CHAPTER 5 SPEED CONTROLLER BY SYMMETRIC OPTIMUM APPROXIMATION METHOD
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1 8 CAPER 5 SPEED CONROLLER BY SYMMERIC OPIMUM APPROXIMAION MEOD 5. INRODUCION In ode o ex he be pefone fo gven elel hne, he pope degn of he peed nd uen onolle pon. oweve ll dve e pee enve o oe degee. donl ehod of onolle degn n he fequeny don ue nonl vlue of he pln pee. he effe of hnge n he pee n be ubequenly heked by envy nly Plly & hnn 987. An lenve ehod popoed n h eon fo he degn of peed onolle fo good pefone dve. Moly he Popoonl Inegl PI onolle ued fo dve pplon beue of ple uue nd obu pefone n wde nge of openg ondon. h onolle depend only on wo pee nely he popoonl gn p nd he negl gn. In h hpe ung nfe funon of he PMSM dve nd SRM dve, he degn of peed onolle fo PMSM dve nd SRM dve by Sye Opu SO ppoxon ehod nlyzed.
2 8 5. DESIN OF SPEED CONROLLER FOR PMSM DRIVE BY SYMMERIC OPIMUM MEOD A popoonl plu negl onolle nolly ued fo ny ndul pplon nd hene exenvely del n ny ex. Sne he PI onolle eond ode n nue deenon of gn nd e onn of he onolle by ung he ye opu ehod ple f he d x o uen ued o be zeo. In he peene of d x o uen, he d nd q uen hnnel e o oupled, he odel nonlne n nue eul of he oque e. he degn of uen onolle nd peed onolle wh ex pee pon o obn he deed nen nd edy e he of he PMSM dve ye. he ye beoe lne he d x uen ued o be zeo nd eeble h of epely exed d oo wh d onn feld exon. he blok dg foon fo he dve beoe ey. he uen loop ppoxon, peed loop ppoxon nd he deenon of he nfe funon of he uen nd peed onolle denl o h of d oo dve. 5.. Blok Dg Foon Wh he d-x uen ued o be zeo, he oo q-x volge Equon beoe V q R L p λ 5. q q f he eleoehnl oque Equon of he dve P e Jp Bl 5.3
3 8 whee he eleogne oque gven by e 3 P. λf 5.4 q If he lod ued o be fonl he lod oque beoe B l 5.5 h led o he eleoehnl Equon 3 P Jp B. λf q. q 5.6 whee B P B B 5.7 l 3 P. λf 5.8 Ung he Equon 5. nd 5.6 he edued blok dg wh he uen nd peed feedbk loop dded hown n Fgue 5.. Fgue 5. Blok dg of he peed onolled PMSM dve
4 83 he nvee nfe funon h gn nd e dely n 5.9 n whee V 65 d n. 5. V n 5. f whee V d he d lnk volge npu o he nvee V he xu onol volge nd f he whng e fequeny of he nvee. he ndued ef due o oo flux lnkge, e e λ 5. f 5.. Cuen Loop he ndued ef loop oe he q x uen loop nd ould be plfed by ovng he pk off pon fo he ndued ef loop fo peed o uen oupu pon. he uen loop nfe funon obned fo Fgue 5.3 gven below
5 84 Fgue 5. Cuen onolle q * q n 5.3 n n { b } whee Lq J ; ; ; ; R R B B b λ f fequeny: he followng ppoxon e vld bou he oove n n whee 5.7 n
6 85 wh h he uen loop nfe funon edued o * q q b n n n 5.8 b whee < < ; I found h.he plfed uen loop nfe funon hen gven by q * q 5.9 whee n 5.3 b 5.3 h uen loop nfe funon ubued n he degn of he peed onolle follow Speed Conolle he peed onol loop nd he plfed uen onol loop e hown n Fgue 5.3. Ne he vny of he oove fequeny, he followng ppoxon e vld bou he oove fequeny
7 whee 5.35 Fgue 5.3 Splfed peed-onol loop he peed loop nfe funon deened ung hee ppoxon nd gven by fo whh he loed loop peed nfe funon obned * 3 g g 5.37 whee
8 87 g 5.38 Equng h nfe funon o ye opu funon wh dpng o of.77 gve he loed loop nfe funon 3 3 * Equng he oeffen of equon 5.37 nd 5.39 nd olvng fo e nd gn onn yeld g ene he popoonl gn p, nd negl gn, of he peed onolle e deved g p g 5.43 he vldy of vou ppoxon vefed hough woked exple.
9 Exple he PMSM dve ye pee e follow: R.4 Ω, L d.56, L q.9, λ f.546 Wb-un, B. N-/d/e, J.6 kg-, P 6, f kz, V V,.5 V/V,.8 V/A, V d 85 V. A ye opu bed peed onolle o be degned bed on he bove pee nd he vldy of upon de n devon vefed. he dpng o equed.77. Soluon Invee nfe funon, : Vd Invee gn onn, n V V V e onn, n.5e f n n Moo elel nfe funon, : Moo gn onn,. 743 R.4 e onn, L R q.9.64e
10 89 Indued ef loop nfe funon, b : 3 P 3 6 oque onn,. λf N / A Mehnl gn, B. d / e/ N b λ f whee he ehnl e onn J B.6..6e Moo ehnl nfe funon, : Equvlen elel e onn of he oo Solvng fo he oo of b whee b n b λ b f 3.6
11 9 hen he nvee of he oo nd e.5775 e.3 e Splfed uen loop nfe funon b Ex uen loop nfe funon [ ] [ ].... b b Speed onolle g.5775 e.55 e g Splfed peed loop nfe funon 3 g g e
12 9 Ex peed loop nfe funon e..... whee All he uen loop nfe funon ep epone, gn nd phe plo e hown n Fgue 5.4, 5.5 nd 5.6. All he peed loop nfe funon ep epone, gn nd phe e hown n Fgue 5.7, 5.8 nd 5.8. In he fequeny egon of nee, noe h he ppoxon hold good boh n gnude nd n phe, n pe of he eduon of he ffh ode ye o n equvlen hd ode n he e of he peed loop nd of hd o f n he uen loop of he dve ye eul e fee of eo. Fo ep epone plo of he ex nd plfed uen loop nd peed loop nfe funon, he e don pefon led n ble 5. nd ble 5..
13 9.4. Sep Repone of ex nd plfed uen loop nfe funon ex plfed Cuen A e. e Fgue 5.4 Sep epone of ex nd plfed uenloop nfe funon n db Ex nd plfed uen loop gn plo Ex Splfed -8 Fequeny d/e 3 4 Fgue 5.5 n plo of Ex nd plfed uen loop gn plo
14 93 Phe plo of ex nd plfed uen loop nfe funon 3 Ex Splfed Phe deg -3-6 Fequeny d/e 3 Fgue 5.6 Phe plo of Ex nd plfed uen loop gn plo ble 5. Copon of e don pefon of uen loop Segy of Conol Ex Cuen loop Splfed uen loop Re e n e Selng e n e % Ovehoo Pek plude Pek e n e
15 Sep Repone of ex nd plfed peed loop nfe funon ex plfed Speed d/e e.5 e Fgue 5.7 Sep epone of ex nd plfed peed loop nfe funon n plo of ex nd plfed peed loop nfe funon 3 ex plfed n db Fequeny d/e 3 Fgue 5.8 n plo of ex nd plfed peed loop nfe funon
16 95 Phe plo of ex nd plfed peed loop nfe funon 45 ex plfed Phe deg Fequeny d/e 3 Fgue 5.9 Phe plo of ex nd plfed peed loop nfe funon ble 5. Copon of e don pefon of peed loop Segy of Conol Ex peed loop Splfed peed loop Re e n e Selng e n e % Ovehoo Pek plude Pek e n e DESIN OF SPEED CONROLLER FOR SRM DRIVE USIN SYMMERIC OPIMUM MEOD he pee of he popoonl-negl onolle need o be djued o effevely onol he poe whoe dyn e debed by e of dffeenl equon.by popely degnng he PIonolle, poble o ke he nen epone o ep npu exhb elvely ll o no ovehoo. In he degn of he peed onolle, he e epone of he
17 96 uen loop wll be ued o be o f h he uen efeene wll be ondeed o onde wh he ul uen. oweve, he dyn of he uen loop ken no oun dung he ulon of he dve ye. he epone of ye nbe ely nlyzed f he ye ould be ppoxed by eond ode ye. heefoe, fo ply n he nly he elel e onn of he oo negleed, he ehnl e onn of h oo uully uh lge hn elel e onn.a peed-onolled SRM dve ye hown n Fgue 5.. Fgue 5. Blok dg of he peed-onolled SRM dve Roo peed onveed o volge gnl hough ho geneo whh hen fleed o povde, whh hen oped wh efeene. he peed eo gnl plfed nd ondoned wh he peed onolle whh nolly popoonl-plu negl ype. he oupu of h peed onolle volge gnl popoonl o uen ond gnl I *. A uen feedbk gnl n vol oped wh h ond gnl o genee uen eo. he uen eo poeed hough PI onolle o podue ond gnl fo he powe onvee. he powe onvee odeled gn wh f-ode lg, nd boh of hee
18 97 onn y be eued o evlued n he degn ge. he powe onvee gn, V no n l d 5.44 V wheev he xu onol volge. he e onn of he onvee,,ung PWM onol of he onvee wh e fequeny of f, gven by f Degn of Cuen Conolle A PI onolle eleed fo he uen onolle beue of ply o pleen nd wde ped ndul ue. he blok dg of he uen loop hown n Fgue 5.. Fgue 5. Blok dg of he uen onol loop he nfe funon of he uen onolle 5.46
19 98 he e dely of he onvee negleed hee due o he upon h he whng fequeny le e gee hn h of he elel e onn n he uen loop. Fuhe, uh n upon plfe he blok dg.sne he ehnl e onn of he ye,, lge, >> n be ppoxed. Wh h ppoxon, he uen loop beoe eond ode ye. he ppoxed ye gven below I 5.47 * I In degnng he uen onolle gn nd e onn, deble o pefy bndwdh fo he uen loop bed on he whng fequeny of he onvee. In ode o ppoxe he onvee ple gn, he bndwdh of he onvee u be en e fe hn he bndwdh of he uen loop. o degn he uen onolle ung he bndwdh ehod, he he equon of he ppoxed uen loop ued, hown below 5.48 Sne eond-ode equon, he nul fequeny of ollon n nd dpng o ζ of eond-ode ye y be ued o obn he uen onolle gn nde onn. ven below e he equon whh pefy he dpng 5.49 nd hen ul fequeny of he ppoxed ye 5.5 ζ n 5.49
20 99 n 5.5 he gn, nd he e onn,, y be olved fo Eq nd 5.5, epevely, fo gven nul fequeny nd dpng o. he followng e equon fo nd : ξ n 5.5 n Exple o vlde he degn ehnque ung he lnezed odel, 5-hp SRM ondeed fo he uen nd peed onolle degn. he pefon fo he 5-hp SRM dve e led below: Moo nd Sye Pee Cond gnl level D lnk volge Mx. uen PWM hoppng fequeny Phe ene Powe Red uen Red peed Roo fon onn ± V 4 V 5 A 8 kz.93 Ω 5 hp A p.u. 5 p.n/d/e
21 Roo ne.6 kg Speed feedbk gn.383 V/d/e Speed feedbk e onn. e Indune of he SRM phe ued o be he en vlue of he unlgned ndune nd lgned ndune he ed uen. h vlue un ou o be.. he lope of he ndune uve needed n ode o lule he lnezed oque/bk ef onn. Ung he ndune vlue he ed uen, he ppoxe lope of he ndune pofle.34 /d. By ung Equon 5.49 nd 5.5, he lnezed oque/bk ef onn, b, nd he lnezed phe ene, R eq, e luled: R eq dl R Ω dθ b dl.34 dθ.34 he followng onn e luled n ode o begn he degn of he onolle:. Convee gn V d v 4 4. Cuen ndue gn v x V/A
22 3. Moo nfe funon B B Bl.. B b RB.8 J B.6 6e..668 e.358e o degn he uen onolle gn nd e onn, Equon 5.5 nd 5.5 eued. Fo bndwdh of 6 z nd dpng o of.77 fo he uen loop pefone, he onolle gn e.44 n 9.36 n.3 e hown n Fgue 5. e he epone of he uen loop. Boh he ppoxed nd unppoxed uen loop epone wee denl, o he unppoxed odel-bed epone hown hee. he fequeny epone hown n Fgue 5.3 nd he bndwdh of he ye ppoxely 6 z.
23 .8 Sep Repone of he edued uen loop nfe funon ung SO Mehod.6.4. Cuen A e eond x -4 Fgue 5. Sep epone of he Cuen loop Fequeny epone of he edued uen loop nfe funon ung SO Mehod n db Phe deg Fequeny d/ Fgue 5.3 Fequeny epone of he Cuen loop nfe funon
24 Degn of he Speed Conolle o plfy he degn of he peed onol loop, ued h he dely of he uen loop neglgble due o he f h uully he peed of epone ofhe uen loop le en e fe hn he epone of he peed loop. o fuhe plfy he degn equon, he uen loop gn ppoxed uny nd e dely negleed vey, vey ll oped o ll ohe eonn. Nolly he dely due o he peed feedbk y be negleed, whh would edue he ye o eond-odeye, bu when he peed feedbk dely opble o he dely of he ohe ubye u be ondeed nhe degn poe. he blok dg of he ppoxed peed loop hown n Fgue 5.4. Fgue 5.4 Appoxed peed loop blok dg Conde he peed loop nfe funon gven b / B Ne he gn oove fequeny, onn,he followng ppoxon de lge oped o ohe e
25 h eul n he peed loop nfe funon whee b 5.49 B Fo h he loed loop peed-nfe funon ppoxely deved. o * 3 o whee he oeffen of he polynol e o o opze he gn of he loed-looppeed-nfe funonhe denono of he gnude epone funon nzed o povde fl fequeny epone.e., ye opu.suh ondon gve elonhp beween he oeffen of he he polynol ledng o evluon of he peed onolle onn gven below
26 5 j * j [ ] 3 3 fo whh he oeffen e eled by o gve fl fequeny epone. Fo he bove wo ondon, he peed onolle onn e evlued Feue of hesye Opu Funon Subung fo nd we n obn he loed-loop peednfe funon ne of 4. * Fo he open-loop gn funon, he one pon e 4 nd wh gno ove fequeny of. In he vny of he gn oove fequeny he lopeof he gnude epone db/dede whh he o deble he fo good dyn behvo. Beue of yey he gn oove fequeny h nfe funon known ye opu funon. Fuhe h nfe funon h he followng feue
27 6. Appoxe e onn of he ye 4.. he ep epone gven by wh e e of 3., xu ovehoo of 43.4% nd elng e of 6.5. / / 4 { e e o 3 / } Sye opu elne he effe due o he dubne vey pdly oped o ohe opu ehnque eployed n pl ye uh lne nd odulu opu, e. h ppoh nde one of he poble ehod o ynheze he peed onolle. he judou hoe of ppoxon bed on he phyl onn of he oo, onvee, nd ndue gn nd dely Sulon Reul An SRM dve gven n Exple nuened wh peed onolle wh gn onn.3 nd e onn.38 e. hown n Fgue 5.5 e he ep nd fequeny epone of he unppoxed peed loop. he bndwdh of he eulng peed loop ppoxely 5.9 z, nd he ovehoo fo he ep epone lge.
28 7.6 Sep Repone of he edued Speed nfe funon ung SO Mehod.4. Speed d/e e eond Fgue 5.5 Sep epone of he peed loop Fequeny epone of he edued peed nfe funon ung SO Mehod n db Phe deg Fequeny d/ Fgue 5.6 Fequeny epone of he peed loop
29 8 5.4 SUMMARY In h hpe Sye Opu ppoxon ehod ued o edue he hghe ode PMSM dve ye nd SRM dve ye no n equvlen edued f ode ye nd peed onolle w degned o he edued ode ye. Boh uen onolle nd peed onolle degned ung Sye opu ehod fo he gven dve ye. h ppoxon ehod ued o nlyze he dve pefone n n ey wy. ee ep epone nd fequeny epone of boh he uen loop nd peed loop e ploed fo boh he ppoxed nd unppoxed e. Fo he eul he ppoxed ep epone wee denl o h of he unppoxed ep epone of he peed nd uen loop.
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