CHAPTER 5 DESIGN OF SPEED CONTROLLER FOR CONVERTER FED PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE

Transcription

1 8 CHAPER 5 DESIN OF SPEED CONROLLER FOR CONVERER FED PERMANEN MANE SYNCHRONOUS MOOR DRIVE 5. INRODUCION he Penent Mgnet Synchonou Moto PMSM develop nuodl bck ef Pfff et l 98 etblhng telf eou copetto to the vecto contolled nducton oto nd the dc oto fo hgh pefonce peed nd poton pplcton. h ptly due to the nceed toque to net to nd powe denty hnn nd Plly 987 when coped to the nducton oto o the dc oto, n the fctonl to 3 HP nge. h h been de poble by the ue of hgh edul flux denty nd hgh coecvty penent gnet. he cuent eech n educng the tepetue dependence nd nceng the thel cpblty of gnet wll pobbly ncee the ue of PMSM dve n the evo nduty. he good pefonce ttnble fo PMSM h popted ognl eech n the degn nd pefonce of the ente oto dve Boule 984, Peon 98. he pplcton of PMSM to n electc vehcle h been exned Boe 987 whle hgh peed opeton h lo been nvetgted Jhn 986 nd Sebtn nd Sleon 986. In ode to extct the bet pefonce fo gven chne, the pope degn of the peed nd cuent contolle potnt. Howeve ll dve e pete entve to oe degee. dtonl ethod of contolle degn n the

2 9 fequency don ue nonl vlue of the plnt pete. he effect of chnge n the pete cn be ubequently checked by entvty nly Plly nd hnn 987. An ltentve ethod popoed n th ecton fo the degn of peed contolle fo good pefonce dve. Motly the Popotonl Integl PI contolle ued fo dve pplcton becue of t ple tuctue nd obut pefonce n wde nge of opetng condton. h contolle depend only on two pete nely the popotonl gn p nd the ntegl gn. he ntl vlue of thee gn e obtned fo educed ode odel of the ognl hghe ode yte wth the help of pole-zeo cncellton technque. Ung genetc lgoth optzton technque, PI contolle gn e tuned tll the degn pecfcton e et wth. he tuned contolle connected wth the ognl hghe ode yte nd the cloed loop epone obeved fo tblzton poce. In th chpte tnfe functon of the PMSM dve deved nd degn of peed contolle fo PMSM dve wth conventonl Syetc Optu SO nd popoed Model Ode Reducton MOR technque ung enetc lgoth A tuned contolle gn ced out. 5. MAHEMAICAL MODEL OF A PMSM DRIVE Detled odelng of PMSM dve yte equed fo pope ulton of the yte. he d-q odel h been developed on oto efeence fe hown n Fgue 5.. At ny te t, the ottng oto d- wth the fxed tto phe x nd the ottng tto -x. Stto f otte t the e peed tht of the oto. he odel of PMSM wthout dpe wndng h been developed on oto efeence fe ung the followng upton:

3 Mgnetc feld tuton neglected. he nduced EMF nuodl. Eddy cuent nd hytee loe e neglgble. hee e no feld cuent dync. Fgue 5. Moto x Stto voltge equton e gven by V R 5. q q q d d V R 5. d d d d q whee R q nd R d e the qudtue nd dect x wndng etnce of PMSM dve, whch e equl nd heefte efeed to R nd the q nd d xe flux lnkge e gven by q L 5.3 q q d L 5.4 d d f

4 gve Subttutng equton 5.3 nd 5.4 nto 5. nd 5. epectvely V R L L 5.5 q q q q q d d f V R L L 5.6 d d d d d f q q Angng equton 5.5 nd 5.6 n tx fo V V q d R q L L q q R d L d L d q d f f 5.7 he electognetc toque developed n PMSM dve gven by e 3 P d q q d 5.8 he echncl toque equton d L B J 5.9 dt Equton 5.9. Solvng fo the oto echncl peed of the dve fo L B dt 5. J whee P 5.

5 In the bove equto the oto echncl peed. 5.3 SPEED CONROLLER DESIN BY CONVENIONAL SYMMERIC OPIMUM MEHOD A popotonl plu ntegl contolle nolly ued fo ny ndutl pplcton nd hence t extenvely delt n ny text. Snce the PI contolle econd ode n ntue detenton of gn nd te contnt of the contolle by ung the yetc optu ethod ple f the d x tto cuent ued to be zeo. In the peence of d x tto cuent, the d nd q cuent chnnel e co coupled, the odel nonlne n ntue eult of the toque te. he degn of cuent contolle nd peed contolle wth exct pete potnt to obtn the deed tnent nd tedy tte chctetc of the PMSM dve yte. he yte becoe lne the d x cuent ued to be zeo nd t eeble tht of eptely excted dc oto wth d contnt feld exctton. he block dg foton fo the dve becoe ey. he cuent loop ppoxton, peed loop ppoxton nd the detenton of the tnfe functon of the cuent nd peed contolle dentcl to tht of dc oto dve Block Dg Foton Wth the d-x cuent ued to be zeo, the oto q-x voltge Equton becoe

6 3 V R L p 5. q q q f he electoechncl toque Equton of the dve P e Jp B l 5.3 whee the electognetc toque gven by e 3. P f q 5.4 If the lod ued to be fctonl the lod toque becoe 5.5 B l tht led to the electoechncl Equton 3 P Jp Bt. f q t. q 5.6 whee B P t Bl B P t. f 5.8 Ung the Equton 5. nd 5.6 the educed block dg wth the cuent nd peed feedbck loop dded hown n Fgue 5..

7 4 Fgue 5. Block dg of the peed contolled PMSM dve he nvete tnfe functon h gn nd te dely n 5.9 n whee V n 65 V dc. 5. c n f c 5. whee V dc V c f c = the dc lnk voltge nput to the nvete = the xu contol voltge nd = the wtchng ce fequency of the nvete.

8 5 he nduced ef due to oto flux lnkge, e e 5. f 5.3. Cuent Loop he nduced ef loop coe the q x cuent loop nd t could be plfed by ovng the pck off pont fo the nduced ef loop fo peed to cuent output pont. he cuent loop tnfe functon obtned fo Fgue 5.3 gven below Fgue 5.3 Cuent contolle q * q H c n n n b 5.3 whee Lq J ; ; ; ; R R B B t t b t f

9 6 he followng ppoxton e vld bout the coove fequency: n n whee 5.7 n wth th the cuent loop tnfe functon educed to * q q b H n n c n 5.8 b whee ; It found tht.he plfed cuent loop tnfe functon then gven by * q q 5.9 whee n b h cuent loop tnfe functon ubttuted n the degn of the peed contolle follow.

10 Speed Contolle he peed contol loop nd the plfed cuent contol loop hown n Fgue 5.4. Ne the vcnty of the coove fequency, the followng ppoxton e vld bout the coove fequency whee Fgue 5.4 Splfed peed-contol loop he peed loop tnfe functon detened ung thee ppoxton nd gven by t H H fo whch the cloed loop peed tnfe functon obtned * H 3 g g 5.37

11 8 whee H t g 5.38 Equtng th tnfe functon to yetc optu functon wth dpng to of.77 gve the cloed loop tnfe functon H * Equtng the coeffcent of equton 5.37 nd 5.39 nd olvng fo te nd gn contnt yeld g 5.4 Hence the popotonl gn p, nd ntegl gn, of the peed contolle e deved p 4 9 g g exple. he vldty of vou ppoxton vefed though woked Exple he PMSM dve yte pete e follow: R =.4 d =.56 H, L q f =.546 Wb-un, B t =. N-/d/ec, J =.6 kg-, P = 6, f c = khz, V c = V, H =

12 9.5 V/V, H c =.8 V/A, V dc = 85 V. A yetc optu bed peed contolle to be degned bed on the bove pete nd the vldty of upton de n t devton vefed. he dpng to equed.77. Soluton Invete nfe functon, : Vdc Invete gn contnt, n V V V c e contnt, n f c.5ec n n Moto electcl nfe functon, : Moto gn contnt,. 743 R.4 e contnt, L R q ec Induced ef loop nfe functon, b : 3 P 3 6 oque contnt, t. f N / A Mechncl gn, B t. d / ec/ N b t f

13 whee the echncl te contnt J B t.6..6ec Moto echncl nfe functon, : t Equvlent electcl te contnt of the oto whee Solvng fo the oot of +b+c= b n H c c b b t f 3.6 hen the nvee of the oot nd e =.5775 ec =.3 ec Splfed cuent loop tnfe functon = =.5775 b.443

14 Exct cuent loop tnfe functon.... H b c b Speed contolle t g H.5775ec.55ec g Splfed peed loop tnfe functon 3 g g e H Exct peed loop tnfe functon..... e whee H

15 All the cuent loop tnfe functon tep epone, gn nd phe plot e hown n Fgue 5.5, 5.6 nd 5.7. All the peed loop tnfe functon tep epone, gn nd phe e hown n Fgue 5.8, 5.9 nd 5.. In the fequency egon of nteet, note tht the ppoxton hold good both n gntude nd n phe, n pte of the educton of the ffth ode yte to n equvlent thd ode n the ce of the peed loop nd of thd to ft n the cuent loop of the dve yte eult e fee of eo. Fo tep epone plot of the exct nd plfed cuent loop nd peed loop tnfe functon, the te don pecfcton lted n ble 5. nd ble Step Repone of exct nd plfed cuent loop tnfe functon exct plfed e ec Fgue 5.5 Step epone of exct nd plfed cuent loop tnfe functon

16 3 Exct nd plfed cuent loop gn plot Exct Splfed Fequency d/ec Fgue 5.6 n plot of Exct nd plfed cuent loop gn plot 3 Phe plot of exct nd plfed cuent loop tnfe functon exct cuent loop plfed cuent loop Fequency d/ec Fgue 5.7 Phe plot of Exct nd plfed cuent loop gn plot ble 5. Copon of te don pecfcton of cuent loop Sttegy of Contol Exct Cuent loop Splfed cuent loop Re te t n ec Settlng te t n ec % Ovehoot Pek pltude Pek te n ec

17 4 3 5 Step Repone of exct nd plfed peed loop tnfe functon exct plfed e ec Fgue 5.8 Step epone of exct nd plfed peed loop tnfe functon n plot of exct nd plfed peed loop tnfe functon 3 exct plfed Fequency d/ec Fgue 5.9 n plot of exct nd plfed peed loop tnfe functon

18 5 45 Phe plot of exct nd plfed peed loop tnfe functon. exct plfed Fequency d/ec Fgue 5. Phe plot of exct nd plfed peed loop tnfe functon ble 5. Copon of te don pecfcton of peed loop Sttegy of Contol Exct peed loop Splfed peed loop Re te t n ec Settlng te t n ec % Ovehoot Pek pltude Pek te n ec SPEED CONROLLER DESIN USIN MODEL ORDER REDUCION MEHOD WIH ENEIC ALORIHM he degn of peed contolle fo nvete fed penent gnet ynchonou oto dve qute dffcult becue t h been pctcl coplexty n thetcl odel nd of hghe ode. he degn of contolle fo hghe ode yte nvolve coputtonlly dffcult nd cubeoe tk. Hence thee need fo the degn of hghe ode yte though educed ode odel. Hee, odel ode educton technque whch co ultplcton of polynol ethod, ued fo educng hghe ode odel nto educed ode odel. he contolle

19 6 degned on the b of educed ode odel hould effectvely contol the ognl hghe ode yte. A contolle degned fo the educed econd ode odel to eet the deed pefonce pecfcton. h contolle ttched wth the educed ode odel nd cloed loop epone obeved. he pete of the contolle e tuned ung genetc lgoth optzton technque to obtn epone wth deed pefonce pecfcton. he tuned contolle ttched wth the ognl hghe ode yte nd the cloed loop epone obeved fo tblzton poce. Hee, PI type contolle ued to coect the oto peed. he popotonl te doe the job of ft ctng coecton whch wll poduce chnge n the output quckly the eo e. he ntegl cton tke fnte te to ct but h the cpblty to ke the tedy tte peed eo zeo. A futhe efneent ue the te of chnge of eo peed to pply n ddtonl coecton to the output dve. h known Devtve ppoch. It cn be ued to gve vey ft epone to udden chnge n oto peed. In ple PID contolle t becoe dffcult to genete devtve te n the output tht h ny gnfcnt effect on oto peed. It cn be deployed to educe the pd peed ocllton cued by hgh popotonl gn. Howeve, n ny contolle, t not ued. he devtve cton cue the noe ndo eo n the n gnl to be plfed nd eflected n the contolle output. Hence the ot utble contolle fo peed contol PI type contolle Cuent Loop Ung the pete n ecton 5.3.4, the cuent loop tnfe functon found fo Fgue

20 7 h thd ode yte. o educe the ode of the yte fo nlytcl degn of peed contolle, odel ode educton technque eve. Ung the co ultplcton of polynol odel ode educton ethod Reh et l, the educed econd ode yte of the cuent contol loop functon obtned n the fo of e d e d e cn be obtned. Mkng Equton 5.44 nd. equl, the followng vlue =3.3 b =34.63 =7.945 b =6.97 b = b 3 =9.6-7 Fo Equton.3 t obtned 3.3 c b Copng Equton 5.45 nd.7, d c b e Snce n th exple =.38 b, t cn be peued d nd e

21 8 Ung thee contnt te d nd e of the educed econd ode odel, the unknown pete d, e nd e of the educed econd ode odel cn be obtned follow. he cuent loop yte tnfe functon coped wth the genel econd ode tnfe functon ngeent, e d e d e 5.49 cn be obtned. By co ultplyng the bove equton, the followng condton e e e d d e 3.3e 7.94e 3.3e 7.94e 3.3e 9.6 d d 9.6 d 6.97d 3.99 d 34.63d 6.97d 34.63d On copng the coeffcent of e powe of te on both de, the followng equton e obtned. Coeffcent of 3 : 7.94e = d d 5.5 Coeffcent of : 7.94e +3.3e = d +6.97d 5.5 Coeffcent of : 7.94e +3.3e = 6.97d d 5.5 Coeffcent of : 3.3e =34.63 d 5.53 Accodng to Equton 5.53, d =3.3e. By ubttutng Equton 5.53 n Equton 5.5 to 5.5 wth d 3. 3 nd e 34.63, the followng Equton e obtned.

22 9 Coeffcent of 3 : 7.94e d = Coeffcent of : 7.94e +3.3e 6.97d = Coeffcent of : 3.3e d = Solvng Equton 5.54,5.55 nd 5.56, the unknown vlue e, e nd d e obtned wth d 3. 3 nd e 34.63, gven below. e =6.97, e =3.996 nd d =7.94. he coepondng educed econd ode odel of the cuent contol loop obtned, d d e e e he ntl educed ode odel obtned, d e e e d e e e S A S B S A B whch utble fo ue n the degn of peed loop. Hence, h educed ode cuent loop tnfe functon ubttuted n the degn of the peed contolle follow. he tep epone, gn nd phe plot of the exct nd educed cuent loop tnfe functon e hown n Fgue 5., 5. nd 5.3.

23 3.4. Step Repone of exct nd educed cuent loop tnfe functon exct educed e ec Fgue 5. Step epone of exct nd educed cuent loop tnfe functon n plot of exct nd educed cuent loop tnfe functon exct educed Fequency d/ec Fgue 5. n plot of exct nd educed cuent loop tnfe functon

24 3 3 Phe plot of exct nd educed cuent loop tnfe functon exct educed Fequency d/ec Fgue 5.3 Phe plot of exct nd educed cuent loop tnfe functon ble 5.3 Copon of tep epone of cuent loop Sttegy of Contol Ognl hghe ode yte Reduced ode yte Re te t n ec Settlng te t n ec % Ovehoot Pek pltude Pek te n ec Speed Contolle he open loop peed tnfe functon wth the educed cuent loop gven by o he coepondng educed ode odel obtned, d d o 5.6 e e e

25 3 he educed ode odel obtned n Equton 5.6 h le ISE wth epect to the hghe ode yte. he coepondng eo ndex clculted.67. he Speed contolle degned fo the yte o uch tht the te don pecfcton of the gven yte educe nd poduce fte output. he contolle degned fo the educed ode odel cn be ppled to the ognl yte to eet out the degne pecfcton. By ung the Pole-Zeo cncellton technque the ntl vlue of p nd e obtned fo the educed econd ode odel : p = 8.76, =8.76. he ntl vlue of p nd obtned though the educed ode odel e fne tuned ung A bed on the nl ettlng te cte. he eultnt vlue of p nd e obtned, p = 8.798, = hee contolle gn e ued fo the degn of peed contolle fo educed yte nd exct yte. he peed loop wth the educed cuent loop hown n Fgue 5.4. Fgue 5.4 he peed loop wth the educed ode cuent loop Fo Fgue 5.4, the cloed loop peed tnfe functon wth the educed ode cuent loop obtned

26 * Fgue 5.5 he peed loop wth the ognl ode cuent loop Fo Fgue 5.5, the cloed loop peed tnfe functon wth the ognl ode cuent loop obtned o * he tep epone of cloed loop peed tnfe functon wth the educed nd ognl ode cuent loop hown n Fgue 5.6. he tedy tte epone of the cloed loop peed tnfe functon wth educed ode cuent loop exctly tchng wth tht of the ognl cuent loop peed tnfe functon. h cn be nlyzed wth the help of te don pecfcton uch e te, ettlng te, tedy tte vlue nd pek vlue whch e gven n ble 5.4. he gntude plot nd phe plot of peed tnfe functon wth ognl nd educed cuent loop e hown n Fgue 5.7 nd Fgue 5.8 epectvely. he fequency epone of the

27 34 educed ode cuent loop peed tnfe functon exctly tchng wth tht of the ognl cuent loop peed tnfe functon. 5 Step Repone of peed loop tnfe functon wth ognl nd educed cuent loop ognl yte educed yte e ec Fgue 5.6 Step epone of peed loop tnfe functon wth ognl nd educed cuent loop functon ble 5.4 Copon of tep epone of peed loop wth ognl nd educed cuent loop Sttegy of Re te Settlng te % Pek Pek te Contol t n ec t n ec Ovehoot pltude n ec Speed loop tnfe functon wth ognl cuent loop Speed loop tnfe functon wth educed cuent loop

28 35 3 n plot of peed loop tnfe functon wth ognl nd educed cuent loop tnfe functon Ognl hghe ode yte Reduced ode yte Fequency d/ec Fgue 5.7 n plot of peed loop tnfe functon wth ognl nd educed cuent loop functon Phe plot of peed loop tnfe functon wth ognl nd educed cuent loop tnfe functon Ognl hghe ode yte Reduced ode yte Fequency d/ec Fgue 5.8 Phe plot of peed loop tnfe functon wth ognl nd educed cuent loop functon

29 COMPARISION OF CONVENIONAL MEHOD AND PROPOSED MODEL ORDER REDUCION MEHOD Fgue 5.9 how the copon of tep epone of peed loop tnfe functon ung ognl cuent loop wth yetc optu pncple nd odel ode educton technque wth genetc lgoth tuned contolle gn. h cn be nlyzed wth the help of te don pecfcton uch e te, ettlng te, tedy tte vlue nd pek vlue whch e gven n ble 5.5. he tep epone of the peed loop tnfe functon wth ognl cuent loop ung popoed odel ode educton technque wth genetc lgoth tuned contolle gn ethod gve bette te don pecfcton thn the conventonl yetc optu pncple ethod. he popoed PI peed contolle evel hote ettlng te whch 6% lowe thn tht of SO tuned PI peed contolle. Moeove the pek ovehoot ound 94% lowe thn the eult obtned by SO tuned peed contolle. he pek te eult tte tht enetc Algoth bed PI contolle 3% lee thn SO PI peed contolle. Wth condeton ove the ettlng te, the enetc Algoth PI contolle effcent thn.57 te.

30 37 Coponof Step Repone of the peed loop tnfe functon wth yetc optu pncple nd MOR wth A tuned gn 3 Syetc optu pncple MOR wth A tuned gn e ec Fgue 5.9 Copon of peed loop tnfe functon ung ognl cuent loop wth yetc optu nd MOR wth A tuned ethod ble 5.5 Copon of tep epone of peed loop ung ognl cuent loop tnfe functon Sttegy of Contol Syetc optu pncple MOR technque wth A tuned ethod Re te t n ec Settlng te t n ec % Ovehoot Pek pltude Pek te n ec Fgue 5. how the copon of tep epone of peed loop tnfe functon ung educed ode cuent loop wth yetc optu pncple nd odel ode educton technque wth genetc lgoth tuned contolle gn. h cn be nlyzed wth the help of te don pecfcton uch e te, ettlng te, tedy tte vlue nd pek

31 38 vlue whch e gven n ble 5.6.he tep epone of the peed loop tnfe functon wth educed ode cuent loop ung popoed odel ode educton technque wth genetc lgoth tuned contolle gn ethod gve bette te don pecfcton thn the conventonl yetc optu ethod. It obeved tht the conventonl ethod h pek ovehoot 3.7% whle tht of the popoed ethod.8%. 3 Copon of tep epone of peed tnfe functon wth Syetc optu pncple nd MOR wth A tuned gn Syetc optu pncple MOR wth A tuned gn e ec Fgue 5. Copon of peed loop tnfe functon ung educed nd plfed cuent loop wth yetc optu nd MOR wth A ethod ble 5.6 Copon of tep epone of peed loop ung educed cuent loop tnfe functon Sttegy of Contol Syetc optu pncple MOR technque wth A tuned gn Re te t n ec Settlng te t n ec % Ovehoot Pek pltude Pek te n ec

32 SUMMARY In th chpte xed ethod of pde ppoxton wth co ultplcton of polynol odel ode educton ethod ued to educe the hghe ode PMSM dve yte nto n equvlent educed econd ode yte nd peed contolle degned to the educed ode odel. Contolle gn e tuned by genetc lgoth optzton technque. he tuned contolle ttched wth the ognl hghe ode yte nd the cloed loop epone obeved fo tblzton poce. he tedy tte pefonce of popoed PI contolle wth the help of A h been coped wth the conventonl SO PI contolle. It obeved tht the conventonl yetc optu ethod h pek ovehoot ppoxtely 94% oe thn the popoed ethod. he ettlng te fo the conventonl ethod ound.363 ec, whee the popoed ethod h the ettlng te ound.4ec. Alo thee oe ocllton n the tnent tte n the ce of conventonl PI contolle. But the popoed ethod ettle t tedy tte wthout ny ocllton. he xu pecentge eo ppoxtely 3 te lowe thn n ce of conventonl contol chee. Accodng to the entvty pont of vew the conventonl contolle oe entve to lod vton, whee, the popoed chee le entve to lod vton.