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2 ERASMUS MUNDUS MASTER STEPS 0&0//0 Intoucton to Vcto Contol of Pmannt Magnt Synchonou Machn ung Engtc Macocopc Rpntaton Aocat Pofo n Elctcal Engnng PhD - HR At t Mét PaTch Lll - Fanc LEP Contol Tam

3 Pagogcal Outcom At th n of th lctu, tunt ha to b abl to: U a mthoologcal appoach to pnt mol of lctcal ytm n o to hlp th ucton of cat contol chm Untan what a th aabl of a Pmannt Magnt Synchonou Machn (PMSM) to b contoll Know, wth th hlp of SIMULINK mulaton, how to contol a PMSM n th abc fnc fam an what a th nhnt lmtaton Know, wth th hlp of SIMULINK mulaton, how to contol a PMSM n th q fnc fam an what a th ncay mathmatcal tanfomaton to mplmnt

4 Agna 4 Mol an Rpntaton fo th contol of lctcal ytm Mollng an Engtc Macocopc Rpntaton (EMR) of Pmannt Magnt Synchonou Machn (PMSM) Pncpl of Inon Ba Contol Inon Ba Contol of Pmannt Magnt Synchonou Machn (PMSM) abc fnc fam Smulaton wth SIMULINK Inon Ba Contol of Pmannt Magnt Synchonou Machn (PMSM) q fnc fam Smulaton wth SIMULINK

5 Mol an Rpntaton 5 What a th quantt to b contoll? Moto Loa T moto t T J t f Equaton a uually wttn wth ffntal opato, how: t t lm0 t ( t t) ( t) t Th toqu at tm t cannot pn on th p at tm t+t Phycally mpobl! Phycal caualty ntgal

6 Mol an Rpntaton 6 What a th quantt to b contoll? If quaton a wttn n ntgal fom, thn: Moto Loa T moto t T J t t 0 f t T moto f T J Th poton at tm t pn on th p up to t Th p at tm t pn on th toqu up to t Th a natual (phycal) caualt

7 Mol an Rpntaton 7 What a th quantt to b contoll? Moto Loa T moto f T J Moto Toqu (T moto ) -> Rotaton of th loa () Acton mpl Racton Moto Toqu (T moto ) x Rotaton of th loa () = Pow Acton x Racton = Pow

8 Mol an Rpntaton 8 Engtc Macocopc Rpntaton mak pobl to pnt a mol n o to: To pct th natual (ntgal) caualty To hghlght acton an acton an pow flow Moto T moto f () T J Loa () Souc * T moto Moto T moto p n T moto p out T p n T p out En p Lo + toag lo Souc p "to "

9 Mollng an EMR of a PMSM 9 Conttuton of a PMSM - Stato compo of th wnng - Roto compo of ufac mount o bu magnt

10 Mollng an EMR of a PMSM 0 Pncpl of functonng of a PMSM - Stato cat a otatng magntc fl (qualnt to a otatng magnt although tato wnng a at tan tll) Each wnng pouc a magntc fl wth a magntu popotonal to th col cunt an a cton coponng to th col ax If th th col a uppl wth a -pha AC n cunt ytm, th ultant magntc fl otatng

11 Mollng an EMR of a PMSM Pncpl of functonng of a PMSM - Stato cat a otatng magntc fl (qualnt to a otatng magnt although tato wnng a at tan tll) - Roto magnt a attact by th otatng fl an otat at th am p (n tay tat) B N B + C S C k B B Toqu Contol qu a VECTOR CONTROL

12 Mollng an EMR of a PMSM Mollng of a PMSM q y q y N S x F F F x Only on pol pa fo th ak of mplcty. Th pmannt magnt qualnt to a wnng uppl wth a DC cunt

13 Mollng of a PMSM Stato flux lnkag quaton a wth L M M M L M M M L an / 4 co / co co max Mollng an EMR of a PMSM M F F max n ca of woun-oto ct max n ca of oto wth pmannt magnt

14 4 Mollng of a PMSM t t R t R Stato oltag quaton a thn t L M M M L M M M L R Mollng an EMR of a PMSM

15 5 Mollng of a PMSM O n a mo conc way (matx notaton) t L R wth Voltag cto Cunt cto EMF cto R Stato tanc L Stato nuctanc matx Mollng an EMR of a PMSM

16 Mollng an EMR of a PMSM 6 Mollng of a PMSM Th pow balanc p n p lo p mag p m Wth p n. t p lo R R R R. t pmag L t L. t t

17 Mollng an EMR of a PMSM 7 Mollng of a PMSM an p m t thn A thn T T m m p t m t T m t t Toqu Contol qu a VECTOR CONTROL

18 8 Mollng of a PMSM If / 4 co / co co max / 4 n / n n max an thn / 4 n / n n max T m Mollng an EMR of a PMSM

19 Mollng an EMR of a PMSM 9 Mollng of a PMSM Quton: Fn th cunt fnc that la to a contant toqu un mnmum copp lo

20 Mollng an EMR of a PMSM 0 Mollng of a PMSM Soluton: p lo R. Fo a gn T, * m.. Thn * T * m mnmum f mnmum k t k * mnmum f collna to k * Tm * T m max

21 Mollng an EMR of a PMSM Mollng of a PMSM Soluton: Fnally T m n * n / max n 4 / Cunt cto collna to EMF cto

22 Mollng of a PMSM If th tato wnng a ta coupl: u u Only two oltag an two cunt a uffcnt to mol th machn: 0 t L M M M L M M M L R Quton: Rwt th oltag quaton wth a aabl,,, u u Mollng an EMR of a PMSM

23 Mollng of a PMSM Soluton: t L R u u c c M L L call th tato cyclc nuctanc Rmak: f w a th am quantty Z (Zo-qunc) to, an, u an u man th am. Mollng an EMR of a PMSM

24 Mollng an EMR of a PMSM 4 EMR of a PMSM Th VSI (Voltag Souc Int) con a an amplf: VSI: Sta couplng: V k k bu, 0 k 0 PMSM: u u R L c t T m Loa: T m T J t f DC bu VSI Sta couplng PMSM Loa Bu V bu [] [u] [] T m En bu [ ] [] [] T []=[*] Mono-phycal conon (lclc) Mult-phycal conon (lcméca)

25 Mollng an EMR of a PMSM 5 Fom EMR to Smulnk Bu Vbu [] [u] [] En Tm Omga T DC Souc [*] bu [] [] [] Omga Loa VSI Sta couplng PMSM PMSM PMSM+Loa R+L EM conon f+j

26 Pncpl of Inon Ba Contol 6 Opn loop an clo-loop contol Contollng a ytm fo output tackng can b ntpt a ntng th ytm u(t) nput (.) y(t) output Sytm u f (t) nput fnc - (.) y f (t) output Contol f w can mplmnt a goo appoxmaton of th ytm n

27 Pncpl of Inon Ba Contol 7 Opn loop contol * Lt tak a mpl xampl: cunt contol of a tanc Contol ytm * R (t) *(t). : R - (.) (t) *(t) Sytm Contol ~ ~ * *. : ( t) R ( t) In ca of acaual latonhp (no accumulaton), opn loop contol pobl (No n of contoll). Th non of th lmnt a ct.

28 Pncpl of Inon Ba Contol 8 Opn loop contol Dct Contol wth EMR fomalm Objct: to contol y u y y y = f(u )+g(u ) u u y k y y = k x u u y = (/k)x u k* u * y * u *=f - ~ (y * )+g(u ) ~ u y * ~ k* = y */u Compnat u Manpulat u

29 Pncpl of Inon Ba Contol 9 Opn loop contol Dct Contol wth EMR fomalm Exampl: cunt no u u Implmnt a compom o potz output. V DC =V DC y y p u p coup =V DC y -f V DC f u k W k Wp u... y p-f ' ' kw yf kwp y pf no maumnt no contoll p wghtng aabl f k W VDC kw f ( kw ) f 0 k W

30 Pncpl of Inon Ba Contol 0 Clo-loop contol * Lt tak a mpl xampl: cunt contol of a R+L ccut Contol ytm * R L (t) *(t). : R L - (.) (t) *(t) Sytm Contol No at n al-tm ~ * ~ ~ *. : ( ) R L ( ) In ca of caual latonhp (accumulaton of ngy), opn loop contol not pobl N of contoll

31 Pncpl of Inon Ba Contol Clo-loop contol * Lt tak a mpl xampl: cunt contol of a R+L ccut Contol ytm * R L (t) *(t). : R L Contoll (t) *(t) Sytm Contol Contoll : * ( ) C * ( ) ( ) In ca of caual latonhp (accumulaton of ngy), clo-loop contol manatoy N of maumnt an contoll (Inct contol)

32 Pncpl of Inon Ba Contol Clo-loop contol Inct Contol wth EMR fomalm (Sytm wth accumulaton of ngy) u u u u * ~ u f u U () + - U () U () + U() + U*() () C() - I() + I*()

33 Inon Ba Contol of PMSM (abc fam) Inon ba-contol of th PMSM n th abc fnc fam Th VSI (Voltag Souc Int) con a an amplf: u u k k bu V, 0 T k R m 0 T m L c T t J f t EMR lgn Engy ouc Monophycal conon lmnt Multphycal conon lmnt Accumulaton lmnt Couplng lmnt Maumnt Dct non Contoll (Inct Inon) Statgy

34 Inon Ba Contol of PMSM (abc fam) 4 Fom EMR an IBC to Smulnk ES DC Souc Vbu VSI [] bu Pak Tanfomaton [q ] [] PMSM R+L [q] [q] PMSM EM conon Tm [q] thta PMSM+Loa f+j Omga Omga MS Loa T Tm * [*] [q *] [q*] Tm* Inon VSI Inon ta couplng z * Cunt Contol Inon EM conon [kq] Moulaton Statgy Toqu Statgy

35 Inon Ba Contol of PMSM (abc fam) 5 Fom EMR an IBC to Smulnk [*] [*] / / u* Vbu / u* [u*] [*] / z * [] [*] [(/t)*] L* u Kp_ [*] [] [*] Tm * [k] R* u n(u) -/(*ph _max) [k] n(u-*p/) thta Omga 0 z *

36 Inon Ba Contol of PMSM (abc fam) 6 Fom EMR an IBC to Smulnk Quton: Ung th Smulnk fl PMSM_abc - Analy th mulaton (Mol-Contol-Statgy) - Commnt th ffct of th knowlg of th ytm paamt an th gan Kp_ on th oall pfomanc - Conclu Soluton: To attan goo pfomanc, y goo knowlg of th ytm paamt ncay (whch ffcult) an a hgh alu fo Kp_ gan qu to pfctly tack th fnc (whch can la to ntablty) Anoth typ of contol qu

37 7 Mollng of a PMSM n th q fnc fam Inon Ba Contol of PMSM (q fam) Th contol of th cunt ffcult bcau th ytm n th abc fnc fam hghly coupl t R u u By ung th followng chang of aabl (call Concoa tanfomaton): C 6 0

38 8 Mollng of a PMSM n th q fnc fam Inon Ba Contol of PMSM (q fam) Th ytm bcom : C t L C C C R C u u C t c t t t Conng: u u C t C t It com: t L L R R c c Th al th pha machn qualnt to a fcttou two npnnt pha machn (All matc a agonal).

39 Inon Ba Contol of PMSM (q fam) 9 Mollng of a PMSM n th q fnc fam q y F F F x q y F F F x How, to obtan a contant toqu, tato cunt ha tll to b nuoal (nc th oto otat!) an thn ffcult to tack.

40 40 Mollng of a PMSM n th q fnc fam Inon Ba Contol of PMSM (q fam) If th tato wnng otat at th am p a th oto, tato cunt wll bcom contant! By ung th followng chang of aabl (call Rotaton): q q R co n n co It com: q q c q c q q L t L R 0 0 Although th ytm (wakly) coupl, cunt n tay tat a contant an thn ay to contol.

41 Inon Ba Contol of PMSM (q fam) 4 Mollng of a PMSM n th q fnc fam y q F F Moo, flux cto to zo ( =0). F x q q q q y F F F pn only on q.thn can b kpt qual Equalnc wth a DC Buhl machn x Vcto contol ay to mplmnt n q fnc fam.

42 Inon Ba Contol of PMSM (q fam) 4 Mollng of a PMSM n th q fnc fam q y F F F q x y F F F x q q q q y F F F x Concoa Rotaton Pak

43 Inon Ba Contol of PMSM (q fam) 4 A Mollng of a PMSM n th q fnc fam A B B C Pak - C A Pak q PARK B C q

44 Inon Ba Contol of PMSM (q fam) 44 EMR of a PMSM n th q fnc fam t u q R R C R R R q q L c t q L c u 0 0 q q q C

45 Inon Ba Contol of PMSM (q fam) 45 Fom EMR an IBC to Smulnk Quton: Ung th Smulnk fl PMSM_q_tunt - Smulat th contol ytm ung th EMR - Conclu

46 Rfnc 46 [] Contol Statg fo Opn-En Wnng D Opatng n th Flux-Waknng Rgon. IEEE Tanacton on Pow Elctonc, 9-0, Alxanu-Paul SANDULESCU, Fabn MEINGUET, Xa KESTELYN, Ec S , Anton BRUYERE [] Mol-ba couplng contol mtho fo ual- ganty tag: A ca tuy wth xpmntal alaton. Contol Engnng Pactc, Vol., N., pag. pp , -0, Ian Mauco GARCIAHERREROS, Xa KESTELYN, Juln GOMAND, Ralph COLEMAN, P-Jan BARRE [] A Vctoal Appoach fo Gnaton of Optmal Cunt Rfnc fo Multpha Pmannt Magnt Synchonou Machn n Ral-tm. IEEE Tanacton on Inutal Elctonc, Vol. 58, N., pag , ISBN , Xa KESTELYN, Ec S [4] Contol of a Symmtcal Dual- Ganty Sytm ung Engtc Macocopc Rpntaton. Sol Stat Phnomna (SSP), Vol. 44, pag. 8-85, ISBN , Xa KESTELYN, Juln GOMAND, Alan BOUSCAYROL, P-Jan BARRE [5] FPGA Implmntaton of a Gnal Spac Vcto Appoach on a 6-Lg Voltag Souc Int. IECON 0 - IEEE Intnatonal Confnc On Inutal Applcaton of Elctonc, N. 7, pag , ISBN , Alxanu-Paul SANDULESCU, Lahoucn IDKHAJINE, Sbatn CENSE, Fééc COLAS, Xa KESTELYN, Ec S , Anton BRUYERE [6] Tachng contol ung Engtc Macocopc Rpntaton - xpt ll. EPE 09, Baclona, Span, Alan BOUSCAYROL, Phlpp DELARUE, Fééc GIRAUD, Xa GUILLAUD, Xa KESTELYN, Btty LEMAIRE-S , Walt LHOMME [7] Vctoal Molng an Contol of Multpha Machn wth Non-alnt Pol Suppl by an Int. Chapt 5 of "Contol of Non-conntonal Synchonou Moto. ISTE Lt an John Wly & Son Inc, pag , ISBN , Xa KESTELYN, Ec S [8] Multpha Voltag ouc Int. Chapt 8 of "Pow lctonc Cont - PWM Statg an cunt contol tchnqu". ISTE Lt an John Wly & Son Inc., pag. 0-4, ISBN , Xa KESTELYN, Ec S

47 Thank fo you attnton