ELECIC VELOCIY SEVO EGULAION Gorg W. Younkin, P.E. Lif FELLOW IEEE Indusril Conrols Consuling, Di. Bulls Ey Mrking, Inc. Fond du Lc, Wisconsin h prformnc of n lcricl lociy sro is msur of how wll h sro dri will minin is commndd lociy undr rying lod disurbncs. h biliy o minin lociy undr lod chngs is prssd s h rgulion of h sro dri usully prssd s prcn rgulion. A ypicl lcric sro dri wih currn loop for orqu rgulion is shown in h block digrm of figur. Sinc h wo sro loops r inrcing, block digrm lgbr is usd o rrrng h block digrm ino wo indpndn sro loops s shown in figur. h rrrngd block digrm of h moor nd currn loop will hn b includd ino lociy fdbck sro loop shown in figur 3. h moor nd currn sro loop hs PI compnsion. h rnl lociy sro loop is shown wih lg/ld compnsion bu could jus s wll lso b PI compnsion. Mos commrcil lcric sros lso h n ddd posiion sro loop, which cn incrs h lociy rgulion o ry lrg n. his discussion is limid o n lcricl lociy sro, which cn b dc
sro dri or brushlss dc (BLDC sro dri. Spd rgulion wih n ddd posiion sro loop is h subjc of nohr discussion. o discuss h rgulion of lociy sro dri, h block digrm of figur 3 is rrrngd in figur 4 o show moor lociy (V o s funcion of orqu lod ( l chngs. h innr currn sro loop of figur 3 is prssd s q.. For h sdy s condiion h currn sro loop is gin s q.. i i ( s l ( bs ( s ( s i3 r q. ( i i s 0 i q ( h rnl lociy sro loop is gin in q (3 wih h sdy s condiion s q (4. V o r ( s q (3 ( bs l [ bs ( r s ( s i ] J s ( s ( s
V o r s 0 q (4 A rdily ilbl prmr of commrcil sro dris is shown s h opn loop gin ( o of h lociy sro. Equion (5 is h opn lociy sro loop gin ( o wih h sdy s soluion in q (6. o ( s ( s A q (5 l ( bs ( s [( bs ( s i( s ]J s ( s ( s A A o q (6 h dri rgulion cn b compud from figur 4 wih q (7 nd q (8 for h sdy s soluion. ( s ( bs ( s A( s ( s J s [ ] L ( s s [( s ( s ( s ] b i q (7 q (8 s 0 A i Equion 8 is rrrngd s gin in q 9. h opn loop sro gin of q (6 is rrrngd in q(0. Subsiuing q (0 ino q (9 rsuls in q (, which is simplifid in q (. s 0 i [ A ] i A q (9 A o q (0 o i q ( 3
i (Spd rgulion quion q ( ( o Dimnsionl Anlysis I is imporn o know h unis of h prmrs in q. ( for boh dc nd BLDC lcric sros. h uni dimnsions r shown s follows: DC DIVES BLDC DIVES ( l l (Armur rsisnc [ohms] [ ohms] ols sc (lg consn [ ] rd ( l l 3 ols sc [ ] rd orqu consn lb in rd lb rd in o (Opn loop gin ol ol ol ol Dimnsionl nlysis of q V o ohms lb in r / s rd / sc [ ] lb in 4
EXAMPLE Moor ollmorgn M607B ( l l 0.89 [ ohm] 0.094 [ ohm] ( l l 3 0.646 3 ol sc 0.379 rd d orqu 396[lb-in] lb in 9. 9 A d Spd 3000[rpm] i Currn loop fdbck consn 3 40A 0.075 A 0 A ol sc 0.086 rd ol 65 ol o ( lociy opn loop gin A 0.086 0 65 ol 000 0.379 ol EGULAION ( i o 0.094 0 0.075 0.379 9.9 ( 000.594 369 ol 0.00043 lb in Spd drop rd orqu nd rd spd- Spd drop rd / sc 0.00043 396 lb in rd sc [ lb in] 0.7 5
rd r 60sc 0.7.66 sc rd min π [ rpm] Chngin spd EGULAION d spd.66 3000 [ rpm] [ rpm] 0.00054 Vlociy sro % EGULAION 0.00054 00 0.054 % If posiion loop is ddd o h lociy sro dri h block digrm is shown in figur (5. h posiion loop lociy consn ( is h posiion opn loop gin. 6
D D ( A q (3 ducing q (3 yilds D ( A q (4 rrnging q (6 yilds q (5 o A Subsiuing q (5 ino q (4 yilds D q (6 ( ( o o rrnging yilds D ( o q (7 From figur 6, h posiion ( s orqu ( is prssd s- D i (sdy s complinc q (8 D i (sdy s siffnss q (9 Subsiuing q (7 ino q (9 yilds ( o i q (0 ( o i ( q ( Figur 5 is h posiion sro block digrm. h inpu commnd nd h oupu o r in rdins. Howr if h inpu commnd is gin posiion or priod of im; h is lociy, nd h oupu posiion follows h commnd wih lg nd his lg is 7
dfind s h following rror in yp posiion sro. hrfor, if h inpu commnd nd h oupu is diffrnid ( s, h dri will b in lociy mod prssd s- o s ( o i rd / sc [ ] lb in q ( Dimnsionl chck of q ( sc[ ohms sc EXAMPLE rd sc A lb in ] A rd lb / sc in Using h sm moor s in h prious mpl wih h sm orqu nd lociy innr sro loop, h nw ribl is h posiion opn loop gin (lociy consn. hus h ribls r rpd s- 0.094 [ohms] 0.379 [ol-sc/rd] d orqu 396 [lb-in] 9.9 [lb-in/mp] d spd 3000[rpm] i 0.075[ol/mp] i 0 [/] A 0.086[ol-sc/rd] 65[ol/ol] o 000[ol/ol] h posiion loop gin will b [ipm/mill] 6.66 [rd/sc] h rgulion of qurion ( cn b clculd s- V ( o i 0.094 0 0.075 6.66( 000 0.379 9.9 o Spd drop rd orqu nd rd spd- Spd drop rd 0.0000589 396 sc rd r 60 sc 0.00 0.0974 sc rd min π rd sc [ lb in] 0.00 [ rpm] 0.0000589 8
[ rpm] chngin spd 0.0979 EGULAION 0.000036 rd spd 3000 rpm Posiion sro in lociy mod % EGULAION0.000036 00 0.0036% frnc: G. Younkin, INDUSIAL SEVO CONOL SYSEMS-Fundmnls nd Applicions, nd Ediion, Chpr, 00, Mrcl Dkkr, Inc, N.Y.,N.Y. 9