduce zeo output and ae known a zeo witching tate. p n A B C Fig.4.- hee phae invete with witching tate 47

66 V(pnn) V(ppn) V3(npn) V4(npp) V5(nnp) V6(pnp) V7(ppp) V8(nnn) Fig.4.3- Eight witching tate topologie of a voltage ouce invete 48

67 4. Voltage Space Vecto Space vecto odulation fo thee leg VSI i baed on the epeentation of the thee phae quantitie a vecto in two-dienional (α-β) plane. Conideing the fit witching tate in Fig.4.4, line-to-line voltage ae given by V a b c Fig.4.4- Fit witching tate V (pnn) Vab = V Vbc = Vca = -V hi can be epeented in (α-β) plane a hown in Fig.4.5 whee Vab, Vbc and Vca ae the thee line voltage vecto diplaced by o in pace. he effective voltage vecto geneated by thi topology i epeented a V (pnn) in Fig.4.5. Hee (pnn) efe to the thee leg /phae a,b,c being eithe connected to the poitive dc ail (p) o to the negative dc ail (n). Fo the fit witching tate V, phae a i connected to poitive dc ail and phae b and c ae connected to negative dc ail. Vab= V Vbc= Vca=-V Vca Vbc -V V - Vca V(pnn) Vab Fig.4.5- Repeentation of topology in (α-β) plane 49

68 Siila to the V, ix non-zeo voltage vecto can be hown a in Fig.4.6. he tip of thee vecto fo a egula hexagon. We define the aea encloed by two adjacent vecto, within the hexagon, a a ecto. V3 V 3 V4 V 4 6 V5 5 V6 Fig.4.6- Non-zeo voltage vecto in (α-β) plane he lat two topologie of Fig.4.3 ae zeo tate vecto. he output line voltage in thee topologie ae zeo. Vab= Vbc= Vca= hee ae epeented a vecto which have zeo agnitude and hence ae efeed a zeo witching tate vecto. hey ae epeented with dot at the oigin intead of vecto a hown in Fig.4.7. Vab= Vbc= Vca= Vbc V7,V8 Vca Vab Fig.4.7- Repeentation of the zeo voltage vecto in (α-β) plane 5

69 4.3 Space Vecto Modulation In the liteatue thee exit a nube of PWM algoith [4, 4]. he pefoance citeia of thee algoith ae baically: -Cuent haonic -Haonic pectu 3-oque haonic 4-Switching fequency 5-Dynaic pefoance 6-Polaity conitency ule he well-known feed-fowad PWM chee ae: a-caie baed PWM b-caiele PWM c-ove-odulation d-optiized feedfowad PWM In thi thei, we have ipleented one of the well-known caie baed PWM technique, SVM and poved it high pefoance with epect to othe technique (e.g. Sinuoidal Modulation) [43]. Now let u look at the baic of SVM. he deied thee phae voltage at the output of the invete could be epeented by an equivalent vecto V otating in the counte clockwie diection a hown in Fig.4.8. he agnitude of thi vecto i elated to the intantaneou agnitude of the output voltage (ee Fig.4.9.) and the peiod thi vecto take to coplete one evolution i the ae a the fundaental tie peiod of the output voltage. Vbc -V V V Vca Vab Fig.4.8- Output voltage vecto (V) in (α-β) plane 5

70 Vbc Vab Vca Fig.4.9- Output line voltage in the tie doain et u conide the ituation when the deied line-to-line output voltage vecto V i in ecto a hown in Fig.4.. hi vecto could be yntheized by the pule width odulation (PWM) of the adjacent SSV V (pnn) and V (ppn), the duty cycle of each being d and d, epectively, and the zeo vecto (V 7 (nnn) / V 8 (ppp)) of duty cycle d : d V + d V = V =.V.e iθ (4.) d + d +d = (4.) whee, < <.866, i the odulation index. V(ppn) d θ d V Secto V(pnn) Fig.4.- Synthei o the equied output voltage vecto in ecto While deteining the duty cycle d, d and d in SVM technique, the only diffeence i the choice of zeo vecto and the equence in which the vecto ae applied within the witching cycle. One i fee about electing the given altenative below in hi SVM algoith: 5

71 -Choice of the zeo vecto uing V 7 (ppp), V 8 (nnn) o both, -Sequencing of the vecto 3-Splitting of the duty cycle of the vecto without intoducing additional coutation. Hee fou diffeent SVM chee ae given oughly accoding to thei epeating duty-cycle ditibution: a-he ight aligned equence (d /, d, d, d / ) b-syetic equence (d /4, d /, d /, d /, d /, d /, d /4) c-altenating Zeo Vecto Sequence (d, d,d, d,d,d ) d-highet Cuent Not-Switched Sequence (d, d, d ) Aong thee SVM technique the coonly pefeed yetic equence, which ha the lowet HD, ha been ipleented in thi tudy [44,45]. Switching equence i given in Fig.4.. Fig.4.- Phae gating ignal in Sy. Seq. SVM 4.4 SVPWM Application to the Static Powe Bidge and Ipleentation Uing DSP Platfo In the cae of AC dive application, inuoidal voltage ouce ae not ued a explained befoe. Intead, they ae eplaced by 6 powe IGB that act a on/off witche to the ectified DC bu voltage. he ai i to ceate inuoidal cuent in the coil to geneate otating field. Owing to the inductive natue of the phae, a peudo-inuoidal cuent i ceated by odulating the duty-cycle of the powe witche. he witche (IGB) hown in the Fig.4. ae activated by ignal (a, b, 53

72 c) and thei copleent value. Eight diffeent cobination ae available with thi thee-phae VSI including two zeo tate. Fig.4.- Powe Bidge It i poible to expe each phae-to-neutal voltage fo evey witching cobination of IGB a lited in able 4.. able 4.. Powe Bidge Output Voltage (V AN, V BN, V CN ) A B C V AN V BN V CN -Vdc/3 -Vdc/3 Vdc/3 -Vdc/3 Vdc/3 -Vdc/3 -Vdc/3 Vdc/3 Vdc/3 Vdc/3 -Vdc/3 -Vdc/3 Vdc/3 Vdc/3 Vdc/3 Vdc/3 Vdc/3 Vdc/3 In field-oiented contol algoith, the contol vaiable ae expeed in otating fae. he cuent vecto I ef that diectly contol the toque i tanfoed into a voltage vecto by the invee Pak tanfo. hi voltage efeence i expeed in the (α-β) fae. Uing thi tanfoation thee-phae voltage (V AN, V BN, V CN ) and the efeence voltage vecto ae pojected in the (α-β) fae. he expeion of the thee phae voltage in the (α-β) fae ae given by geneal Clake tanfoation equation: V V α β = 3 3 V V 3 V AN BN CN (4.3) 54

73 Since only 8 cobination ae poible fo the powe witche, V α,v β can alo take finite nube of value in the (α-β) fae (able 4.) accoding to the IGB coand ignal (a, b, c). able 4.. Stato Voltage in (α-β) fae and elated Voltage Vecto A B C Vα Vβ Vecto V -Vdc/3 -Vdc/ 3 V -Vdc/3 Vdc/ 3 V -Vdc/3 V3 Vdc/3 V4 Vdc/3 -Vdc/ 3 V5 Vdc/3 Vdc/ 3 V6 V7 he eight voltage vecto e-defined by the cobination of the witche ae epeented in Fig.4.3. Now, given a efeence voltage (coing fo the invee β V () V 6 () 5 3 V 3 () V 4 () α 4 6 V () V 5 () Fig.4.3 -Voltage Vecto Pak tanfo), the following tep i ued to appoxiate thi efeence voltage by the above defined eight vecto. he ethod ued in appoxiating the deied tato efeence voltage with only eight poible tate of witche i to cobine adjacent vecto of the efeence voltage and odulate the tie of application of each adjacent vecto. In Fig.4.4, the efeence voltage V ef i in the thid ecto and the application tie of each adjacent vecto i given by: = Vef = V4 + V6 (4.4) 55

74 β V 6 () V βef Vef V 6 6 / 6 V 4() V 4 4 / x α Fig Pojection of the efeence Voltage Vecto he deteination of the aount of tie 4 and 6 i given by iple pojection: 6 V βef = V6 co(3 ) V = 4 αef V4 + x (4.5) V βef x = tg(6 ) Finally, with the (α-β) coponent value of the vecto given in the able 4., the aount of tie of application of each adjacent vecto i: 4 6 = = Vdc 3 V Vdc ( 3V 3V ) αef βef βef (4.6) he et of the peiod pent in applying the null-vecto. Fo evey ecto, coutation duation i calculated. he aount of tie of vecto application can all be elated to the following vaiable: X = Y = Z = 3V 3 3 βef V V βef βef V V αef αef (4.7) 56

75 In the peviou exaple fo ecto 3, 4 = -Z and 6 = X. Extending thi logic, one can eaily calculate the ecto nube belonging to the elated efeence voltage vecto. he following baic algoith help to deteine the ecto yteatically. If X > then A= ele A= If Y > then B= ele B= If Z > then C= ele C= Secto = A+B+4C Application duation of the ecto bounday vecto ae tabulated a; Secto : t = Z t = Y : t = Y t =-X 3: t =-Z t = X 4: t =-X t = Z 5: t = X t =-Y 6: t =-Y t =-Z Satuation If (t + t ) > PWMPRD then t at = (t / t +t )*PWMPRD t at = (t / t +t )*PWMPRD he thid tep i to copute the thee neceay duty cycle a; t t t aon bon con = t aon bon he lat tep i to aign the ight duty cycle (t xon ) to the ight oto phae (in othe wod, to the ight CMPRx) accoding to the ecto(ee Fig.4.6). able 4.3 depict thi deteination. PWMPRD t = = t + t + t t able 4.3- Aigned duty cycle to the PWM output CMPR t bon t aon t aon t con t bon t con CMPR t aon t con t bon t bon t con t aon CMPR3 t con t bon t con t aon t aon t bon 57

76 CMPR t con CMPR t bon CMPR3 t aon Fig.4.5- Secto 3 PWM Patten and Duty Cycle (cae hown in Fig.4.4) 4.5 Event Manage Configuation of DSP fo SVPWM MS3F/CXX ha pecific peipheal in ode to handle pace vecto odule eaily and optially. ie egite, copae egite, PWM output and PWM inteupt and pogaable tie-adc ynchonization help u fo eay ipleentation. Howeve, although thee tool ake deign eay they ae not ue fiendly fo a beginne and athe coplicated. ie i the bae tie of the PWM inteupt geneation and oveall contol algoith i ynchonized with tie, PWM undeflow inteupt. Duing the exceively long tie pecification fo tie undeflow the algoith i un in an infinite loop. Fo the next peiod again tie undeflow inteupt i extacted fo thi infinite loop. By thi way PWM output and the oveall contol algoith un ynchonouly. A an altenative, one ay wite an inteface poga fo viualizing the oftwae tate without changing poga intead of an infinite loop. ie i configued in up-down counting ode to geneate the yetical PWM patten. he tie contol egite CON i pogaed in ode to get a 5n eolution: the pe-cala clock of the tie i et to giving the highet poible eolution. wo conecutive wite to CON ae equied to enue the ynchonization of the GP tie when CON [6] i ued to enable GP tie o 3: ) Configue all othe bit with CON [6] et to. ) Enable GP tie and, thu, GP tie o GP tie and 3, by etting CON[6] to. Othewie the PWM output cannot be obeved. 58

77 Configuation of CON i given below: plk #PWMPRD,PER plk #,CN plk #A8h,CON ;Set PWM inteupt peiod ;Ignoe Eulation upend ;Up/Down count ode(ut) ;x/ pecala(optional) ;Ue own ENABE ;Diable ie(fo the fit loading) ;Intenal Clock Souce(ut) ;Reload Copae Regite when CN= (ut) ;Diable ie Copae opeation he copae egite ut be continuouly eloaded with calculated duty cycle value (t aon, t bon, t con ). plk #7h,COMCON plk #87h,COMCON ;Diable fo the fit loading ;Reload Full Copae when CN=(ut) ;Diable Space Vecto ;Reload Full Copae Action when CN= ;Enable Full Copae Output (ut) ;Diable Siple Copae Output(SC not ued) ;Select GP tie a tie bae(ut) ;Full Copae Unit in PWM Mode(ut) ;enable copae opeation wo conecutive wite to COMCON ae equied to enue the pope opeation of full copae unit in the PWM ode: ) Enable PWM ode without enabling copae opeation. ) Enable copae opeation by etting COMCON[5] to without changing any othe bit. he output of the Copae opeation ae not diectly ent to the Output ogic but ae peviouly tanfeed though the PWM Deadband on-chip cicuit. Depending on the powe bidge pe-dive ued, the contol egite DBCON ha to be pogaed. he dead-band unit i deigned to aue that no ovelap occu between the tun-on peiod of the uppe and lowe device that ae contolled by the two copae/pwm output aociated with each full copae unit (ee Fig.4.6). 59

78 Fig.4.6- Dead tie band hi aue that no ovelap will occu unde any condition. Although IGB gate dive cad povide ufficient dead tie, we alo added oftwae dead tie fo eliability. Howeve, at vey low peed ange effect of dead tie band at the output voltage becoe eakable and ut be copenated. Bit in the full copae action contol egite (ACR) contol the action that take place on each of the ix copae output pin (PWMx/CMPx, x = 6) on a copae event. he polaity of the PWM pin i choen in the Full Copae Action Contol Regite (ACR) a follow: ldp #DP_EV plk #666h,ACR ;Bit 5- not ued, no pace vecto ;PWM copae action ;PWM5/PWM6 - Active ow/active High ;PWM3/PWM4 - Active ow/active High ;PWM/PWM - Active ow/active High 4.6 Siulation and Expeiental Reult of SVPWM he SVPWM algoith ipleented hee by DSP i iulated befoe expeiental wok to veify it eult. In the fit iulation (Fig.4.7), SVPWM Fig SVPWM 6 Algoith Siulation

79 algoith i iulated tep-by-tep and all the oftwae vaiable in the algoith ae copaed with the expeiental DSP poga output. It i hown that both of the eult ae the ae, and coect. In Fig.4.8. duty cycle of two PWM witche ae hown ( t aon, t bon,t con ).In Fig.4.9 ecto nube of the otating efeence voltage vecto i given. A caeful eade will notice that the ode of the ecto i the ae a in Fig.4.3 of a vecto Fig.4.8- Siulated wavefo of duty cycle, ( t aon, t bon,t con ) Fig.4.9- Secto nube of voltage vecto otating in the diection of counteclockwie. In Fig.4. duation of the to bounday ecto vecto ae hown. In Fig.4. pojection vecto of the efeence voltage vecto on (a b c) plane ae hown in tie doain (ee Fig.4.8). 6

80 Fig.4.- Duation of two ecto bounday vecto (t,t ) Fig.4.- he pojection of the Va, Vb and Vc of the efeence voltage vecto in the (a b c) plane -(X, Y, Z) In the econd iulation, a taightfowad SVPWM algoith i ipleented ignoing optial condition fo pactical application. In thi iulation one can obeve line-to-line voltage in the fo of fequent pule and the apled ignal (efeence voltage) fo vaying odulation contant (ee Fig.4.-.4) 6

81 Fig.4.- A typical line to line voltage output of SVPWM Fig.4.3- SVPWM output with the ignal apled (=.4) 63

82 Fig.4.4- SVPWM output with the ignal apled (=.6)-Zooed he expeiental output confi the theoetical and iulation output. Given two efeence voltage vecto aociated with the efeence cuent and toque equieent SVPWM oftwae paaete ae obeved and copaed with the iulated one. Fig.4.5 how duty cycle of one of the PWM witche. he duty cycle i figued out by DAC output of the DSP poceo. Fig.4.5- Duty cycle of PWM 64

83 Fig.4.6- ow-pa filteed fo of PWM pule A SVPWM deigne ut check the coectne of the ix PWM output geneated by thi SVPWM odule. A iple low pa filte RC cicuit ay be ued to filte out the high fequency coponent. he R and C value (o the tie contant) ae choen fo a deied cut off fequency (fc) uing the following equation: ie contant = RC = /πf c Fo exaple, R =.8 k. and C = nf, give fc = 884. Hz. hi cut off fequency ha to be lowe than the PWM fequency. hi low pa filte i connected to the PWM pin of the x4x/x4xevm, the filteed veion of the PWM ignal ae onitoed by ocillocope. he wavefo hown on the ocillocope hould be the ae a the one hown in Fig.4.5. In Fig.4.7 the ecto nube of the otating efeence voltage vecto i hown (ee Fig.4.9 iulation output). Fig.4.7-Secto nube of the efeence voltage 65

84 Fig.4.8- Duation of two bounday vecto (t,t ) Fig.4.8 i the expeiental confiation of iulation hown in Fig.4., duation of two bounday vecto. Fig.4.9 i the expeiental eult of pojection vecto in abc plain (X,Y in tie doain- ee Fig.4.) Fig.4.9- Pojection vecto in abc plain (X,Y in tie doain) 66

85 Fig.4.3- ypical phae cuent of an induction oto diven by SVPWM unde heavy load condition. 67

86 CHAPER 5 KAMAN FIER 5. Senole Contol In contolling AC achine dive peed tanduce uch a tachogeneato, eolve, o digital encode ae ued to obtain peed infoation. Uing thee peed eno ha oe diadvantage hey ae uually expenive, he peed eno and the coeponding wie will take up pace, In defective and aggeive envionent, the peed eno ight be the weaket pat of the yte Epecially the lat ite degade the yte eliability and educe the advantage of an induction oto dive yte. hi ha led to a geat any peed enole vecto contol ethod [46]. On the othe hand, avoiding eno ean ue of additional algoith and added coputational coplexity that equie high-peed poceo fo eal tie application. A digital ignal poceo have becoe cheape, and thei pefoance geate, it ha becoe poible to ue the fo contolling electical dive a a cot effective olution. Soe elatively new fully digitized ethod, ued fo peed enole field-oiented contol, utilize thi enhanced poceing capacity [47]-[49]. Uually enole contol i defined a a contol chee whee no echanical paaete like, peed and toque, ae eaued. aditional vecto contol yte ue the ethod of flux and lip etiation baed on eaueent of the phae cuent and DC link voltage of the invete but, thi ha a lage eo in peed 68

87 etiation paticulaly in the low-peed ange. MRAS (odel efeence adaptive yte) technique ae alo ued to etiate the peed of an induction oto [9]- []. hee alo have a peed eo in low-peed ange and ettle to an incoect teady-tate value. In ecent yea, non-linea obeve ae ued to etiate induction oto paaete and tate [7-8], [3-3, 5]. 5. Obeve All tate ae not available fo feedback in any cae and one need to etiate unavailable tate vaiable. Etiation of uneauable tate vaiable i coonly called obevation. A device (o a copute poga) that etiate o obeve the tate i called a tate-obeve o iply an obeve. If the tateobeve obeve all tate vaiable of the yte, egadle of whethe oe tate vaiable ae available fo diect eaueent, it i called a full-ode tate-obeve. An obeve that etiate fewe than the dienion of the tate-vecto i called educed-ode tate-obeve o iply a educed-ode obeve. If the ode of the educed-ode tate-obeve i the iniu poible, the obeve i called iniu-ode tate-obeve. Baically, thee ae two fo of the ipleentation of an etiato a openloop and cloed-loop. he diffeence between thee two i a coection te, involving the etiation eo, ued to adjut the epone of the etiato. A cloedloop etiato i efeed to a an obeve. In open-loop etiato, epecially at low peed, paaete deviation have a ignificant influence on the pefoance of the dive both in teady tate and tanient -tate. Howeve, it i poible to ipove the obutne againt paaete iatch and alo ignal noie by uing cloed loop obeve An obeve can be claified accoding to the type of epeentation ued fo the plant to be obeved. If the plant i deteinitic, then the obeve i a deteinitic obeve; othewie it i a tochatic obeve. he ot coonly ued obeve ae uenbege and Kalan type []. he uenbege obeve (O) i of the deteinitic type, and the Kalan Filte (KF) i of the tochatic type. he baic Kalan filte i only applicable to linea tochatic yte, and fo non-linea yte the extended Kalan filte (EKF) can be ued, which can povide etiate of the tate of a yte o of both the tate and paaete. he EKF i a ecuive filte (baed on the knowledge of tatitic of both the tate and noie ceated by 69

88 eaueent and yte odelling), which can be applied to non-linea tie vaying tochatic yte. he baic uenbege obeve i applicable to a linea, tieinvaiant deteinitic yte. he extended uenbege obeve (EO) i applicable to non-linea tie vaying deteinitic yte. In uay it can be een that both EKF and EO ae non-linea etiato and the EKF i applicable to tochatic yte and EO i applicable to deteinitic yte. he iple algoith and the eae of tuning of the EO ay give oe advantage ove the conventional EKF. Howeve, EKF being inenitive to paaete change and ued fo tochatic yte (eaueent and odeling noie taken into conideation) it i, theefoe, coonly pefeed in field-oiented contol application. Vaiou type of peed obeve ae dicued in liteatue, which can be ued in high pefoance induction oto dive uch a full-ode adaptive tate obeve. In the full-ode adaptive tate obeve the oto peed i conideed a a paaete, but in EO and EKF the oto peed i conideed a tate. When the appopiate obeve ae ued in high-pefoance peed enole toque-contolled induction oto dive, table opeation can be obtained ove a wide-peed ange, including vey low peed [6-3], [5-54]. 5.. Geneal heoy on Obeve An obeve can be ued to etiate tate which cannot be eaued, o whee the eaueent ae coupted by noie. If a yte can be decibed in dicete tie a: x(k + ) = A x(k) + Bu(k) y(k) = Cx(k) (5.) and the yte i obevable, i.e. the obevability atix, M o, ha full ank, the tate can be etiated by ( 5.) whee M CF CF = M n CF x ˆ(k + ) = Axˆ(k) + Bu(k) xˆ(k + ) = Axˆ(k) + Bu(k) + ( y(k + ) Cxˆ(k + ) ) (5.) 7

89 Syte + x(k+) x(k) y(k) B Z - + C + A Z u(k) Obeve y(k+) B y^(k+) + x^(k+) x^(k) x(k+) Z - A C A Fig.5. Block diaga of an obeve Fig.5. how the block diaga of the obeve which i decibed by (5.). he output vecto, y, i ued to calculate the cuent etiate of the tate vecto, x. he eo of the obeve i defined by: e(k) = ˆ x(k) xˆ (k) e(k + ) = ˆ ( A CA)e(k) (5.3) whee i the obeve gain 5.3 Kalan Filte When applied to a phyical yte, the obeve decibed in ection 5., will be unde the influence of two noie ouce:. Poce noie - i.e. theic noie in a eito, which i a pat of the yte.. Meaueent noie - i.e. quantization noie. Conideing thee two noie ouce (5.) can be ewitten a: x(k + ) = Ax(k) + Bu(k) + G v v(k) y(k) = Cx(k) + w(k) (5.4) whee v(k) i the poce noie and w(k) i the eaueent noie. 7

90 In the following, v(k) and w(k) will be egaded a zeo ean, uncoelated white noie equence with covaiance, V (k) and V (k). he objective of the Kalan algoith i to deteine a gain atix,, which iniize the ean quae of the eo, e. hi can be achieved with the algoith decibed in able 5., whee: xˆ (k n) = ˆ E{ x(k) y(), y()...y( n) { } ( k + ) = ˆ E e ( k + ). e ( k + ) } Q (5.5) State etiate tie update: xˆ ( k k -) = A( k ) xˆ ( k k -) + B( k ) u( k ) (5.6) Covaiance ie update: Q ( k) A( k ) Q( k ) ( k ) + B( k ) V ( k ) ( k ) = A B (5.7) Kalan Gain Matix: [ ] ( k) = Q( k) C ( k) C( k) Q ( k) C ( k) + V ( k) (5.8) State etiate eaueent update: xˆ ( k k) xˆ ( k k -) ( k) [ y( k) C( k) xˆ ( k k -) ] = + (5.9) able 5.-Dicete Kalan Filte If anything but x kept contant, the covaiance atix will convege towad the olution to the dicete Riccati equation: ( k) = A( k) Q( k) A ( k) + G ( k) V ( k) G ( k) ( k) C( k) Q( k) A ( k) Q whee v [ C(k) Q(k) C (k) + (k)] (k) = A(k) Q(k) C (k). V v (5.) (5.) 7

91 Since the vaiable in Riccati equation (5.) ae atice, it i athe coplicated to olve ybolically. hee exit two pecial function to olve algebaic Riccati equation. he function cae( ) in Matlab can olve continuou-tie algebaic Riccati equation and the function dae( ) can olve dicete-tie algebaic Riccati equation whoe geneal equation [55]: E XE = A XA - (A XB + S)(B XB + R) (A XB + S) - + Q G = (B XB + R) - (B XA + S ) hi geneal fo i applied to the Kalan filte epeentation by edefining the eleent in Riccati equation a: A=A B=C Q=G v V Gv R=V E=I S= he tationay covaiance atix, Q, and the tationay gain atix, can be found by ubtituting: Q=X =B hi i ued in the yte in ode to get a tating gue of the paaete. Note: he eaon fo uing athe than i that the equation coepond to the cloed dicete Kalan filte, diplayed on Fig.5.. Howeve they will convege towad the ae eult. 73

92 Syte + x(k+) x(k) y(k) B Z - + C + A V (k) AQA + G v V G v Kalan Filte u(k) + Q(k+) Q(k) Z - - CQA V (k) AQC (CQC + V ) - (k) (k) y^(k+) + x^(k+) x^(k) x(k+) B Z - A C + A Fig.5. Block Diaga of Kalan Filte 74

93 5.4 Extended Kalan Filte An Extended Kalan Filte i a ecuive optiu tate-obeve that can be ued fo the tate and paaete etiation of a non-linea dynaic yte in eal tie by uing noiy onitoed ignal that ae ditibuted by ando noie. hi aue that the eaueent noie and yte noie ae uncoelated. he noie ouce take account of eaueent and odeling inaccuacie. In the fit tage of the calculation, the tate ae pedicted by uing a atheatical odel (which contain peviou etiate) and in the econd tage; the pedicted tate ae continuouly coected by uing a feedback coection chee. hi chee ake ue of actual eaued tate, by adding a te to the pedicted tate (which i obtained in the fit tage). he additional te contain the weighted diffeence of eaued and etiated output ignal. Baed on the deviation fo the etiated value, the EKF povide an optiu output value at the next input intant. In an induction oto dive the EKF can be ued fo the eal-tie etiation of the oto peed, but it can alo be ued fo tate and paaete etiation. Fo thi pupoe the tato voltage and cuent ae eaued (o the tato voltage ae econtucted fo DC link voltage and the invete witching ignal) and, fo exaple, the peed of the achine can be obtained by the EKF quickly and peciely [56] Application of the Extended Kalan Filte In the peent ection the Extended Kalan Filte (EKF) i ued fo the etiation of the oto peed of an induction oto. he EKF i uitable fo ue in high-pefoance induction oto dive, and it can povide accuate peed-etiate in a wide peed ange including vey low peed a well [7-3], [5-54]. he ain deign tep fo a peed enole induction oto dive ipleentation uing the dicetized EKF algoith ae a follow: Selection of the tie-doain induction achine odel, Dicetization of the induction achine odel, Deteination of the noie and tate covaiance atice, Ipleentation of the dicitized EKF algoith; tuning. Fo the pupoe of uing an EKF fo the etiation of the oto peed of an induction achine, it i poible to ue vaiou achine odel. Fo exaple, it i poible to ue the equation expeed in the oto flux-oiented efeence fae, o in tato 75

94 flux-oiented efeence fae. In ode to avoid exta calculation and oe nonlinea tanfoation, tationay efeence fae i pefeed [48]. he ain advantage of uing the odel in tationay efeence fae ae: Reduced coputation tie, Salle apling tie, Highe accuacy, Moe table behavio. hu, we have choen tationay efeence fae in ou iulation and expeiental ipleentation Moto Model fo EKF he odel fo induction oto developed in tationay efeence fae and ued in the peviou tudie [], [8] i given below: + = q d q d q d l R l R q d q d V V K w ψ ψ i i w w K R K w K K K w K R K K w ψ ψ i i dt d (5.) ψ ψ = q d q d q d w i i i i (5.3) whee ( ) R / R R σ στ σ σ R K K + = + = + =,, ae oto, tato and ain inductance, ae oto and tato tie contant 76

95 hi odel ha a diadvantage; it ode i highe. hi will be a dawback when the EKF algoith ha to be ipleented in eal-tie. One geat advantage of thi odel, howeve, i that it doe not need peed eaueent, o neithe the flux peed no the oto peed ha to be known. he othe i that, the flux odel entioned in Chapte can be oitted, ince thi odel alo etiate the flux, and o the angle of the flux and any othe paaete can be diectly calculated. It hould be noted that in (5.) it ha been aued that the oto-peed deivative i negligible, dw /dt=. Although the lat ow of the A [5x5] atix in (5.) coepond to infinite inetia in eality it i not and the equied coection i accoplihed by the Kalan filte (by the yte noie copenation, which alo take account of the coputational inaccuacie ) [48]. If the load-toque i not known, the change of w cannot be found fo the eaining tate and contol ignal. hi poble can be ovecoe by intoducing the echanical peed a a paaete athe than a tate []. w i aued to be contant duing the tate etiate tie update coputation but it i included in covaiance tie update coputation. he peed will, theefoe, be etiated in the tate etiate eaueent update tep. Futheoe, it hould be noted that the effect of the atuation in agnetic path of the achine have been neglected in the odel. hi auption i jutifiable. It can be hown that the EKF i not enitive to change in inductance, ince change in the tato paaete ae being copenated by EKF. he application of (5.) to the EKF will give not only the oto peed, but alo the oto flux-linkage coponent (and conequently the angle and odulu of the oto flux-linkage pace-vecto will alo be known). hi i ueful fo high pefoance field-oiented dive ipleentation. It i ipotant to ephaize that the oto peed ha been conideed a a tate vaiable and the yte atix A i non-linea and it contain the peed, A=A (x). he copact fo of (5.) and (5.3) ae: dx dt = Ax + Bu (5.4) y = Cx (5.5) whee: 77

96 ( ) ( ) ( ) ( ) ( ) k x k y k u k x k x d d d C B A = + = + (5.7) (5.6) = = = C B w w K R K w K K K w K R K K l R l R A and i the tate vecto, u i the input vecto,, A i the yte atix, and C i the output atix. q d q d ] w i [i x ψ ψ = q d ] V u = [V Dicetized augented achine odel he oto equation (5.4) and (5.5) ae to be dicetized fo the digital ipleentation of EKF a: (5.8) A d and B d atice in the (5.7) ae dicetized yte and input atice, epectively. hey ae: (5.9) [ ] ( ) (5.) whee i the apling tie. Note that the dicete output atix C d =C i defined in (5.6). When the lat te in (5.9) and (5.) ae ignoed, then vey hot aplingtie, they equie, ae attainable to have a table and accuate dicetized odel. AB B B A I A d d + = A exp A + + = 78

97 Howeve, a bette appoxiation i obtained with the given econd-ode eie expanion at (5.9) and (5.). In geneal to achieve an adequate accuacy, the apling-tie hould be appeciably alle than the chaacteitic tie-contant of the achine. he final choice fo thi hould be baed on obtaining adequate execution tie of the full EKF algoith and alo atifactoy accuacy and tability. he econd-ode technique obviouly inceae the coputational tie. If the econd-ode te ae neglected in (5.9) and (5.) then the dicete fo of (5.4) and (5.5) becoe: (5.) (5.) ( ) ( ) ( ) ( ) ( ) k y C x k k u k x k x d A d B d = + = + whee (5.3) (5.4) (5.5) (5.6) (5.7) = w w K R K w K K K w K R K K A R R d d d ζ ζ d A d A d d A A + = I e B B = e B C = C = = C and B 79

98 x(k) = [ i (k) i ( k) ψ ( k) ψ ( k) w (k)] d q d q (5.8) u (k) = [ V (k) V (k)] d q (5.9) By conideing the yte noie ( k) zeo-ean white-gauian and independent of yte odel becoe: v ( v i the noie vecto of tate), being x ( k) with a covaiance atix Q, the x ( k + ) = A x( k) + B u( k) + v( k) d d (5.3) By conideing a zeo-ean white-gauian eaueent noie, (noie in the eaued tato cuent) which i independent of k and v k with a covaiance atix R, the output equation becoe : w( k) y ( ) ( ) ( k) = Cx( k) w( k) y + (5.3) Ipleentation of the Dicetized EKF Algoith Deteination of the noie and tate covaiance atice o be oe pecific, the goal of the Kalan filte i to obtain uneauable tate (i.e. covaiance atice Q, R, P of the yte noie vecto, eaueent noie vecto, and yte tate vecto (x) epectively). In geneal, by ean of noie input, it i poible to take coputational inaccuacie, odeling eo, and eo in eaueent into account in odeling the yte. he filte etiation ( xˆ ) i obtained fo the pedicted value of the tate ( x ) and thi i coected ecuively by uing a coection te, which i poduct of the Kalan gain () and the deviation of the etiated eaueent output vecto and the actual output vecto ( y yˆ ). he Kalan gain i choen to eult in the bet poible etiated tate. hu filteing algoith contain baically two ain tage, a pediction tage and a filteing tage. Duing the pediction tage, the next pedicted value of the tate ( k ) x + ae obtained by uing a atheatical odel (tate vaiable equation) and alo the peviou value of the etiated tate. Futheoe, the pedicted-tate covaiance atix (P) i alo obtained befoe the new eaueent ae ade and fo 8

99 thi pupoe the atheatical odel and alo the covaiance atix of the yte (Q) ae ued. In the econd tage which i the filteing tage, the next etiated tate, x ˆ ( k + ), ae obtained fo the pedicted etiate x( k + ) by adding a coection te ( y yˆ ) to the pedicted value. hi coection te i a weighted diffeence between the actual output vecto ( y ) and the pedicted output vecto ( ŷ ), whee i the Kalan gain. hu the pedicted tate-etiate (and alo covaiance atix) i coected though a feedback coection chee that ake ue of actual eaued quantitie. he Kalan gain i choen to iniize the etiation eo vaiance of the tate to be etiated. he coputation ae ealized by uing ecuive elation. he algoith i coputationally intenive, and the accuacy alo depend on the odel paaete ued. A citical pat of the deign i to ue coect initial value fo the vaiou covaiance atice. hee can be obtained by conideing the tochatic popetie of the coeponding noie. Since thee ae uually not known, in ot cae they ae ued a weight atice, but it hould be noted that oetie iple qualitative ule can be et up fo obtaining the covaiance in the noie vecto. With advance in DSP technology, it i poible to ipleent an EKF conveniently in eal tie [48,49]. he yte noie covaiance atix (Q) i [5x5], and the eaueent noie covaiance atix (R) i [x] atix, o in geneal thi would equie the knowledge of 9 eleent. Howeve, by auing that the noie ignal ae not coelated, both Q and R ae diagonal, and only 5 eleent ut be known in Q and eleent in R. Howeve, the paaete in α and β axe ae the ae, which ean that the fit two eleent of the diagonal ae equal (q=q), the thid and fouth eleent in the diagonal of Q ae equal (q33=q44), o Q=diag (q,q,q33,q33,q55) contain only 3 eleent which have to be known. Siilaly, the two diagonal eleent in R ae equal (=), thu R=diag (, ). It follow that in total only 4 noie covaiance eleent need to be known. 8

100 Qi d Qi q Ri d Q = Qψ = d R ψ Ri Q q Qw q (5.3) Stating value of the tate vecto x and the tating value of the noie covaiance atice Q and R ae et togethe with the tating value of the tate covaiance atix P, whee P i the covaiance atix of the tate vecto. he tating tate covaiance atix can be conideed a diagonal atix, whee all eleent ae equal. he initial value of the atice eflect the degee of knowledge of the initial tate: the highe thei value, the le accuate i any available infoation on the initial tate. hu the new eaueent data will be oe heavily weighted and the covaiance peed of the etiation poce will inceae. Howeve, divegence poble o lage ocillation of the tate etiate aound the tue value ay occu when too high initial covaiance value ae choen. A uitable election allow u to obtain atifactoy peed convegence, and avoid divegence poble o unwanted ocillation. he accuacy of the tate etiation i affected by the aount of infoation that the tochatic filte can extact fo it atheatical odel and the eaueent data poceing. Soe of the etiated vaiable, epecially uneaued one, ay indiectly and weakly be linked to the eaueent data, o only poo infoation i available to the EKF. Afte deciding how to initialize the covaiance atice, the next tep i pediction of the tate vecto. -Pediction of the tate vecto Pediction of the tate vecto at apling tie (k+) fo the input u (k), tate vecto at peviou apling tie, x k k, by uing A d and B d i obtained fo x = A k+ d x + Bd u k k k x = ˆ F (k +, k, x k+ k k k (k),u(k)) (5.33) (5.34) whee 8

101 ψ + ψ + ψ ψ + + ψ + ψ + ψ + ψ + = q d q q d d q q d q R d q d d R w w i w i V K K w K R i K K V K K w K R i K K F (5.35) = = + q d k k d i i x ˆ h C (5.36) he notation k k x + ean that it i a pedicted value at the (k+)-th intant, and it i baed on eaueent up to k-th intant. In the following tep of the ecuive EKF coputation, covaiance atix of pediction i coputed. -Pediction covaiance coputation he pediction covaiance i updated by: k k k k k k x x x ˆ whee = = + = + F M Q M MP P (5.37) with (5.38) ψ ψ ψ ψ = w w K K R K w K K K K w K R K K x d q d R q R F = x h (5.39) 83

102 In (5.38) thee ae 7 eleent which ae contant and 8 eleent which ae vaiable. hu, in eal tie application poduct involving the peed and the flux-linkage have to be coputed. Next tep i the coputation of the Kalan filte gain atix. 3-Kalan Gain Coputation he Kalan filte gain (coection atix) i coputed a; h k = Pk k N [ NPk k N + R] whee N = (5.4) x x = xˆ k k 4-State Vecto Etiation he pedicted tate-vecto i added to the innovation te ultiplied by Kalan gain to copute tate-etiation vecto. he tate-vecto etiation (filteing) at tie (k) i deteined a: whee x ˆ ( y ŷ ) k k = x k k + k k k (5.4) y k = Cd x k k (5.4) 5-Etiation Covaiance Coputation he lat tep i etiation covaiance coputation a; P k k h = Pk k k x= xk k P x k k (5.43) afte all tep executed, et k=k+ and tat fo the tep- to continue the coputation ecuively. he EKF decibed hee can be ued fo eithe teady-tate o tanient condition of the induction achine fo the etiation of the oto peed. he peed etiation chee equie the onitoed tato voltage and tato cuent. Intead of uing onitoed tato voltage, the tato voltage can alo be econtucted by uing DC link voltage and invete witching tate, but epecially at low peed it i 84

103 neceay to have appopiate dead-tie copenation and alo the voltage dop aco the invete witche ut be conideed. he tuning of the EKF involve an iteative odification of the achine paaete and covaiance in ode to yield the bet etiate of the tate. Changing the covaiance atice Q and R affect both the tanient- and the teady-tate opeation of the filte. Alo in the ipleentation of the EKF diffeent Q and R atice ay be tied to detect the optiu cae which inceae pefoance of the EKF. Fo contant Q and R value eithe teady-tate o tanient condition have poo pefoance. If high accuacy i equied fo both condition then an algoith that witche to diffeent covaiance value at diffeent opeating point ay be added to the ain EKF algoith (Noie evel Adjutent). hi i alo tudied fo both tanient- and teady-tate condition and pefect eult ae obtained by thi way. It hould be noted about the following qualitative tuning ule: -) If R i lage then i all and tanient pefoance i fate. -) If Q i lage then i lage and tanient pefoance i lowe []. Howeve, if Q i too lage, o if R i too all intability ay occu 5.5 State Etiation Siulation with EKF In thi pat, the tate etiation pefoance of EKF i iulated. he iulation i ipleented with Matlab/Siulink. In thi iulation input voltage and eaued cuent in tationay efeence fae ae poduced by FOC iulation which wa ipleented in Chapte. It i quite difficult to ipleent all atix opeation and oveall coputation uing only Siulink. hu, EKF algoith i developed a a S-function and than ineted to Siulink in the fo of S-function block. S-function (yte-function) povide a poweful echani fo extending the capabilitie of Siulink. S-function ue a pecial calling yntax that enable you to inteact with Siulink equation olve. hi inteaction i vey iila to the inteaction that take place between the olve and built-in Siulink block. he fo of an S-function i vey geneal and can accoodate continuou, dicete, and hybid yte. A a eult, nealy all Siulink odel can be decibed a S- function. 85

104 he ot coon ue of S-function i in ceating cuto Siulink block. You can ue S-function fo a vaiety of application, including: Adding new geneal-pupoe block to Siulink, Incopoating exiting C code into a iulation, Decibing a yte a a atheatical et of equation, Uing gaphical aniation. An advantage of uing S-function i that one can build a geneal pupoe block that can be ued any tie in a odel, vaying paaete with each intance of the block []. he iulink odel and S-function code i given in Appendix B. In the iulation paaete of a -hp oto ae ued. Bae excitation fequency i 6 Hz. he obevable tate in thi odel a entioned in (5.8) ae: { i (k) i (k) ψ (k) ψ (k) w (k) }. In Fig.5.3 peed eveal of the oto d q d q ie(ec) Fig.5.3 High Speed, No-oad, Fou Quadant Speed Etiation with EKF (in (P/)* [ad/ec]) at no-load i given with efeence peed he etiated peed (jittey) and the efeence peed (linea) ae plotted togethe. Meaueent and tate covaiance ae choen o that both the tanient and teady tate peed eo ae optiized. One ay 86

105 chooe diffeent covaiance and obtain alot zeo teady-tate peed eo with a poo tanient peed etiation a hown in Fig.5.5 o vice vea. ie(ec) Fig.5.4 (Fig.5.3-Zooed at teady tate) High Speed, No-oad, Fou Quadant Speed Etiation with EKF at Steady State (in (P/)* [ad/ec]) w peed eo ie(ec) Fig.5.5- High Speed, No-oad, Speed Etiation with EKF Steady State Pefoance Optiized (in (P/)* [ad/ec]) In the cae of Fig.5.5 iulation, tate covaiance i deceaed; the algoith begin to behave uch that the tate pace odel give oe accuate etiate copaed to eaued value o it aign le ipotance to the eaueent. hi caue a deceae in Kalan gain which educe the coection peed of the cuent. In the 87

106 exta tie ued fo cuent coection the algoith find oppotunity to deceae the teady-tate eo. ie(ec) Fig.5.6 ow Speed, No-oad, Fou Quadant Speed Etiation with EKF (in (P/)* [ad/ec]) ie(ec) Fig.5.7 (Fig.5.6-Zooed) ow Speed, No-oad, Speed Etiation with EKF at Steady State to anient State (in (P/)* [ad/ec]) ow peed etiation pefoance of the EKF i alo quite atifactoy and cloe to efeence peed a hown in Fig (5.6)-(5.7). 88

107 ie (ec) Fig.5.8- High Speed, Full-oad, Speed Etiation with EKF (in (P/)* [ad/ec]) In Fig.5.8 ated echanical load i applied to the oto between ec. to veify the pefoance of EKF unde loaded condition. A hown above EKF wok popely even unde fully loaded cae. One ay deceae teady-tate eo to vey low level with appopiate tate covaiance optiized fo teady tate. ie(ec) Fig.5.9- High Speed, No-oad, Speed Etiation uing EKF with Adjutable Noie evel (in (P/)* [ad/ec]) 89

108 In Fig.5.9 diffeent fo Fig.5.3 both the teady tate and tanient tate eo ae iniized individually with adjutable noie level technique (AN). In AN, diffeent covaiance ae aigned fo cetain ange of tie both at teady tate and tanient-tate by a baic witching logic peed-eo i iniized epaately in each ange. ie(ec) Fig.5.- Etiated State in (5.8) Repectively at No oad In Fig 5. all the tate etiated by EKF ae given togethe. he aplitude of the tato cuent inceae at tanient tate due to inetia of the oto and deceae to vey low value at teady tate a hown in Fig. 5. and 5.. Note that, when the peed of the oto i cloe to zeo, the fequency of the cuent and fluxe deceae and becoe dc. hi ange i vey pobleatic in induction oto FOC contol due to exteely low fequency. he etiated peed wavefo of EKF lightly deviate becaue of thi eaon. At low peed pefoance of EKF i being affected negatively due to added negative effect of oe othe facto uch a inaccuate paaete value, peence of voltage dop on the witche which ae not accounted in the odel, etc., a well. In Fig.5. dq-axi oto fluxe and oto flux agnitude ae hown in enlaged fo. he contant aplitude flux and ooth flux agnitude i vital fo FOC a entioned in Chapte. hi deand i povided by EKF etiate a long a pope FOC technique i applied to the yte. 9

109 ie (ec) Fig.5.- State I & II (dq-axi Stato Cuent ) 9

110 ie(ec) Fig.5.- State III & IV (dq-axi Roto Fluxe with thei agnitude) 9

111 ie(ec) Fig.5.3- Injected noie to the tato cuent in pu ie(ec) Fig.5.4- Etiated oto peed with eaued noiy cuent (in (P/)* [ad/ec]) In Fig. 5.3 the injected noie to the tato cuent i hown. he noie i zeo ean, white and Gauian. he ai of the cuent injection i to obeve the low pa filte chaacteitic of EKF. A hown in Fig. 5.4, the etiated peed i not affected too uch fo the injected noie. he peed etiation accuacy ay be inceaed by inceaing the eaueent noie covaiance unde noiy condition thu the yte odel will have oe ipotance. 93

112 5.6 Uncented Kalan Filte Uncented Kalan filte (UKF) i a novel etiation tool intoduced by Julie and Uhlann [34-35] to eplace EKF in nonlinea filteing poble. A well-known, EKF i a iple olution deived by diect lineaization of the tate equation fo extending the faou (linea) Kalan filte into nonlinea filteing aea. Although it i taightfowad and iple, EKF ha well-known dawback[36]. hee dawback include:. Intability due to lineaization and eoneou paaete.. Cotly calculation of Jacobian atice. 3. Biaedne of it etiate. 4. ack of analytical ethod fo uitable election of odel covaiance. UKF i popoed in ode to ovecoe the fit thee of thee diadvantage. he ain advantage of UKF i that it doe not need lineaization in the coputation of the tate pediction and covaiance. Due to thi, it covaiance and Kalan gain etiate ae oe accuate. hi accuate gain, at the end, lead to bette tate etiate. In thi tudy, UKF i intoduced into the poble of peed and flux etiation of an induction oto. Geneal iulation eult ae given and a bief copaion i ade between peed etiation pefoance of UKF and EKF. he filteing poble involved in thi thei i to find the bet (in the ene of iniu ean quae eo (MMSE)) linea etiate of the tate vecto of the induction achine which evolve accoding to the dicete-tie nonlinea tate tanition equation k+ = f (x k, u k ) w k (5.44) x + whee i the induction achine dynaic, x i the tate of the induction f (.,.) achine at apling intant k, tie k and w k i the known input to the induction achine at i the additive white poce noie te epeenting odeling eo. Alo, it i aued that we have a et of noiy eaueent u k the tate vecto of the induction achine by the linea elationhip; k k k k z k x k which ae elated to y = Cx + v (5.45) whee C i the popely ized obevation atix and i the white eaueent noie elated with the eauing device ued. he additive white-noie vecto v k 94

113 w and ae Gauian and uncoelated fo each othe with zeo ean and k v k covaiance Q and R, epectively. he tate of the yte i aued to be unknown, and theefoe, the ai of the etiation poce i to find a MMSE etiate of the tate xˆ whee xˆ k k = E { x Y k } k k k which i given by (5.46) k Y = {, y,..., y } and E{ x y} denote the expected value of the quantity x, y given the infoation y k. Alo, taditionally, one calculate the eo etiate given by the covaiance atix P k k defined a P k k k {[x k xˆ k k ][x k xˆ k k ] Y = E } (5.47) hee diect definition being too difficult to calculate, ecuive fo ae adopted fo both the tate and covaiance etiate. he ecuive update equation fo the ae given a; xˆ k+ k + = xˆ k+ k + k+ υk+ (5.48) υ P k+ k + = Pk + k k+ Pk + k k+ (5.49) whee the vecto xˆ k + k (State Pediction), υ (Innovation) and the atice k+ k + υ (Kalan Gain), (State Pediction Covaiance), and (Innovation P k + k P k + k Covaiance) ae dependent on the quantitie xˆ and with the following k k P k k equation. xˆ k+ k = {, u ) Y k } E f (x k k {[x xˆ ][x xˆ ] Y k } P k+ k = E k+ k+ k k+ k+ k ẑ k+ k = k+ k υ Cxˆ k+ = y k+ ŷ k+ k υ Pk k CPk k C + R + = + (5.5) (5.5) (5.5) (5.53) (5.54) K xy υ k Pk + k (Pk + k ) (5.55) = + P C (5.56) xy P k+ k = k+ k he quantitie xˆ k + k and P k+ k, which ae called tate pediction and pediction 95

114 covaiance of the tate, epectively. hey ae vital fo the oveall filte pefoance. (5.5) and (5.5) do not pecify how thee quantitie ae calculated. EKF aue that eo in the tate etiate ae all enough to appoxiate (5.5) and (5.5) to thei fit ode aylo eie. A a eult, xˆ k + k and P k+ k ae calculated in EKF a follow; xˆ EKF k + k = f (xˆ k k, u k ) (5.57) P EKF k + k = f x Pk k f x + Q (5.58) whee denote the Jacobian atix of the function f with epect to the tate x. f x hi lineaization in EKF fequently yield wong eult in the etiate of the covaiance and thu the tate. UKF olve the pediction poble by apling the ditibution of the tate in a deteinitic anne and then tanfoing each of the aple uing the nonlinea tate tanition equation. he n -dienional ando vaiable x with ean xˆ and covaiance P i k k k k k appoxiated by n + weighted aple o iga point elected by the algoith. χ ( k k) = xˆ k k W = κ (n + κ) (5.59) χ (k k) = xˆ i k k + ( (n + κ)(p W = /((n + κ)) i k k + Q)) i (5.6) χ i+ n (k k) = xˆ W k k i+ n ( (n + κ)(p = /((n + κ)) k k + Q)) i (5.6) fo i =, K, n whee κ R i a fee eal nube uch that n + κ, ( ( n +κ )( P k k + Q) i i the th i colun of the atix, quae oot of n + κ)(p Q), and i the weight ( k k + W i aociated with the th i point. Given thee et of aple, the pediction poce i a;. Each iga point i tanfoed though the poce dynaic f ; χ i ( k + k) = f ( χ i (k k), u k ). he tate pediction i coputed a; (5.6) xˆ n k + k = Wiχ i (k + k) i= 3. he pediction covaiance i calculated a; (5.63) 96

115 n P k + k W i[ χi (k + k) xˆ k+ k ].[ χi (k + k) xˆ k+ k ] i= = (5.64) he equation (5.63) and (5.64) eplace (5.5) and (5.5). he othe UKF opeation ae the ae a (5.5) to (5.56). Note that, opeation in the new et of equation copoed by (5.63), (5.64), (5.5) - (5.56) togethe with eaueent update given in (5.48) and (5.49) ue only tandad vecto and atix opeation and need no appoxiation fo both deivative and Jacobian. Alo, the ode of calculation i the ae a that of EKF. In the next ection, a detailed induction achine odel ued in the ipleentation of UKF i given Siulation Reult A nube of iulation wee caied out to veify the pefoance of the tate etiation, paticulaly of the peed etiation with UKF. In Fig.5.5 Fig.5., the tate etiation pefoance of UKF i iulated and in Fig. 5., 5.3, accuacie obtained fo EKF and UKF ae copaed fo the peed etiation. Fig.5.5 how the actual tate vaiable of the oto; tato cuent, oto fluxe and oto peed at no-load in a high peed eveal chee. Fig.5.6 how coeponding etiated tate vaiable with UKF unde the ae condition. hee ae alot no diffeence between the actual and the etiated vaiable. 97

116 a b c d e ie () Fig.5.5- Induction oto actual tate at no load fou quadant high peed eveal (a-b) d-q axi tato cuent, (c-d) d-q axi oto fluxe, (e) oto peed. a b c d e ie () Fig Induction oto etiated tate with UKF at no load fou quadant high peed eveal (a-b) etiated d-q axi tato cuent, (c-d) etiated d-q axi oto fluxe, (e) etiated oto peed. 98

117 Fig.5.7 and Fig.5.8 illutate agnified etiated peed wavefo at no-load in fou quadant high peed and low peed eveal chee epectively. Both the high peed and low peed etiated wavefo confi that UKF pefoance i quite good in peed etiation fo all quadant without cauing intability. 5 ) p ( d e pe d a t e E ti ie () Fig Induction oto etiated peed at no-load fou quadant high peed eveal (in p). 5 ) p ( d e pe d a te E ti ie () Fig Induction oto etiated peed at no-load fou quadant low peed eveal (in p) 99

118 a b c d e ie () Fig Induction oto etiated tate at % ated toque and peed (a-b) etiated d-q axi tato cuent, (c-d) etiated d-q axi oto fluxe, (e) etiated oto peed (load toque applied between.75-.5) In Fig.5.9, etiated tate vaiable of the induction oto ae hown unde % ated load toque and % ated peed condition. Note that echanical load i applied to the oto between only.75 and.5. In addition to high pefoance at no-load, UKF give quite atifactoy eult unde full-load condition. In Fig.5., and Fig.5., actual and etiated peed chaacteitic ae given on top of each othe fo % and % ated toque and peed cae. In the tanient pat of the wavefo, thee appea a diffeence between the etiated and actual value which i the eult of the fact that, in induction oto odel, the peed i conideed a a contant paaete and coected only in the eaueent update of the UKF. In iulation tet, we alo noticed that thee uually exit a all teady-tate eo between the etiated and actual peed value but that ee to be at negligible level.

119 ) p ( d e pe d a te E ti 8 4 ie () Fig. 5.- Induction oto etiated peed at % ated toque and peed (load toque applied between.75-.5) ) p ( d e pe d a te E ti ie () Fig. 5.- Induction oto etiated peed at % ated toque and peed (load toque applied between.75-.5). In Fig.5. and 5.3, the peed etiation pefoance of UKF and EKF with identical paaete ae copaed at % ated toque and peed. Siulation of Fig.5. and 5.3 wee caied out fo diffeent covaiance value. Covaiance value wee elected o that the teady tate pefoance in Fig.5. and the tanient pefoance in Fig.5.3 i optiized. It i obeved fo the figue that, although the pefoance of the EKF and UKF ae cloe to each othe, UKF educe the tanient- and teady-tate peed etiation eo by up to p unde ated condition.

120 79 ukf a ekf ) p ( d e pe d a t e E ti ie () b Fig. 5.- (b) Induction oto etiated peed optiized fo teady tate pefoance at % ated toque and peed uing EKF and UKF. (a) gaphic in (b) zooed at the echanical loading initiation. (load toque applied between.75-.5) 8 ukf a 76 7 ) p ( d e pe d a t e E ti 68 5 ekf b ie () Fig (b) Induction oto etiated peed optiized fo tanient pefoance at % ated toque and peed uing EKF and UKF. (a) gaphic in (b) zooed at the echanical loading initiation. (load toque applied between.75-.5) It ha been hown that UKF i a good a EKF at leat in tate obevation, and it yield even lightly bette peed etiation pefoance than EKF. hi eult encouage futhe tudy in the aea to obtain bette tate etiation pefoance fo nonlinea yte to ovecoe the well-known defect of EKF and othe taditional nonlinea filteing technique.

121 5.6. Expeiental Reult In addition to copute iulation of the dicued etiato, EKF and UKF, the expected eult ae alo confied with the expeiental eult. While obtaining the expeiental eult, the eal tie tato voltage and cuent ae poceed in Matlab with the aociated EKF and UKF poga. Fig.5.4 how etiation of tate I&II (dq axi tato cuent) ade by EKF and the actual tate I&II eaued fo the expeiental etup. It ay eaily be noticed that the etiated tate ae quite cloe to the eaued one. ie (ec) Fig he etiated tate I&II (uppe one_ dq axi tato cuent) by EKF and the eaued tate I&II (lowe one) ie (ec) Fig he etiated tate II&III by EKF (lowe one_dq axi oto fluxe) and the agnitude of the oto flux (uppe one) 3

122 Fig.5.5 how the etiated dq axi oto fluxe in tationay efeence fae. he agnitude of the oto flux jutifie that the etiated dq coponent of the oto flux do not involve dc offet and othogonal to each othe. In ode to exaine the oto peed (tate V) etiation pefoance of EKF expeientally unde vaying peed condition, a tapezoidal peed efeence coand i ebedded into the DSP code. A hown in Fig5.6, EKF oto peed etiation uccefully tack the tapezoidal path. ie (ec) Fig.5.6- Roto peed tacking pefoance of EKF obtained expeientally (in P/*ad/ec) he ae tate of the induction oto odel etiated by EKF ae alo etiated by UKF. Fig.5.7 how etiation of tate I&II (dq axi tato cuent) ade by UKF and the actual tate I&II eaued fo the expeiental etup. One ay eaily notice that the etiated tate ae quite cloe to the eaued one. Fig.5.8 how the etiated dq axi oto fluxe in tationay efeence fae by UKF. he agnitude of the oto flux jutifie that the etiated dq coponent of the oto flux ae etiated accuately. 4

123 ie (ec) Fig he etiated tate I&II (uppe one_ dq axi tato cuent) by UKF and the eaued tate I&II (lowe one) Fig he etiated tate II&III by UKF (lowe one_dq axi oto fluxe) and the agnitude of the oto flux (uppe one) 5

124 ie(ec) Fig.5.9- Roto peed tacking pefoance of UKF obtained expeientally (in P/*ad/ec) he ae tapezoidal efeence i alo applied to the UKF peed tacking expeient. A hown in Fig 5.6, UKF oto peed etiation uccefully tack the tapezoidal path. In ode to copae both type of the obeve, EKF and UKF, the covaiance atice egading to both type have been initialized with the ae entie unde the ae opeating condition. he etiated oto peed wavefo, when plotted togethe a hown in Fig.5.3, confi that the etiation accuacy of UKF i upeio ove EKF a claied befoe when dicuing the iulation eult elated to both obeve deign technique. he iulation eult wee hown in Fig.5. and Fig Etiated Speed (p) efeence peed EKF UKF Etiated Speed (p) 8 UKF EKF 75 load eoved ie(ec). 3.5 ie (ec) 6. Fig.5.3. Roto peed wavefo obtained expeientally by UKF and EKF unde the ae expeiental condition (in p) 6

125 A expected fo iulation in the Fig.5. and 5.3, the peed etiation accuacy of UKF i bette than EKF unde the ae expeiental condition. he ean of the tate etiation eo in UKF i.65 ad/ec at teady tate, and that in EKF i 5.8 ad/ec. hi eult how that the etiate of EKF have eiou bia poble copaed to UKF. A dicued ealie, the deivative fee algoith of UKF without a lineaity appoxiation contibute it etiate poitively. Futheoe, the noie apling featue of UKF i oe ealitic appoach intead of auing the noie diectly a Gauian. hi popety alo ake it etiation accuacy bette than EKF. 7

126 CHAPER 6 MODE REFERENCE ADAPIVE SYSEMS 6. Adaptive Contol Adaptive contol ay be defined in any way. A poible definition of adaptive contol i a yte that adapt itelf to change in the poce. Anothe definition, that i often ued but pobably too vague to be ueful, i a yte which i deigned fo an adaptive point of view. A oe ueful one i a yte that conit of a piay feedback that take cae of poce ignal vaiation and a econday feedback that deal with poce tate change. In thi definition, the piay feedback i ued a in non-adaptive contol, and the econday feedback ake the yte adaptive. Fo thi definition it i clea that poce tate vaiation give ie to adaptation of the yte. he ai of eacting to tate change i to attept to aintain a high yte pefoance, even if the poce tate ae unknown o vaying [57]. In the liteatue thee exit eveal adaptive contol technique. In thi thei Model Refeence Adaptive Syte i applied to induction oto dive a a tate obeve. 6. Model Refeence Adaptive Syte Model Refeence Adaptive Syte (MRAS) i one of the ot popula adaptive contol ethod ued in oto contol application fo tacking and obeving yte paaete and tate [9-],[5,8,-5,58-64]. hee exit a nube of diffeent odel efeence adaptive contol technique uch a paallel odel, eie odel, diect odel and indiect odel etc. MRAS ued in thi thei i paallel 7

127 odel MRAS that copae both the output of a efeence odel and adaptive odel, and pocee the eo between thee two accoding to the appopiate adaptive law that do not deteioate the tability equieent of the applied yte. A genealized paallel MRAS chee i hown in Fig.6. whee the piay contolle i ued to obtain uitable cloed-loop behavio, a in non-adaptive contol chee. Howeve, becaue the poce paaete ae unknown o ay vay with tie, a fixed paaete etting fo the piay contolle, uch that the cloed-loop behavio i acceptable unde all cicutance, cannot be found. In the MRAS technique, the deied poce epone to a coand ignal i pecified by ean of a paaetically defined efeence odel. An adaptation echani keep tack of the poce output y p and the odel output y and calculate a uitable paaete etting uch that diffeence between thee output tend to zeo. In addition to poce output y p, the poce x p, if available, and the poce input u o the efeence ignal ay be ued by adaptation echani. Refeence Model y Paaete Adaptive aw Piay Contolle u Poce y p Fig.6.- Geneal paallel MRAS chee An ipotant iue in MRAS i the deign of adaptive law. he fit exaple of adaptive law deign ade ue of enitivity odel, and late the tability theoy of yapunov, and Popov hypetability theoy, eved a tandad deign ethod, yielding a guaanteed table adaptive yte. (ee Appendix A) 8

128 6.3 Intoduction to MRAS pactice in oto contol application In a MRAS yte, oe tate vaiable, x d,x q (e.g. back e..f coponent (e d, e q ) eactive powe coponent (q d, q q ), oto flux coponent (Ψ d, Ψ q ) etc.) of the induction achine, which can be obtained a ened vaiable uch a tato voltage and cuent, ae etiated in efeence odel. hey ae then copaed with tate-vaiable xˆ d and xˆ q etiated by uing adaptive odel. he diffeence between thee tate-vaiable i then ued in adaptation echani, which output the etiated value of the oto peed (w) and adjut the adaptive odel until atifactoy pefoance i achieved. Such a chee i hown in Fig.6. whee copact pace-vecto notation i ued. Howeve, Fig.6.3 coepond to an actual ipleentation, and hee coponent of the pace vecto ae hown in detail. u i Refeence Model x + Adaptive Model xˆ ŵ Adaptation Mechani Fig.6.- Genealized Model Refeence Adaptive Syte u D u Q i D i Q Refeence Model x d ε d ε q x q Adaptive Model ŵ xˆ d xˆ q Adaptation Mechani v = [ ε d, ε q ] Fig.6.3- MRAS baed peed etiato chee uing pace vecto 9

129 he appopiate adaptation echani can be deived by uing Popov citeion of hypetability. hi eult in a table and quick epone yte, whee the diffeence between the tate vaiable of the efeence odel and adaptive odel ae anipulated into peed tuning ignal ( ε ), which i then input to a PI-type of contolle that output the etiated oto peed. wo of the chee will be dicued in the following ection: eactive powe and back e..f eo ae ued a peed tuning ignal. In thee expeion i and u denote the tato voltage and tato cuent pace vecto epectively in the tationay fae e denote the back ef pace vecto alo in tationay efeence fae a e = e ê. he ybol ^ denote the quantitie etiated by the adaptive odel. In addition to thee claical MRAS chee, atificial intelligence technique aited MRAS peed etiato ae alo dicued in the liteatue. hey contain neithe any atheatical adaptive odel, no any adaptation echani incopoated into the tuning of appopiate atificial intelligence baed netwok (which can be a neual netwok, a fuzzy-neual netwok, etc.) [3-4, 6]. o ipove the pefoance of the obeve decibed in thi ection, vaiou pactical technique ae alo dicued which avoid ue of pue integato. Pue integato lead dift and initial condition poble in digital application, o ecent peed enole algoith tend to avoid pue integato. Mot of the taditional vecto contol algoith ue low-pa filte intead of pue integato, although they alo caue eiou poble at low peed ange. Recent MRAS algoith entioned in thi thei avoid both pue integato and low-pa filte. Reactive powe chee decibed below i obut to both tato and oto eitance vaiation, and can even be applied at vey low peed (but not zeo peed). Both of the obeve (eactive powe and back ef chee) decibed below ue onitoed tato cuent and tato voltage. In a voltage-ouce inveted-fed dive, howeve, it i not neceay to onito the dc link voltage and the tato voltage ince the latte can be econtucted by uing the invete witching tate.

130 6.4.Application of Popov hypetability theoe and integal inequality hi pat contain a hot deciption of the election of the appopiate adaptation echani, pove why thee i a PI contolle in the chee decibed in MRAS chee ued in thi thei, and alo how the fo of peed tuning ignal to be ued. In geneal, a odel efeenced adaptive peed etiato yte can be epeented by an equivalent non-linea feedback yte which copie a feedfowad tie-invaiant linea ubyte a well a a feedback non-linea tie-vaying ubyte. hi i hown in Fig u = w w inea tie invaiant feedfowad ubyte v Non-linea tie vaiant feedback ubyte Fig.6.4- Equivalent non-linea feedback yte In Fig.6.4 the input to the linea tie-invaiant yte i u (which contain the tato voltage and cuent), it output i v, which i the peed-tuning ignal v =[ ε d,εq ]. he output of the non-linea tie invaiant yte i w, and u = -w. he oto peed etiation algoith (adaptation echani) i choen accoding to Popov hypetability theoy, wheeby the tanfe function atix of the linea tie invaiant yte ut be tictly poitive eal and the non-linea tie-vaying feedback yte atifie Popov integal inequality, accoding to which v w dt in the tie inteval [, t] (ee appendix B). hu to obtain the adaptation echani, fit the tanfe function F() of the linea tie-invaiant feed-fowad ubyte ha to be obtained. It can be hown by lengthy calculation that in both of the chee decibed in the following pat thi i tictly poitive eal. A poible poof ue the tate-vaiable fo of the eo equation, dv/dt = Av-w, which i obtained by ubtacting the tate vaiable equation of the adjutable odel fo the tate-vaiable equation of the efeence odel (whee A i the tate atix).

131 he feed-fowad path tanfe atix of the linea tie-invaiant ubyte hown in Fig.6.4 i F() = [I-A],whee I i an identity atix. It follow fo the deivation of the eo tate equation that w (whee = [ŵ w ][ q x d ] d q ae etiated by adaptive odel), thu w i ubtituted into Popov integal xˆ xˆ and xˆ inequality, letting ŵ v w dt p i, it can be hown that thi inequality can be atified by = (K + K / p) ε. In thi equation /p epeent an integato and ε i the appopiate peed-tuning ignal. In geneal, the tate vaiable in the efeence and adaptive odel ae x d, x q and xˆ d, xˆ q, epectively. Speed tuning ignal i I( x xˆ ), whee the ateik denote the coplex conjugate. Speed-tuning ignal ae obtained fo I( e ê ) and I( q qˆ ) whee e and q epeent back ef and eactive powe, epectively. It can be een that when a pecific tate-vaiable i ued (on the output of the efeence and adaptive odel), then a coeponding peed tuning ignal of a pecific fo i obtained by Popov integal inequality. Fo the peviou dicuion it i noted that when the etiated oto-peed with the adaptive odel change in uch a way that the diffeence between the output of the efeence odel and the adaptive odel i zeo, then the etiated oto peed i equal to the actual oto peed. he eo ignal actuate the oto-peed identification algoith, which ake thi eo convege ayptotically to zeo. he phyical eaon fo the integato (in PI contolle) i that thi enue that the eo convege ayptotically to zeo. In ecent yea eveal MRAS chee ae tudied fo vecto contol of ac dive without peed eauing eno. Mot of thee chee have low peed poble due to the low-pa filte o pue integato. hee chee obtain peed tuning ignal fo tate vaiable, x d,x q (e.g. active powe coponent (p d, p q ), oto flux coponent (Ψ d, Ψ q ), toque coponent (te d,te q ), voltage coponent (v d,v q ) etc.). In addition to thee chee, ecently popoed chee uing back ef and eactive powe enhanced the pefoance of the MRAS olution excluding pue integato in thei algoith [6]. Alo eactive powe MRAS odel i tuly obut to tato eitance change. he detail of thee chee will be given in the next ection.

132 6.5 Back ef MRAS Schee In thi MRAS chee the back ef (e ) i ued a peed tuning ignal. When the back ef i ued then the poble aociated with the pue integato in the efeence odel diappea, ince in thi cae the efeence odel doe not contain any integato. Equation fo an induction oto in the tationay fae can be expeed a: V di dt di = R i + σ + e dt = w i i + i (6.) (6.) whee w i a vecto whoe agnitude w i oto electical angula velocity, and whoe diection i deteined accoding to ight hand yte of coodinate a hown in Fig.6.5 denote the co poduct of vecto epectively. q w i w q d ê Fig.6.5- Coodinate in tationay efeence fae e Fo (6.) and (6.), e and tuctue of MRAS can be deived a follow: 3

133 e e di = V R i + σ dt di = dt w i i + i = (6.3) (6.4) (6.5) If we ewite the equation above fo the diect and quadatue-axi back ef in the following fo: e e d q = = V = = V d q di dt d = R i dψ di R i d + σ dt di q dψ q = dt dt q + σ dt d di d q dt (6.6) (6.7) If we ue the counteelectootive foce (ef) vecto e intead of oto flux vecto which wa ued in the peviou MRAS chee [8] fo peed identification, then a new MRAS yte i obtained. Fig.5.6 illutate the new tuctue of the new MRAS fo peed etiation. wo independent obeve ae configued to etiate the coponent of the counte-emf vecto, one baed on (6.6) and the othe baed on (6.5) and (6.7). he obeve baed on (6.6) can be egaded a a efeence odel of the induction oto ince (6.6) doe not involve the quantity w, and the one baed on (6.5) and (6.7) can be egaded a adjutable odel becaue (6.5) and (6.7) do involve w. he eo between the output of the two obeve i then ued to dive a uitable adaptation echani which geneate the etiate ŵ fo the adjutable odel. 4

134 Fig.6.6- Stuctue of the MRAS yte fo peed etiation When the chee hown in Fig. 6.5 i eployed in a peed-enole vecto contolled dive, ince the efeence odel doe not contain pue integation a atifactoy pefoance can be obtained even at low peed if an accuate value of the tato eitance i ued. Howeve, the tato eitance vaie with tepeatue, and thi affect the tability pefoance of the peed obeve, epecially at low peed. A MRAS chee which i intenive to tato eitance vaiation can be obtained by uing uch a peed-tuning ignal, which i obtained fo a quantity which doe not contain the tato eitance. hi i dicued late. On the othe hand, oe of the application ue paaete etiation o paaete tacking algoith to copenate the eo caued by paaete deviation. hu, in liteatue thee exit eveal on-line paaete etiation algoith at eal tie. Paaete deviation effect on MRAS algoith will alo be dicued in thi thei Adaptation Mechani and Stability of MRAS It i ipotant to enue that the yte will be table and the etiated quantity will convege to the actual value fo the adaptation echani of MRAS algoith. In geneal w i a vaiable; thu the odel ae linea tie-vaying yte. Fo the pupoe of deiving an adaptation echani, howeve, it i valid to initially teat w a a contant paaete of the odel. By diffeentiating both ide of (6.7), we get 5

135 (6.8) dt di e + e w dt de = Hee, letting, and ubtacting (6.8) fo the adjutable odel fo (6.8) fo the efeence odel, we obtain the following tate eo equation: ε ê = e (6.9) W A ê ) w ( w d ε ε = ŵ dt ε = ε whee. J, I and ê ê ) w (ŵ ê ) w (ŵ W J, w I w w A d q = = = = + = = Since i poduced by adaptation echani, (6.9) decibe a nonlinea feedback yte a hown in Fig.6.7. Hypetability equie that the linea tie-invaiant fowad path tanfe atix be tictly poitive and eal, and that the nonlinea feedback including the adaptation echani atifie Popov citeion fo hypetability. ŵ 6

136 inea Block + W + + A ε e + w ŵ Adaptation Mechani Non-linea tie vaying block Fig.6.7- Equivalent nonlinea feedback yte of MRAS Popov citeion equie that t ε W dt γ fo all t (6.) whee γ i a eal poitive contant and i dot poduct. Hee, letting ŵ = K p K + p i (ê ε) (6.) and ubtituting fo W in inequality (6.), (6.) becoe t t ε W dt = ε {(ŵ w ) ê }dt (6.) t = ( ε ê ) w (K p + K p i )(ê ε) dt γ 7

137 Uing the following well known inequality: t d dt f (t) f (t)dt f () (6.3) it can be hown that inequality (6.) i atified Reactive Powe MRAS Schee In the peviou pat, back ef i ued a tuning ignal and the pefoance of the MRAS i poved to be pefect in the iulation. Since the efeence odel doe not equie pue integation, thi yte can achieve good pefoance even at low peed, a long a the value of tato eito i known peciely. he tato eitance, howeve, vaie with the tepeatue of the tato. he tato eitance theal vaiation affect the pefoance and tability of MRAS peed etiato, epecially at low peed a hown late in thi thei. heefoe, a peed identification yte with low enitivity to the tato eitance vaiation i neceay fo application of lowpeed dive. Hee, anothe appoach to peed identification which i copletely obut to tato eitance vaiation i popoed. hi chee can be epeented in two diffeent way whoe baic ae the ae. Fit let u define a new quantity q a the co poduct of the counte EMF vecto e and the tato cuent vecto i. hat i, q = i e (6.4) q i a vecto, whoe diection i hown in Fig.4, and whoe agnitude q epeent the intantaneou eactive powe aintaining the agnetizing cuent. Subtituting the (6.6) and (6.7) fo e in (6.4) noting that i i,we have = q q = i = v (i σ i )w di dt + i i (6.5) (6.6) Uing (6.5) and (6.6) a the efeence odel and the adjutable odel, epectively. An MRAS yte can be dawn a in Fig.6.7, whee popotional and integal (PI) 8

138 opeation ae utilized a the adaptation echani. Fo (6.5) and (6.6), it i evident that the peed etiation yte of Fig.6.8 i copletely obut to the tato eitance, beide equiing no integal calculation. Refeence Model u i Equation (5.5) q + ε qˆ Equation (5.6) Equation (5.5) Adaptation Mechani Adjutable Model ŵ Fig.6.8- Syte tuctue of oto peed obeve uing the tuning ignal I e i ) ( he infoation equied fo thi odule i tato voltage and tato cuent coponent in the d-q tationay efeence fae. wo et of equation ae developed to copute eactive powe of the induction oto in the efeence and adaptive odel. he efeence odel doe not involve the oto peed while the adaptive odel need the etiated oto peed to adjut the coputed eactive powe to that coputed fo the efeence odel. Notice that the epeentation of coplex nube i defined fo the tato voltage and cuent in the tationay efeence fae i.e., v = vd + jvq and i = id + ji q. 9

139 6.6. Refeence Model Continuou ie Repeentation he back ef of the induction oto can be expeed in the tationay fae a follow: ê d = dψ dt d di d = v d R i d σ dt (6.7) ê q = dψ dt q = v q R i q σ di dt q (6.8) e = e d + je q (6.9) he eactive powe of the induction oto can be coputed fo co poduct of tato cuent and back ef vecto a follow: q di di = i e = i v R i σ = i v i σ dt (6.) dt whee i i = idiq iqid = and σ = (leakage cofficient). A a eult the eactive powe hown in (6.) can futhe be deived a di q di d q = σ i i d v q i q v d i d q (6.) dt dt 6.6. Adaptive Model Continuou ie Repeentation he etiated back ef coputed in the adaptive odel can be expeed a follow: ê d = di dt d = ( ŵ i i + i ) q d d (6.) ê q = di dt q = ( ŵ i i + i ) d q q (6.3) ê = ê d + jê q (6.4)

140 whee = equation: R i the oto tie contant, i d,i q ae coputed fo the following di dt d = ŵ i q i d + i d (6.5) di dt q = ŵ i d i q + i q (6.6) Once the etiated back ef coputed by (6.)-(6.6), the etiated eactive powe can be coputed a follow: qˆ = i ê = i d ê q i q ê d (6.7) hen, the PI contolle tune the etiated oto peed uch that the eactive powe geneated by adaptive odel atche that geneated by efeence odel. he peed tuning ignal i the eo of eactive powe that can be expeed a follow: ε e = i ( e eˆ ) = q qˆ (6.8) When thi obeve i ued in a vecto-contolled dive, it i poible to obtain atifactoy pefoance even at vey low peed. he obeve can tack the actual oto peed with a bandwidth that i only liited by noie, o the PI contolle gain hould be a lage a poible. he chee i inenitive to tato eitance vaiation. he paaete ha a negligible influence on the opeation of both of the oveall MRAS vecto contol yte. If the MRAS uccefully aintain nealy zeo eo, and if the ae value of i ued in the MRAS adjutable odel and in the function block fo calculating w lip, then we have the following elation: w = ŵ and w = ˆ ŵ whee vaiable without ^ ae actual value, and e e lip lip one with ^ epeent the coeponding value ued in the MRAS vecto contol yte. hu, if ˆ, then w lip ŵ lip, but o ŵ o w =, which i ued fo oienting the tato cuent vecto. heefoe, coplete field-oientation can be achieved even if the value of i quite wong. he eo in the value of, howeve, poduce an eo in the peed feedback, thu affecting the accuacy of the peed contol a follow:

141 ε w = wˆ w = ˆ w lip (6.9) hi alo hold fo the peviou MRAS chee. Howeve, the accuacy of the peed etiation yte dicued depend on the tanient tato inductance and alo efeed agnetizing inductance. he latte quantity i not too pobleatic, ince it doe not change with tepeatue. Futheoe, deviation of fo it coect value poduce a teady-tate eo in the etiated peed and thi eo becoe ignificant at low peed Dicete tie epeentation fo icocontolle ipleentation Fo ipleentation on DSP baed yte, the diffeential equation need to be tanfoed to diffeence equation. Due to high apling fequency copaed to bandwidth of the yte, the iple appoxiation of nueical integation, uch a fowad, backwad, o tapezoidal ule, can be adopted [65]. Conequently, the eactive powe equation in both efeence an adaptive odel ae dicetized a decibed in the next ection Refeence Model Accoding to (5.) efeence odel eactive powe i given a : q = i d v q i q v d σ i d di dt q i q di dt d Uing backwad appoxiation: q (k) = i d σ (k)v i d q (k) i i (k) q q (k)v d (k) (k) iq (k ) i q i (k) d (k) i d (k ) (6.3) And thi equation can be futhe iplified a: q (k) = i d σ (k)v (k) i ( k)v (k) ( i (k )i (k) i (k)i (k ) ) d q q q d d q (6.3) whee i the apling tie.

142 Adaptive Model Accoding to (6.7), eactive powe in adaptive odel i deived a : qˆ = i ê = i d ê q i q ê d whoe dicete-tie epeentation i: q ˆ ( k) = i (k)ê ( k) i d q q (k)ê d (k) (6.3) In ode to copute ê d (k) and ê q (k) conide thei continuou tie epeentation di d ê d = = dt ( ŵ i i + i ) q d d (6.33) ê q = di dt q = ( ŵ i i + i ) d q q which have the dicete-tie epeentation a; ê d (k) = ( ŵ (k)i (k) i (k) + i (k)) q d d (6.34) ê q (k) = ( ŵ (k)i (k) i (k) + i (k)) d q q and i d (k),i q (k) can be olved by uing tapezoidal integation ethod which yield continuou tie epeentation di dt d = ŵ i q i d + i d (6.35) di dt q = ŵ i d i q + i q and dicete-tie epeentation a; i d (k) = i d (k ) ŵ (k) + + (6.36) i q (k )ŵ (k) + i d (k) i q (k)ŵ (k) 3

143 i q (k) = i q (k ) ŵ (k) + + i d (k )ŵ (k) + i q (k) i d (k)ŵ (k) (6.37) Pe unit, dicete tie epeentation Fo the ake of geneality, the pe unit concept i ued in all equation. Howeve, fo the iplicity the ae vaiable ae alo ued in the pe unit epeentation Refeence Model Dividing (6.3) by bae powe of V b I b, then it pe unit epeentation i a follow: q (k) = i d K (k)v (k) i (k)v (k) ( i (k )i (k) i (k)i (k ) ) d q q q d d q (6.38) Reaanging (6.38) to have the one in (6.39); q ( v (k) K i (k ) ) i (k)( v (k) + K i (k ) )pu (k) = i (k) (6.39) d q q q d d whee K σ b =, V b i bae voltage, and I b i bae cuent. V I b Adaptive Model Dividing (6.34) by bae voltage V b, then yield ê d (k) = K ( K ŵ (k)i (k) i (k) + i (k)) 3 q d d pu (6.4) ê q (k) = K ( K ŵ (k)i (k) i (k) + i (k))pu 3 d q q 4

144 whee K I w = i bae electical angula b b, K 3 = w b = and w b = πf b Vb R velocity. Siilaly, dividing (6.36) and (6.37) by bae cuent I b, then yield i d (k) = i d (k ) [ K ŵ (k) + K ] 4 5 i q (k )ŵ (k)k 6 + i d (k)k 7 i q (k)ŵ (k)k 8 i q (k) = i q (k ) [ K ŵ (k) + K ] 4 5 i d (k )ŵ (k)k 6 + i q (k)k 7 i d (k)ŵ (k)k 8 (6.4) whee K 4 w b = and K 8, K w b = 5 = +, K 6 = w b, K 7 = Siulation of the MRAS Schee In thi thei both the back ef and the eactive powe chee ae tudied in detail. In addition to the tudie elated with the theoetical bae of the odel, the iulation of the odel ae ipleented to confi the theoetical eult uing Matlab Siulink. In thee iulation the voltage and cuent output of induction achine odel ae ued a the input of MRAS chee. wo independent obeve ae configued to etiate the coponent of back ef and eactive powe. he obeve that doe not involve oto peed i called efeence odel, and the othe obeve including oto peed i called adaptive o adjutable odel. he eo between the output of the two obeve i then ued to deive a uitable adaptation echani which geneate the etiated peed fo the adaptive odel a hown in Fig.6.9 and Fig. 6.. In Fig.6.9 the adaptive odel i configued baed on (6.3)-(6.5) and iilaly the efeence odel i configued accoding to equation (6.6)-(6.7). In Fig.6. the adaptive odel i configued accoding to (6.5) and the efeence odel i configued accoding to (6.6). 5

145 Moto Model Fig.6.9- he Siulink odel of back ef MRAS chee Moto Model Fig.6.- he Siulink odel of eactive powe MRAS chee 6

146 5 hp ind. oto fou quadant peed tacking etiated peed (/ec) iq(ap) toque(n) et. peed(/ec) ie(ec) (a) 5 hp ind. oto fou quadant peed tacking ie(ec) (b) Fig. 6.- Fou-quadant peed eveal of 5 hp induction oto uing eactive powe MRAS chee at no_load up to ated peed (a) etiated peed, poduced toque due to inetia (J), q-axi tato cuent (b) etiated peed, peed eo (diffeence between the actual and etiated peed) 7

147 hp ind. oto fou quadant peed tacking iq(ap) toque(n) et. peed (/ec) ie(ec) (a) hp ind. oto fou quadant peed tacking etiated peed (/ec) ie(ec) (b) Fig. 6.- Fou-quadant peed eveal of hp induction oto uing eactive powe MRAS chee at no_load up to ated peed (a) etiated peed, poduced toque due to inetia (J), q-axi tato cuent (b) etiated peed, peed eo (diffeence between the actual and etiated peed) 8

148 5 hp ind. oto % ated toque % ated peed hp ind. oto % ated toque % ated peed Etiated peed(/ec) Speed eo Etiated peed(/ec) Speed eo (a) ie(ec) (a) ie(ec) 5 hp ind. oto % ated toque % ated peed hp ind. oto % ated toque % ated peed Etiated peed(/ec) Speed eo Etiated peed(/ec) Speed eo (b) ie(ec) (b) ie(ec) 5 hp ind. oto % ated toque % ated peed hp ind. oto % ated toque % ated peed Etiated peed(/ec) Speed eo Etiated peed(/ec) Speed eo (c) ie(ec) (c) ie(ec) Fig.6.3-5hp induction oto peed et. (a) % ated toque - % ated peed (b) % ated toque-% ated peed (c) % ated toque - % ated peed hp induction oto peed et. (a) % ated toque - % ated peed (b) % ated toque-% ated peed (c) % ated toque - % ated peed note: load toque applied between.75 to.5 in all figue 9

149 5 hp ind. oto peed etiation % ated toque % ated peed iq(ap) toque(n) et. peed (/ec) (a) ie(ec) 5 hp ind. oto peed etiation % ated toque % ated peed iq(ap) toque(n) et. peed (/ec) (b) ie(ec) 5 hp ind. oto peed etiation % ated toque % ated peed iq(ap) toque(n) et. peed (/ec) ie(ec) (c) Fig.6.4-5hp induction oto etiated peed peed uing eactive powe MRAS chee, applied toque and tato q-axi cuent (a)% ated toque, % ated peed (b)% ated toque, % ated peed (c)% ated toque, % ated peed note: load toque applied between

150 hp ind. oto peed etiation % ated toque % ated iq(ap) toque(n) et. peed (/ec) (a) ie(ec) hp ind. oto peed etiation % ated toque % ated peed iq(ap) toque(n) et. peed (/ec) iq(ap) toque(n) et. peed (/ec) (b) ie(ec) hp ind. oto peed etiation % ated toque % ated peed (c) ie(ec) Fig.6.5- hp induction oto etiated peed uing eactive powe MRAS chee, applied toque and tato q-axi cuent (a)% ated toque, % ated peed (b)% ated toque, % ated peed(c)% ated toque, % ated peed note: load toque applied between

151 Speed etiation uing back ef MRAS chee etiated peed (/ec) peed eo ie(ec) (a) Speed etiation uing back ef MRAS chee etiated peed (/ec) peed eo ie(ec) (b) Fig.6.6- A typical etiated peed uing back ef MRAS chee (a) hp ind. oto % ated toque % ated peed (b) 5hp ind. oto % ated toque % ated peed note: load toque applied between Fig.6. and Fig.6. how iulation eult fo fou-quadant peed tacking pefoance of the eactive powe MRAS chee with hp and 5 hp induction oto. he iulation hee ae ipleented unde no-load condition. Fig.6. (a) and Fig.6. (a) include etiated peed in ad/ec, geneated electoagnetic toque duing acceleation and deceleation due to inetia te (J) in n., and tato q axi cuent in ap. 3

152 In Fig.6. (b) and Fig.6. (b), oe accuate peed etiation and peed eo (diffeence between the actual peed and etiated peed) ae hown. No-load pefoance of the peed obeve i vey high a een in thee figue even at vey low peed ange. Since thee doe not exit any iediate tanient peed change due to echanical loading, peed output obtained in the iulation ae vey ooth with negligible peed eo. In Fig.6.3, peed etiation of 5 hp and hp induction oto ae iulated unde vaying-load condition. In Fig.6.3 (a) and (a) % ated toque i applied at % ated peed, in Fig. 6.3 (b) and (b) % ated toque i applied at % ated peed and in Fig.6.3 (c) and (c) % ated toque i applied at % ated peed. Heavy loading caue highe tanient peed eo due to high intantaneou peed change whee light-loading peed eo ae uch alle fo both % ated peed and % ated peed condition in pecentage. In all of the ituation tanient peed tacking at tating and at teady-tate, the peed etiation pefoance ae quite high. In Fig.6.4 and 6.5 the geneated electoagnetic toque and q axi tato cuent ae hown with etiated peed fo both 5 hp and hp induction oto at the ae loading condition given above. Fig.6.6 how typical peed etiation fo both of the oto unde full-load condition. hey ae obeved uing back ef MRAS chee. he peed obevation pefoance of two MRAS chee ae alot the ae except low-peed ange, the nea zeo peed. he back ef chee becoe highly dependent on the PID paaete paticulaly at low peed ange, theefoe, thee ay exit even intability poble which i neve een in eactive powe chee. So, eactive powe chee i upeio to back ef chee not only in iunity againt the paaete deviation (tato eitance), but alo in vey low peed pefoance a well. Futheoe, tanient peed change in back ef chee have highe ovehoot when copaed to eactive powe chee. heefoe, eactive powe chee i uch bette than all othe MRAS chee including pue integal and back ef chee, thu, ecoended fo peed obevation in ac dive. 33

153 6.8 Expeiental Reult A tate etiato ade by uing MRAS ha been teted expeientally a well. he expeiental data; the eal tie tato voltage and cuent ae obtained fo the etup i poceed by Matlab in the hot copute whee the aociated MRAS poga i unning. he output of the poceing ae diplayed in Fig.6.7, 6.8. Gain of PI can be changed to ipove the ettling tie, ovehoot, ie-tie, etc of the peed wavefo while the yte i going though the tanient-tate. he teady-tate accuacy of MRAS eet the expectation and quite ucceful. Alo, Fig. 6.8 how the peed tacking pefoance of the back ef MRAS chee. It i een that thi tacking pefoance of the peed etiato ee to be quite atifactoy. Fig.6.7 Roto peed etiated by MRAS expeientally at no-load by back ef chee (eaued. peed: 34 ad/ec) ie(ec) Fig Speed tacking of the back ef MRAS chee (in P/*ad/ec) 34

154 he iulation and expeiental wok how the geat poie of the tudied MRAS chee. Howeve, due to equipent liitation thee ethod ae not teted ove a wide peed and toque ange. Futhe, the expeiental wok i equied to ipleent thee technique in the entie toque peed ange of the induction oto. 35

155 CHAPER 7 FUX AND SPEED OBSERVERS FOR SENSORESS DIREC FIED ORIENAION In thi chapte, obeve configued fo diect field-oientation (DFO) ae invetigated. he field oientation i ipleented in two way a dicued in Chapte ; Diect Field-Oientation and Indiect Field-Oientation. he baic diffeence of thee ethod undelie in the anne of detecting the ynchonou peed. In IFO, the lip-angle i coputed and added to the oto peed to find the ynchonou peed. heefoe, one ut calculate the lip-angle and etiate the oto angle. In the cuent odel eployed in the IFO, d q-axe tato cuent and pecie oto tie-contant ae needed to find lip angle (o lip peed). Aftewad, adding thee two angle will give the ynchonou angle (ee chapte fo detail). In the liteatue, a nube of the algoith ae popoed to calculate the oto angle (o oto peed). hu, peviouly popoed obeve (deigned by uing MRAS and/o EKF technique) ae eployed in IFO due to thei oto-peed etiation popety. On the othe hand, in DFO, the ynchonou peed i coputed fo the atio of dqaxe fluxe. heefoe, one ut etiate the fluxe if enole contol without halleffect eno i equied. Flux etiato ued in thi chapte can copute both the ynchonou peed and the oto peed. Since the induction oto odel applied to EKF in Chapte 5 etiate the oto fluxe, it can alo be applied to DFO. Futheoe, MRAS algoith explained in Chapte 6 ay be added to flux-obeve ued in a DFO fo peed contol. he diffeent cobination of thee obeve can be ipleented in both field-oientation ethod. 35

156 7.. Flux Obeve he flux obeve odule defined in thi chapte i ued fo coputing dqtationay-axi fluxe and oto-flux angle. he input of the obeve ae dqtationay-axi cuent and voltage. he logic undelying thi flux obeve i baically an advanced voltage odel appoach [66] in which integation of the backef i calculated with a diffeent ethod. he well-known diadvantage of thi odel ae paaete dependency (i.e. R ) at low-peed and difting off of the integal of the ened vaiable. hee poble ae copenated with a cloed-loop in thi flux obeve. Baically, the fluxe obtained by cuent odel ae copaed with thoe obtained by the voltage odel then the eo i fed to a PID block to obtain copenating voltage thoe ae added to ened tato voltage. hee exit eveal algoith in the liteatue which coect the voltage odel with efeence to the cuent odel, o the cuent odel with efeence to the voltage odel accoding the ange in which one of thee odel i upeio to othe. In thi flux obeve, the voltage odel i coected by the cuent odel though a baic PI block. In the end, the tato fluxe ae ued to obtain oto fluxe and oto flux angle. he oveall obeve tuctue i given below: Continuou ie: he oto flux dynaic developed by cuent odel in ynchonouly otating efeence fae (w=w e ) can be hown a: dψ dt e,i d = i e d ψ e,i d + (w e w ) ψ e,i q (7.) dψ dt e,i q = i e q ψ e,i q + (w e w ) ψ e,i d (7.) whee, upecipt (i) epeent cuent odel dynaic and (e) epeent ynchonou fae. w e i ynchonou peed and w i the electical oto peed in ad/ec. In oto field-oientation, the ain goal i to align the oto-flux vecto to the d-axi tato cuent, thu q- axi oto-flux i egaded to be zeo. hat i: e,i e,i e,i ψ = ψd and ψq = 36

157 hu, (7.) and (7.) can be iplified to: dψ dt e,i d = i e,i d ψ e,i d (7.3) ψ e,i d = (7.4) hen the oto flux-linkage ae tanfoed into the tationay efeence fae by the invee pak tanfoation: ψ,i d = ψ e,i d co( θ ψ ) ψ e,i q in( θ ψ ) = ψ e,i d co( θ ψ ) (7.5) ψ,i q = ψ e,i d in( θ ψ ) + ψ e,i q in( θ ψ ) = ψ e,i d in( θ ψ ) (7.6) whee θ ψ i the oto-flux angle upecipt () epeent the tationay efeence fae. he tato fluxe ae obtained fo (7.5) and (7.6) a: ψ,i d = i d + i d = i d + ψ,i d (7.7) ψ,i q = i q + i q = i q + ψ,i q (7.8) whee, the tato and oto elf-inductance, epectively, and efe to the agnetizing inductance. he ae quantitie will be obtained with voltage odel a;,v ψ = ( u i R u ) dt d d d cop,d (7.9) ψ,v q = ( u i R u ) dt q q cop,q (7.) whee R i the tato eitance and paenthei in the integation i back ef with copenated voltage. he upecipt (v) indicate that the equation ae developed by conideing the voltage odel. Afte calculating the tato fluxe with voltage odel in (7.9) and (7.), they ae copaed with the tato fluxe calculated by 37

158 cuent odel in (7.7) and (7.8). hen the eo i fed to a PI block to obtain copenated voltage. u cop,d = K p ( ψ,v d ψ,i d ) + K I ( ψ,v d ψ,i d )dt (7.) u cop,q = K p ( ψ,v q ψ,i q ) + K I ( ψ,v q ψ,i q ) dt (7.) Once the tato fluxe obtained, oto-flux vecto i econtucted in tationay fae by uing (7.3) and (7.4) :,v,v ψ d = i d + ψ d (7.3) ψ,v q = i q + ψ,v q (7.4) hen the oto-flux angle baed on the voltage odel i calculated a: θ ψ = tan ψ ψ,v q, v d (7.5) 7.. Open-oop Speed Etiato he open-loop peed etiato eployed in thi FOC tuctue i a wellknown ethod baed on tationay efeence fae. he diadvantage of thi ethod i the paaete enitivity a in the cae of all open-loop etiato [67]. Howeve, the tuctue of thi algoith i quite eay when copaed to the advanced etiation technique. he atheatical bae of the etiato i given below that can eaily be extacted fo induction achine equation. ψ d = i d + i d (7.6) ψ q = i q + i q he oto cuent can be expeed a: (7.7) i d = ( ψ i ) d d (7.8) (7.9) i = q ( ψ i ) q q 38

159 he oto voltage can be expeed a: = R i d + w ψ q dψ + dt d (7.) = R i q w ψ d dψ + dt q (7.) whee R i the oto eitance. Subtituting (7.8) and (7.9) into (7.) and (7.), oto cuent ae extacted fo the oto flux dynaic a: dψ dt d = ψ d + i d w ψ q (7.) dψ dt q = ψ q + i q + w ψ d (7.3) Since we know the oto fluxe fo the peviou flux etiation odule, one can calculate the oto flux agnitude and angle: ψ θ ψ = ( ψ ) + ( ψ ) d q (7.4) ψ q = tan (7.5) ψ d hen the ynchonou peed, w e, can be calculated by the deivative of (7.5) a: w e = dθ dt ψ = ψ ( ψ d ) ( ψ ) d dψ q ψ dt ( ψ ) q dψ dt d (7.6) hen, (7.) and (7.3) ae ubtituted into (7.6) w e dθ = dt ψ = w + ( ψ ) ( ψ i ψ i ) d q q d (7.7) w lip 39

160 Finally, oto peed i calculated a: w = w e ( ψ ) ( ψ i ψ i ) d q q d (7.8) 7.3. Expeiental Reult he pefoance of the flux etiato and open-loop peed etiato ae teted in ou expeiental etup. It i hown that both etiato wok popely. he expeiental eult follow the ae equence with the equation to have eae in tacing the output tate tep by tep. he tato cuent and voltage ae quite cloe to a pue inuoidal wavefo due to highly pecie appoxiation of SVPWM. hu, the output of the flux etiato ae expected to be ufficiently cloe to inuoidal and the agnitude of the flux i ooth enough fo toque contol opeation. In Fig.7., typical input tato cuent and tato voltage wavefo ae given thoe ae obtained duing the expeient. 4

161 (a) (b) (c) Fig.7.- (a) tato phae cuent unde heavy load condition (b) tato phae cuent unde no-load condition (c) tato phae voltage 4

162 he dq-axe oto fluxe in tationay fae obtained fo cuent odel ((7.5), (7.6)) ae hown in Fig.7.. Fig.7.- dq-axe oto fluxe in tationay fae obtained fo cuent odel he dq-axe tato fluxe in tationay fae obtained fo the cuent odel oto flux etiate (( 7.7),(7.8)) ae hown in Fig.7.3 Fig.7.3- dq-axi tato fluxe in tationay fae obtained fo the cuent odel 4

163 he dq-axe tato fluxe in tationay fae obtained fo the voltage odel ((7.9),(7.)) conideing the copenating voltage ae hown in Fig.7.4. he back ef with added copenating voltage ((7.9),(7.)) ae hown in Fig.7.5. Fig7.4-he dq-axe tato fluxe in tationay fae obtained fo the voltage odel Fig.7.5- Back ef with added copenating voltage 43

164 Finally, the output of the flux obeve odule, dq-axe tationay fae oto fluxe econtucted by the voltage odel ((7.3),(7.4)), ae hown in Fig.7.6 and the agnitude of the thi oto flux i hown in Fig.7.7. Fig dq-axe tationay fae oto fluxe econtucted by the voltage odel Fig.7.7. q-axi tationay fae oto flux econtucted by voltage odel with oto-flux agnitude 44

165 he ooth flux agnitude in Fig.7.7 guaantee a fat and contant toque epone a in the cae of dc oto. Anothe output of the flux etiato odule, oto-flux angle (7.5), i hown in Fig.7.8. Fig.7.8- Roto-flux angle baed on the voltage odel he et of the figue illutate the etiated peed that i the output of open-loop peed etiato and the aociated efeence peed. Fig.7.9- Refeence peed (uppe one) and etiated peed (lowe one) (tapezoid liit ae.7 pu to.4 pu) 45

166 Fig.7.- Refeence peed (uppe one) and etiated peed (lowe one) (tapezoid liit ae.4 pu to.5 pu) 46

167 CHAPER 8 HE HARDWARE & SOFWARE In thi chapte, the hadwae configuation of expeiental etup and the oftwae oganization will be uaized. he hadwae configuation of the poject i baically the cobination of an aynchonou oto, a oto dive and a icopoceo. he oftwae of the poject involve aebly code of the FOC and tate obeve in odula tategy. 8. Hadwae Oveview 8.. he Moto he expeiental etup of thi thei i a hown in Fig.8.. While teting the etup, diffeent oto ize ae ued, but in the actual expeiental tage 3kW quiel cage induction oto (Sieen ake) i ued. In ode to obtain oto paaete, claical no-load and locked-oto tet ae caied out on the oto. o get a ough tating gue of the paaete ued in the FOC algoith, teady-tate odel of the induction oto i eployed a hown in Fig.8.. In the eal tie application, oto dive ae expected to obtain oto paaete at the beginning with injected ignal and on-line etiation of the paaete ae ebedded to FOC algoith. hee ethod ae kipped in thi wok and conideed a futue wok. In thi thei, diffeent fo on-line paaete etiation, cloed-loop obeve (e.g. EKF) ae expected to copenate the paaete deviation effect egading the paaete eo a yte noie. 47

168 Fig.8. Oveall hadwae configuation of the expeiental etup I R X l R Xl + V I e I R c X R (-)/ - Fig.8. - Appoxiate pe Phae Equivalent Cicuit fo an Induction Machine R in the equivalent cicuit of Fig.8. i obtained by dc-tet, R c and X ae deteined by no-load and the et of the paaete ae deteined by locked-oto tet. he tato eitance of each tato winding can be eaued independently by applying a dc-cuent to one phae a hown in Fig

169 Fig.8.3 Diaga of dc eaueent he tato eitance i eaued on the oto teinal by applying a cuent though a eito and eauing the coeponding voltage, o without a eito applying low-level dc voltage. o obtain a oe accuate eaueent eult, one ut get eveal nube of eaued data and take the aveage of thee data fo each phae. he leakage-eactance x l, x l and the oto eitance ae deteined when the oto peed i et to zeo, i.e. =. Since the agnetizing banch eleent ae lage enough copaed to the et of the equivalent coponent, thee ae neglected in thi tet. It i futhe aued that leakage eactance ae equal to each othe accoding to IEEE tet tandad. Since tato eitance i eaued and leakage eactance ae aued to be equal, oto eitance can eaily be calculated fo the eaued data. he eaueent ae done aound the ated cuent of the oto and than the aveage of the eaueent ae coputed to obtain oe appoxiate paaete. When the oto i unning without load, the lip will be cloe to zeo. hu, the vaiable lip eitance will be vey lage. heefoe, in the no-load tet one ay conide the agnetizing banch a the appoxiate cicuit of the oto odel. he no-load data ae eaued aound the ated voltage, and agnetizing banch eleent ae calculated aound the ated voltage of the oto. he calculated oto paaete and ating of the oto ae given in able-8. 49

170 able 8.- Moto Paaete R (tato eitance), oh R ( efeeed oto eitance),78 oh Rc 5 oh X (agnetizing eactance) 65,5 oh Xl,Xl (leakage eactance),68 oh, (tato & oto induc.),5 H l,l (leakage induc.),85 H (agnetizing induc.),7 H (oto tie cont.), 8... he Moto Dive he dive cicuit ued hee ha been developed in anothe wok [4] but odified to uit to the equieent of thi wok. he dive ainly include a ectifie, dc-link cicuit and an invete. he ectifie ued in thi dive i Seikon- SKD8 that conit of ix uncontolled diode. he ated cuent of the ectifie i 8 A and the ated opeating voltage i 3 V. Duing the tet, the thee-phae voltage i upplied ove an autotanfoe to the ectifie. In the dc-link cicuit, the ectified voltage i a ooth dc filteed by dc-link capacito. he filte i ade of two µf capacito connected in eie. In addition to the a eito of W,.4 Moh i connected aco each capacito to balance the voltage on the. he dc link voltage i upplied to the capacito though a elay yte a hown in the Fig Fig.8.4 Dc_link Cicuit 5

171 At the beginning, the capacito ae chaged to a cetain level though a 5 W eito to pevent the inuh cuent at tating. When the capacito ae chaged to pedefined level, the elay diconnect the eito. One can change the elay on-off voltage level by adjuting the contolling potentioete on the inteface cad. Futheoe, by adding a anual witch, on-off tate of the elay can be contolled anually by thi witch. A a futue wok at thi point, a dynaic baking cicuit (feewheeling path contolled by a witch) ay be added to avoid fo ove-chaging the capacito while the oto i lowing down apidly. he invete on the dive i Seikon_Seitan IGB odule (SKM 4 GD 3 D). he ated value of V ce in thi IGB package i V and I c i 4/3 A depending on the cae tepeatue. he witching ie tie of the IGB witche i 55 n and the witching fall tie of the witche i 4 n. hi package ay be ued fo application at witching fequencie above 5 khz. IGB in thi odule ae tiggeed by a gate dive cad, Seikon ix IGB dive (SKHI 6 H4). he gate dive cad povide hot-cicuit potection fo all ix IGB in the full bidge. Shot cicuit potection chee i baed on the collecto-eitte voltage of the device. It witche off all IGB at once and give an ala in cae a fault i detected. In ou etup, thee eo output of the gate-dive cad ae ued fo fat hadwae inteupt. he intelock cicuit block iultaneou tuning on of IGB of the ae a. One IGB cannot be tuned on befoe the gate chage of the othe IGB i copletely eoved. he output of the invete i connected to the oto though cuent eno to acquie infoation about cuent in eal-tie. Oveall diaga of the invete i hown in Fig

172 Fig.8.5 Invete Cicuit 8..3 he DSP In ode to un the eal-tie contol algoith and ceate PWM ignal, exa Intuent (I) MS3 poceo i ued in thi wok. exa Intuent MS3 faily conit of fixed-point, floating-point, ultipoceo digital ignal poceo (DSP). MS3 DSP have an achitectue deigned pecifically fo ealtie ignal poceing. he F/C4 i a ebe of the C DSP platfo, and i optiized fo contol application. he C4x eie of DSP contolle cobine thi eal-tie poceing capability with contolle peipheal to ceate a uitable olution fo vat ajoity of contol yte application. he following chaacteitic ake the MS3 faily a uitable choice fo a wide ange of poceing application: Flexible intuction et, Inheent opeational flexibility, High-peed pefoance, Innovative paallel achitectue, Cot effectivene. 5

173 MS3F4 veion of thi faily i the one ued in thi application. It ue a 6-bit wod length along with 3-bit egite fo toing inteediate eult, and ha two hadwae hifte available to cale nube independent of the CPU. he C4x DSP contolle take advantage of an exiting et of peipheal function which include: ie, Seial counication pot (SCI, SPI), Analog-to-digital convete (ADC), Event anage, Syte potection, uch a low-voltage detection and watchdog tie. o function a a yte anage, a DSP ut have obut on-chip I/O and othe peipheal. he event anage of the 4 i application-optiized peipheal unit, coupled with the high-pefoance DSP coe, enable the ue of advanced contol technique fo high-peciion and high-efficiency full vaiable-peed contol of oto. Included in the event anage ae pecial pule-width odulation (PWM) geneation function, uch a a pogaable dead-band function and a pace vecto PWM tate achine fo 3-phae oto that povide quite a high efficiency in the witching of powe tanito. hee independent up/down tie, each with it own copae egite, uppot the geneation of ayetic (non-centeed) a well a yetic (centeed) PWM wavefo Inteface Cad In ode to convey infoation back and foth between the powe tage and DSP an inteface cad ha been deigned. Moeove, uitable ignal aplification, ignal filteing and hadwae potection popetie ae added to thi inteface cad (ee Appendix C). he dc-link voltage i ened with a voltage eno (V5_P) on the inteface cad. he inulation popety of the voltage eno i quite ufficient to potect the digital cicuit and low voltage analog cicuit fo high voltage pat. he dc-link voltage value i ened to e-build the phae voltage in the contol oftwae with the 53

174 infoation of duty cycle of the IGB. hi eno i not neceay fo the cloedloop FOC algoith unle the pecie voltage infoation i equied. Since the efeence voltage value obtained fo feedback infoation and ued a input of SVPWM can be conideed a actual dq-voltage. Epecially, at low peed ange, the voltage dop on the witche becoe ignificant and the efeence voltage do not eflect the actual voltage value due to thi voltage dop. In thi cae one ut ebed a voltage dop copenation odule to the contol algoith o ue a voltage eno. Anothe ai of the voltage eno i to ene the ovechage on the dc-link capacito. If the voltage level exceed the pedefined liit that i deteined by the ue, a copaato give an eo ignal. hi eo ignal i ued fo iediate hadwae inteupt and all the IGB ae et to off-tate. Finally, to dicad the powe eitance, the ai of which i to pevent the in-uh cuent at tating, the voltage level infoation i needed to opeate the elay aco thi eitance. he voltage eno alo povide thi voltage infoation whethe it exceed the adjuted voltage level o not. If thi echani i eployed then the elay will opeate autoatically afte the tat coand in a vey hot tie. he othe ened vaiable ae tato cuent uing cuent-eno on the inteface cad. Fo thi pupoe S 5-NP cuent tanduce ae ued. hee eno ae capable of ening AC, DC and ixed cuent wavefo. he eno ha ulti-ange cuent ening option depending on the pin connection. he eno ue hall-effect phenoena to ene the cuent. hey have excellent accuacy and vey good lineaity in the opeating ange. he output of thee eno i between -5V and unipola. Since the ADC on the DSP boad cannot ene the negative voltage and equie ignal between -5V, ou cuent eno eliinate exta hadwae, and oftwae odule due to it entioned popetie. Noally, one ut add offet to the AC cuent ignal to copenate the negative pat and then ubtact thi aount in the oftwae. Futheoe, the cuent ignal ut be noalized between the -5V ange uing aplifie befoe the ADC. All of thee pocedue caue exta uncetainty that affect the accuacy of the ened infoation. In cae of noiy phae cuent, optional low-pa filte ae placed on the inteface cad with khz cut-off fequency. Howeve, at high fequency ange above 5Hz thee filte ay caue eiou phae lagging poble. he output of the cuent tanduce ae alo ued to povide ove-cuent potection. Afte deteining 54

175 the ove-cuent liit, the potentioete in the potection cicuit ae et to thi citical liit. In cae of ove-cuent poble a copaato give eo ignal to et the IGB into off-tate. In addition, the PWM ignal geneated by DSP ae aplified to ake the copatible with the gate dive cad input. Fo thi pupoe, ix PWM ignal ae adjuted to 5V individually without any othe change. Finally, all the eo, gate dive cad eo, ove-voltage eo, ove-cuent eo, and an extenal eo ae OR gated. he ingle eo output i aigned to contol PWM-OFF cicuit to et the all IGB to off-tate in cae of any fault. he pictue of the inteface cad, DSP and invete ae given below. Fig.8.6- Expeiental etup (Inteface cad, DSP and invete) 55

176 Fig Inteface cad 8. Softwae Oveview In thi pat geneal oftwae flowchat will be explained. Futheoe, oftwae odule and pecific fixed-point nueical ethod will be analyzed. he expeiental output of the each odule will be onitoed to how that the odule un popely. 8.. Softwae Oganization Oveall algoith of thi poject ay be divided into two: initialization and the un tie odule a hown in Fig.8.8. he initialization odule define and initialize the oftwae vaiable, contant and pecific egite. Moeove, oe of the look-up table eployed in the algoith ay alo be addeed in thi pat. Initialized egite in the initialization odule ae watchdog tie egite, event anage egite, auxiliay egite addeing, eial counication egite, clock egite. Soe of thee egite ay be edefined in the pecific odule if the odula algoith i ued. Aong the egite above initialization of the eial counication egite i optional. he oftwae contant and uninitialized oftwae vaiable ay be defined in thi pat o in the initialization of the each odule. 56