Analog Speed-Control of DC-Motor Using Proportional and Proportional-Integral Controllers

Transcription

1 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 Anlog peedconol o DCMoo Uing Popoionl nd Popoionlnegl Conolle Dei Hlboo Mohuen Ai eue AlMuniiy Univeiy Engineeing College Copue nd owe Dep. dei_ohuen@yhoo.o Ab A yei developen o he nlyi, deign, nd eing by iulion o loedloop peed onol o epely exied d oo dive ye i deibed in hi ppe. he oo onolled ue volge i upplied o heephe ully onolled bidge onvee. Cloedloop onol i nlyzed by uing ne union ehnique nd he neeiy o n inne uen onol loop i deoned. Deign o boh popoionl nd popoionlinegl onolle e oulined by uing ne union ehnique. A o ing onep i ued o edue he vlue o ing uen. he eed owd loop i ued o edue he ee o lod oque diubne. he peed nd uen epone e lo peened o lod nd nolod e. الخالصة تحل ل وتصو ن وأختباس بالوحاكاة ل ظام الحلقت الوغلقت للس طشة على سشعت ظام سىاقت هحشك ت اس هستوش رو أحاسة ه فصلت تن وصفها ف هزا البحج. فىلت ت الحشض الوس طش عل ها تن تجه زها عبش هحىل قذسة هت اوبت الى قذسة هستوشة حالح الطىس جسشي. ظام الس طشة بالحلقت الوغلقت تن تحل له بأستخذام تق ت دالت التحى ل وتن ب اى الحاجت الى حلقت ت اس داخل ت. تصو ن كل هي الوس طش P والوس طش P ب ي بأستخذام تق ت دالت التحى ل. لتقل ل ت اس بذء التشغ ل تن أستخذام هفهىم بذء التشغ ل ال اعن أو الوتذسد. حلقت التغز ت األهاه ت تن أستخذاهها لتقل ل تأح ش األظطشاباث الت تحذث بسبب الحول. أستجابت الت اس والسشعت لل ظام تن تخب تها لحالت الحول وبذوى حول. 05

2 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N noduion DC dive, being ey o onol, e widely ued in ny viblepeed dive ye []. Openloop opeion o d oo y no be ioy in ny ppliion. Howeve, i he dive equie onn peed opeion he iing ngle h o hnge o inin onn peed. hi n be hieved in loedloop onol ye. A loedloop ye genelly h he dvnge o gee uy, ipoved dyni epone, nd edued ee o diubne uh loding. hen he dive equieen inlude pid eleion nd deeleion, loedloop onol i neey. n loedloop ye even he dive heii n be odiied. hu, he ye n be de o opee onn oque o onn hoepowe ove ein peed nge. Ciui poeion uen liie n be povided in loedloop ye []. n hi ppe he epone o loedloop ye nd onol deign udied by uing ne union ehnique. he neeiy nd igniine o he onol loop nd dieen pee e hown. Fo ipliiy nd ee o undending, he ye i edued o he lowe poible ode by negleing oe lle ie onn.. Cloedoop Conol ye he bi blo dig o loeloop onol ye i hown in Fig.. he eo w ued o onol he ue volge. he pplied ue volge i onolled uing heephe ully onolled bidge onvee. he ppopie iing onol ehnique eployed line elionhip beween he onol volge E nd he ue volge E n be obined, heeoe he onvee behve eenilly powe pliie wih line volge ne heii [35]. he ll dely ie oied wih he onvee i negleed, hen E 3 6V ph K E Eˆ ˆ Coepond o E 0 iing ngle nd V ph i he phe volge. Powe upply peed Conolle E Convee E DC Moo Feedb Eleen Fig. : i blo dig o loedloop peedonol ye 06

3 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N DCMoo ne Funion he peed onol o he epely exied d oo i elively ey, beue he epe exiion. Conide epely exied d oo wih ue volge onol, hown in Fig.. he volge loop equion i e di eg Ri d hee e g w 3 he oque blne equion i dw w j d 4 hee i 5 n he ple doin, equion hough 5 n be wien E E g E R 6 g 7 J 8 9 hu, o equion 6 E E R E E / R g g 0 hee R Fo equion 8 =eleil ie onn o he oo ue iui. / J hee J blo dig o in Fig. b. =ehnil ie onn o he oo. hee elionhip e hown in 07

4 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 R i i onn e e g w,, J K E R E g K b E d. Noe he eedb loop peen in he o o he b EMF. hi povide he odee peed egulion inheen in he epely exied d oo [, 6]. Fo Fig. b he hnge in peed due o diubne in pplied volge E nd lod oque n be expeed in he ollowing expeion. E R R we negle he lod oque e, o equion 3 E R whih i lo lwy he e, hen n be negleed, nd he expeion ipliie o E Fig. : Developen o oo ne union. epely exied d oo odel. b Funionl blo dig ipliied unionl blo dig 08 R d 3 R R d

5 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N hee d R R 3b R d 3 d Fo Fig. b 4 heeoe, o equion 3 nd 4 E E d d d 5 hu he oo n be epeened, o he pupoe o nlyzing i o ue volge onol, wo blo hown in Fig.. he gin onn, nd d hown in Fig. e ollow. R 5 5b d 5.. Cloedoop peed Conol evel ype o peed onolle e poible, wo o he oe oon one e popoionl P nd popoionlinegl P [7]. Fi popoionl onolle i ued. Fo Fig. 3, he ol ne union i d 6 hee i popoionl onolle onn. le

6 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N nd d, hen nd d Alo 7 he uen epone o ep hnge in inpu i A A hee A A e 8 Fig. 3: peedonol loop he nien ove uen i undeible o he ndpoin o onvee ing nd poeion. An inpu hnge in eul nien ove uen, hi udden hnge in uen whih dey lowly oding o equion 8. he peviou nlyi evel h i would be bee o lii he uen o xiu llowble vlue. hi liiing n no be uing he oniguion o Fig. 3 whee he oo volge i onolled by he peed eo. Any ep o lp hi peed eo will lii he oo volge. d E E 3 Φ DC Moo

7 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 ue loe e negleed, lping he peed eo will lii he peed, bu no he uen. Howeve, uen lii n be ipleened i we i onu n inne uenonol loop uing he lped peed eo he uen eeene [, 6]..3. Cloedoop Cuen Conol he inne uen onol loop i hown in Fig. 4. n hi igue he gin o he uen onolle i, whih hee i ued o be popoionl onolle. A uen eedb ignl n be geing vi uen ndue pling eio in he ue iui. he gin o he uen ndue i. Fo Fig. 4 he ne union i d C 9 d hee C 9 d 9b ine C nd 0 d 0 Alo, heeoe 0b Fo equion 9 nd 0b, i ppe h polezeo nellion i poible, euling in no oveho o ie dely. hen; C eue i diely eled o, lii on will eeively lii he uen. hi inne loop n now be inopoed wihin he peedonol loop, uing he lped peed eo he uen eeene. he ipleenion o hi hee i hown in he blo dig o Fig. 5. he blo dig n be ipliied, by uing expeion nd by negleing he nonline lping, o he dig in Fig. 5b. Reeing o Fig. 5b,

8 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 hee C C C C b C Fo C nd, C Alo, o equion nd 4 3 hile equion 3 i no vey dieen o equion 7, he expeion in he oe equion i only ue while i le hn he liiing vlue., duing eleion o lod hnge, he peed eo i lge uh h i lped he xiu vlue, he uen i liied o xiu vlue ˆ C. 3 Φ E E d DC Moo Fig. 4: Cuenonol loop

9 [ Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N Φ E E d C d 3. Deign o peed nd Cuen Conolle 3.. Popoionl P Conolle he pee nd onn o epely exied d oo h ued in he loedloop peed onol o d dive e deibed in he Appendix. he lping vlue o i hoen o be 3A. he eedb gin nd ued e ixed hee vlue given in he Appendix. he popoionl onolle pee nd o peed nd uen onolle e hoen on he bi o edye eo onideion, whee G hu Fig. 5: Popoionl peed onol wih inne uenonol loop. Funionl blo dig. b ipliied unionl blo dig 0 G H 0 Fo he uen onol loop, nd H 0 b 3

10 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 hee i he deied edye uen eo. A pil vlue igh be 0%, hen n he e nne, he peed onolle gin n be luled, n hi e. G H 0 Fo he peed onol loop G 0 C C nd H 0 hee N i he deied edye peed eo. Fo 0.5% eo, he ye epone i geing by uing MAA pge. Fig. 6 how he uen nd peed epone o he ye when he uen nd peed onolle e popoionl ype onolle, wih eeene peed 0d/. b Fig. 6: Repone o popoionl onol o ep hnge in peed eeene Cuen epone b peed epone 3.. Popoionlnegl P Conolle o eliine he edye eo nd o edue he owd gin equied, he popoionl peed onolle i epled by Pype onolle. he popoionl plu inegl ype o onolle h been ued o hieve good dyni nd edye epone [8]. he new onolle ne union i /. he euling blo dig i hown in Fig. 7. 4

11 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 he onolle gin nd i pole / n be deigned o he onideion o dping nd nul equeny. he ovell ne union beoe C 4 C Fo C hee C C 5 5 C he heii equion o he ye i hen hen 0 w n o w, lo wn n Fo dping io o nd nul equeny i 0d/, boh he gin nd he ie onn n be luled , nd C.70 hen he Ponolle ne union i / 5

12 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 C Fig. 7: peedonol loop wih Ponolle. he iulion epone o Ponolle ep hnge in peed eeene i hown in Fig. 8. b Fig. 8: Repone o Ponol o ep hnge in peed eeene Cuen epone b peed epone 4. oing Conep Aoding o equion 3, ing, he b EMF i equl o zeo beue he peed i zeo. ine he ue iui eine i ll, hen he ue ing uen i vey lge nd y be dge he onvee wihing devie. o edue he dngeou o ing uen oing onep i ued. n hi onep he ue volge i ineed in ll ep ove ho peiod ing o enue h he ing uen in llowble vlue. Fig. 9 nd Fig. 0 e how he ye epone wih oing ehnique by uing popoionl nd popoionlinegl onolle epeively. ' le o he uen epone h he ing uen wih hi ehnique i le hn wihou uing oing ehnique, bu he nien peed epone i low down. 6

13 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 b Fig. 9: Repone o Ponol o ep hnge in peed eeene wih oing ehnique Cuen epone b peed epone b Fig. 0: Repone o Ponol o ep hnge in peed eeene wih oing ehnique Cuen epone b peed epone 5. ep neing nd Deeing o Reeene peed he oo eeene peed inee, he peed eo w inee. hi in un hnge he iing ngle o he onvee, nd hu inee he oo ue volge E. An inee in he oo volge develop oe oque o inee he oo peed o eh ppoxiely o he eeene peed. Fig. how he peed nd uen epone o ep ineing in he eeene peed, while Fig. how he ye epone o deeing eeene peed e. b Fig. : Repone o Ponol o ep ineing in peed eeene Cuen epone b peed epone 7

14 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N b Fig. : Repone o Ponol o ep deeing in peed eeene Cuen epone b peed epone 6. od oque Diubne n oe ppliion lod i uddenly pplied o he oo, heeoe he ee o uh lod oque diubne i onideed now in wo e. 6. Popoionl PConolle Fig. 3 how he oplee blo dig o he peed loop wih popoionl peed onolle. hnge in he eeene peed e negleed, n expeion o he uen n be wien in e o he peed hnge. Fo Fig. 3 ]} [ { R 6 ] [ R 7 ine nd R 8 he blo dig hen ipliie o h hown in Fig. 3b. hu J J ] [ 9 hee

15 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 ine nd, hen C C ine C N 30 he uen epone o equion 8 nd 30 i 3 hi lo how iil eondode epone. 3 Φ E K E R J Eb K K J b Fig. 3: Ee o lod oque diubne. Funionl blo dig. b ipliied Funionl blo dig. Fig. 4 i he ye epone wih popoionl onol o ep hnge in lod oque. n be een h he epone i eondode nd h hee i edye hnge in peed nd uen. 6.. Popoionlnegl PConolle he onolle ne union deigned by in Fig. 3 i epled by he Pne union /. 9

16 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N J J 3 eue hen 33 hee Fo Fig. 3b, o he Ponolle, 34 Now, o equion 33 nd 34, Fig. 5 how he ye epone wih Ponolle due o ep hnge in lod oque. he ne union in equion 33 h zeo he oigin. heeoe, hee will be no edye peed hnge o ephnge in lod oque; hi i hown in he Fig. 5b. b Fig. 4: Repone o ep inee in lod oque wih Ponol Cuen epone b peed epone

17 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 b Fig. 5: Repone o ep inee in lod oque wih Ponol Cuen epone b peed epone o edue he dyni peed viion o he d oo due o he ep hnge in lod oque, eed owd hee i peened hown in Fig. 6. n hi hee he equied uen o opene he diubne ee o lod oque i dded o he eeene uen. he lod uen i opued ollowing. ine 37 hen 37 ine 38 Fig. 7 how he epone o ep inee in lod oque wih Ponolle nd eed owd loop. K 3 Φ K K R E J Eb K Fig. 6: peed onol o d oo wih eed owd loop

18 [[[ Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 b Fig. 7: Repone o ep inee in lod oque wih Ponol nd eed owd onol loop Cuen epone b peed epone 7. Conluion A loedloop peed onol o doo ye h been deibed. he loedloop onol ehnique i ued ined o openloop ehnique o ineing he uy, ipoved he dyni epone, nd eduion o he ee o diubne uh udden loding. A ne union ehnique i ued o deign he onolle pee. he uen liie i ued o lii he ue uen o oe xiu llowble vlue 3A. he iulion epone o he ye i ound o peed popoionluen popoionl nd peed popoionl plu inegluen popoionl onolle. he edye eo i edued by uing Ppeed onolle. he ovehoo o uen gee hn ed uen i pevened by uing oing ehnique, bu in hi e he epone o he ye i lowe hn wihou oing. he epone o he ye o ep ineing nd deeing o eeene peed i geing, nd ound h he oupu o he ye i ed he eeene peed. An ipoved epone i hieved by uing eed owd loop wih lod oque e. he opeion onn peed nd onol o peed ove wide nge n be eily peoed. 8. Appendix he pee nd onn o loedloop onol ye o epely exied d oo dive e lied below: 8.. DC Moo 80v, /3hp, 3300p: R 4 : Aue iui eine R 0. 5 : pling eine 80H : Aue iui eine

19 Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N 8378 J=0.005N /d =0.00 N/d : oen o inei o oo nd lod : Viou iion o oo nd lod. A : Red uen o oo 0.54v/ d : EMF nd oque onn 8.. Pee nd Conn 0,. 5, d d A / v, 54d /. A, 0.08v. / d , C, / 0.5 v / A 3

20 ine Plo Abee 8v*8 od N Jounl o Engineeing nd Developen, Vol. 5, No. 3, epebe 0 N Reeene. Pdeep K. Nnd nd Peh C. en, Anlog nd Digil peed Conol o DC Dive Uing Popoionlnegl nd negl Popoionl Conol ehnique EEE, nion on nduil Eleoni, Vol. E34, No., My 987, pp. 7 Righ Colun 33. e Colun. en P.C., hyio DC Dive, John iley nd on, K.. Ni, hi ingh, P. Agwl nd A.K. Goel, Fiing Ciui o 3Ø Vible Fequeny Deleion hyio idge nvee, 4..R. Pelly, hyio Phe Conolled Convee nd Cylo Convee, John iley nd on, nde C.. Powe Eleoni, MGwHill, Peh C. en nd Muy. Mdonld, hyioized DC Dive wih Regeneive ing nd peed Revel EEE, nion on nduil Eleoni nd Conol nuenion, Vol. EC5, No. 4, Nov. 978, pp Og K. Moden Conol Engineeing PenieHll, Englewood li NJ, Kihnn nd. Rwi, peed Conol o DC Moo Uing hyio Dul Convee EEE, nion on nduil Eleoni nd Conol nuenion, Vol. EC3, No. 4, Nov. 976, pp