Modelling and Simulation of Armature-Controlled Direct Current Motor Using MATLAB

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1 SSRG Inernionl Journl of Elecricl nd Elecronics Engineering (SSRG-IJEEE) volume Issue 3 Mrch 015 Modelling nd Simulion of Armure-Conrolled Direc Curren Moor Using MATLAB Jide Julius Poool 1, Oldele Joshu Oldejo, nd Chriy Segun Odeyemi 3 1 Dermen of Elecricl nd Elecronics Engineering, Federl Universiy of Technology, Akure, Nigeri Dermen of Elecricl nd Elecronics Engineering, Federl Universiy of Technology, Akure, Nigeri 3 Dermen of Elecricl nd Elecronics Engineering, Federl Universiy of Technology, Akure, Nigeri ABSTRACT : Technology resen needs fser nd esier mens of conrolling equimen wih few numers of comonens. One of such equimen is he direc curren (DC) moor, whose seed is direcly roorionl o he suly volge. Using his eslished relionshi eween he seed nd he suly volge, his er invesiges he effecs of differen lods nd inus on he ouu resonse of he rmure conrolled direc curren moor. The im is o eslish relionshi eween he seed of DC moor nd he lod orque differen volges s well s invesiging he erformnce of closed-loo sysems when differen volges re lied o he rmure circui of he moor when consn volge is sulied o he field circui of he moor. The sudy ws crried ou in wo sges. The firs sge involved mhemicl modeling of he sysem while he second sge cenered on he simulion of n rmure conrolled direc curren moor using Simulink environmen in MATLAB. The erformnce nlysis of he modeled sysem shows h usge of feedck enhnces he erformnce of he rnsien resonse of he rmure conrolled DC moor. In ddiion he resul oined shows h differen inu volges, he seed he DC moor is inversely roorionl o he lod orque. eywords - Model, DC moor, Bck emf, DC moor clssificions, Elecricl nd mechnicl vriles I. INTRODUCTION The universe we live undergoes coninul chnge. This chnge is no lwys ren if he ime scle is long s exerienced in some geologicl rocesses. However in engineering where siuions h re ime-deenden re imorn, idel descriion of ojecs or rocesses mus include roer iming. This kind of descriion is clled or known s model. A model is simly reresenion of he consrucion nd working of some sysems of ineres [1]. According o he uhor, model is similr o u simler hn he sysem i reresens. The rocess of roducing model is known s modeling. Bsiclly, good model is judicious rdeoff eween relism nd simliciy. One of he imorn issues in modeling is model vlidiy, which is he rocess of simuling he model under known inu condiions nd comring model ouu wih sysem ouu [1]. Bsiclly, simulion of sysem is he oerion of model of he sysem, which cn e reconfigured nd exerimened wih. Thus, oerion of he model cn e sudied in order o infer some deils on he roeries concerning he ehvior of he cul sysem or is susysem. Generlly, ccording o [1], simulion is ool o evlue he erformnce of sysem, eiher exising or roosed, under differen configurions of ineres nd over long eriods of rel ime. Hence, for his rmure conrolled DC moor modeling, he nlysis ws crried ou using oh he se nd imulse resonses. All he d sed on inernl circui of he modeled rmure conrolled DC moor for his sudy were nlyed oh y conrol sysem design clculion nd y MATLAB sofwre. In order o enhnce oh he undersnding nd roer resenion of he sudy reored in his er, he remining rs of his er re orgnied s follows. In Secion II, in deh informion on DC moor such s is rincile of oerion, clssificion nd differen mehods of conrolling he seed of DC moors were resened. Secion III rovides in deil, he mehodology used in crrying ou he sudy reored in his er. The resuls oined re resened, inerreed nd discussed in Secion V while he conclusions mde re resened in Secion V. II. DIRECT CURRENT MOTOR The DC moor is one of he firs mchines devised o conver elecricl ower ino mechnicl ower moor [ 4]. Is origin, ccording o [3], cn e rced o disc-ye mchines conceived nd esed y Michel Frdy, who formuled he fundmenl conces of elecromgneism. The DC moor uses elecriciy nd mgneic field o roduce orque, which cuses i o urn. I requires wo mgnes of oosie olriy nd n elecric coil, which cs s n ISSN: Pge 19

2 SSRG Inernionl Journl of Elecricl nd Elecronics Engineering (SSRG-IJEEE) volume Issue 3 Mrch 015 elecromgne. The reellen nd rcive elecromgneic forces of he mgnes rovide he orque h cuses he moor o urn. I lso consiss of one se of coils, clled rmure winding, inside se of ermnen mgnes, clled he sor. Alying volge o he coils roduces orque in he rmure, resuling in moion. The rincile of oerion on DC moor s shown in Figure 1 requires DC volge source. When he wo ends of he coil re conneced cross DC volge source, i will cuse curren, I, o flow hrough i. Hence, force is exered on he coil s resul of he inercion of mgneic field nd elecric curren. The force on he wo sides of he coil is such h he coil srs o move in he direcion of force. In DC moor, severl such coils re wound on he roor, ll of which exerience force, resuling in roion. The greer he curren in he wire, or he greer he mgneic field, he fser he wire movemen ecuse of he greer force creed. A he sme ime, orque is eing roduced s he conducors re moving in mgneic field. A differen osiions, he flux linked wih i chnges, which cuses n elecromgneic force (emf) o e induced s shown in Figure. This volge is in oosiion o he volge h cuses curren flow hrough he conducor nd is referred o s couner-volge or ck emf. The vlue of curren flowing hrough he rmure is deenden uon he difference eween he lied volge nd his couner-volge. The curren due o his couner-volge ends o oose he very cuse for is roducion ccording o Len s lw. I resuls in he roor slowing down such h he force creed y he mgneic field equls he lod force lied on he shf. Then he sysem moves consn velociy. Bsiclly, he oerion of DC moor is sed on he rincile h when curren crrying conducor is lced in mgneic field, he conducor exeriences force. This force ccording o [5], lys n imorn role o roduce owerful orque. The mgniude of he force is given mhemiclly in [5] s; F BIl (1) where B is he flux densiy in Weer er squre meer W / m, I is he curren in mere (A) nd l is he lengh of he conducor in meer (m). Figure 1: Torque roducion in DC moor [6] Figure : Induced volge in rmure winding of DC moor [6] Bsiclly, here re hree yes of DC moors. The wo commonly crieri usully use in clssifying hem re heir chrcerisics nd he connecion of heir exciing windings or circuis. Bsed on hese crieri, he hree common yes re: shun, series nd comound moors. In shun DC moor, only one exciing winding, which is conneced cross he rmure erminls nd is hus in rllel or in shun wih he rmure. The field winding consiss of lrge numer of urns of fine wire on ech ole, nd usully he windings on ll he oles re conneced in series in one circui. The curren in he field deends uon he line volge nd uon he resisnce of he field winding. The resisnce of he field winding is urosely mde high so h he field curren will e eween 1 nd 5 er cen of he full-lod curren of he moor. In his clss of DC moor, rheos is normlly conneced in series wih he field o conrol he moor when he seed is ove norml ring [7]. The series DC moor, on he oher hs only one exciing winding, which is conneced in series wih he rmure, so h ll curren flows hrough he field s well s he rmure. The field ISSN: Pge 0

3 SSRG Inernionl Journl of Elecricl nd Elecronics Engineering (SSRG-IJEEE) volume Issue 3 Mrch 015 winding consiss of few urns of hick wire on ech ole, nd he windings on ll oles re conneced in series. The curren in he field deends uon he lod nd is hus lrge wih hevy lod nd smll wih ligh lod. The resisnce of he field winding is urosely mde low so h he loss of volge nd ower in h circui will e smll. According o [7], he only hing h limis he seed of series moor is he moun of lod conneced o i. The hird clss known s he comound or cumulive moor hs oh series winding nd shun winding on ech ole, which re wound nd conneced so h he wo windings ssis ech oher in he roecion of mgneism. I is cominion of shun nd series moor. The comound-wound moor hs wo exciion windings, oh on he min field oles. According o [8], in his ye of DC moor he mjoriy of he flux resuls from he convenionl shun winding wih ddiionl exciion from series-conneced winding. Generlly, DC moors re much more dle seed drives [4] hn lerning curren (AC) moors which re ssocied wih consn seed roing field. Indeed one of he rimry resons for he srong comeiive osiion of DC moors in modern indusril drives is he fine seed conrol. The seed of DC moor ccording o [9] is given s; E IR N.. () where, E I R is he ck emf e. There re hree mehods of conrolling he seed of DC moor: rmure volge seed conrol, field flux seed conrol nd volge conrol. In his sudy, he rmure mehod ws emloyed. The modeling nd simuling rocedures involved in crrying ou he sudy re resened in Secion III. III. MODEL DEVELOPMENT In modeling he rmure conrolled DC moor for his sudy, simle elecricl circui of rmure conrolled DC moor digrm s shown in Figure 3 ws emloyed while he civiies involved were roken down ino four sges. The four sges involved re resened in he following su-secions s follows. 3.1 ARMATURE CONTROLLED DC MOTOR CIRCUIT DIAGRAM REPRESENTATION This sge focus ws on develomen of n rmure conrolled DC moor s shown in Figure 3 wih orque nd roor ngle. Figure 3: Armure-conrolled DC moor [10] rmure, In Figure 3, R is he resisnce of he L is he inducnce of he rmure winding, iis he rmure curren, i f is he field curren, he ck emf, eis he lied rmure volge, e is TM is he orque develoed y he moor, is he ngulr dislcemen of moorshf, J is he equivlen momen of ineri of moor shf nd lod referred o he moor while f is he equivlen coefficien of moor nd lod referred o he moor shf. 3. DERIVATION OF THE SYSTEM EQUATION The civiy in his sge involves he develomen of oh he elecricl nd mechnicl vriles in Figure 3. The vriles of ineres on he elecricl side re volge nd curren while he vriles of ineres on he mechnicl side re orque nd seed. The wo sic equions rele hese four vriles nd form he foundion of rmure conrolled DC moor nlysis. According o [8], he develoed orque y moor is defined mhemiclly s; T i i. (3) where ws denoed s. Similrly, he uhors defined he ck elecromoive force e mhemiclly s; e 60 However, since; n (4) ISSN: Pge 1

4 SSRG Inernionl Journl of Elecricl nd Elecronics Engineering (SSRG-IJEEE) volume Issue 3 Mrch n. (5) Susiue (5) ino (4), o oin e (6) where ws denoed s The fcor s orque consn. is frequenly referred o in (3) nd volge consn in equion (6). Since consn,, which is defined in [8] s;, new (7) Since he field srengh is fixed, he flux er ole is merged wih o yield noher consn,, which is exressed mhemiclly s; (8) where is referred o s he mchine consn. Hence, (3) cn e re-exressed s; T i... (9) Likewise, (6) cn e re-exressed s; e. (10) For clriy uroses so h i will e esy o differenie eween elecricl nd mechnicl vriles, he consn in (9) nd (10) re relced wih nd o oin (11) nd (1) resecively giving s follows; T i... (11) nd e (1) Alying irchhoff Volge Lw (VL) in Figure 3, he differenil equion of he rmure circui is; di L Ri e e (13) d Similrly, he rmure curren roduces he orque h is lied o he ineri nd fricion o oin he orque equion; d J d d f T i... (14) d 3.3 DERIVATION OF THE SYSTEM EQUATION Tking he Llce rnsform of (1), (13) nd (14) resecively, ssuming ero iniil condiions; E s s s.. (15) L s R I s Es E s (16) Js fs s T s I s Susiue (17) E s in (15) in (16) o oin; L s R I s Es s s Mke oin;.. (18) I s he sujec of he formul in (18) o s s E s Is Ls R (19) Susiue (19) in (17) o oin; Js fs s s E s L s R s... (0) Re-rrnge (0) o oin; ss Es s Js fs L sr Hence, he sysem rnsfer funcion is exressed mhemiclly s; s Js fs L sr E s s s... (1) 3. CONVERSION OF TRANSFER FUNCTION TO MODEL BLOC From (1), he lock digrm for he rmure conrolled DC moor ws develoed. The lock digrm is shown in Figure 4. The lock digrm of he rmure conrolled DC moor ws imlemened in he simulink environmen in he MATLAB. The model creed in simulink oolox of MATLAB is shown in Figure 5. ISSN: Pge

5 SSRG Inernionl Journl of Elecricl nd Elecronics Engineering (SSRG-IJEEE) volume Issue 3 Mrch 015 E s 1 s sjs f Ls R E s s Figure 4: Block Digrm of n Armure conrolled DC moor Figure 6: Plo of rmure volge gins moor seed Figure 5: Model creed in SIMULIN Toolox of MATLAB IV. SIMULATION RESULTS AND DISCUSSIONS The simuled model ws nlyed sed on is rnsien nd sedy se resonses. The sndrd es inu signls for rnsien resonse were se funcion nd imulse funcion. However, for he sedy se resonse, he grhs of orqueseed chrcerisics for differen rmure volges nd rmure seed chrcerisics were considered. The moor secificions re 3h, 15V nd 1500rm while is rmeers: R 0.6, L 6mH, J 0.093kgm, , 0.6, 0.008Nmrd s. B m For he nlyses, ll he iniil condiions re ssumed o e ero, so here is no curren flowing hrough he moor when i firs sred. The vlues ove were inu ino he model nd simulion ook lce. The resecive resuls under he sedy se resonse nd rnsien resonse re resened in he following su-secions. The sedy se resonse s shown in Figure 6 shows he vriion in he seed s he volge increses. The resul oined s shown in Figure 6 shows h he volge-seed chrcerisics of rmure conrolled DC moor seed increses wih increse in volge. This imlies h he seed of he DC moor is direcly roorionl o he rmure volge. In ddiion, under he sedy se resonse, he vriion of he orque seed chrcerisics for he DC moor differen rmure volges ws exmined. The oined resul s shown in Figure 7 shows h differen inu volges, he higher he seed he lower he lod orque. This imlies h he seed of he DC moor differen volges is inversely roorionl o he lod orque. The Figure shows h he orque-seed curve is shifed uwrd y incresing he rmure volge while he sloe of he curve remins consn s i is heoreiclly execed. 4.1 STEADY STATE RESPONSE The sedy se resonses of his rmure conrolled DC moor model show he erformnce of he moor under differen oering condiions. The sedy se resonses o e considered re: rmure volge seed chrcerisics nd orque seed chrcerisics for differen rmure volges. Figure 7: Torque-seed chrcerisics for hree differen rmure volges ISSN: Pge 3

6 SSRG Inernionl Journl of Elecricl nd Elecronics Engineering (SSRG-IJEEE) volume Issue 3 Mrch TRANSIENT RESPONSE Similrly, he rnsien resonse of he modeled rmure conrolled DC moor ws exmined. The resonse shows how he use of feedck hels in imroving oh he erformnce nd siliy of he moor. On erformnce nlysis, he moor erformnces under differen vlues of wih uni inu were considered. The resonses oined were shown grhiclly in Figures In Figure 8, he mliude srs ero ime,, equls ero. However, s ime,, increses, he vlue of mliude ends o 1.649rs. By his, i kes 0.6 ime uni for mliude in Figure 8 o rech he sedy se vlue. I cn lso e seen from Figure 8 h he mliude incresed sedily wihou ny oscillion. Since he erformnce ojecive is o hve mliude rck he uni se, i is resonle o sy h he modeled moor erforms resonly well s execed hough i long ime for mliude of Figure 8 o ge o is sedy se. However, when he vlue of ws incresed in Figure 9 nd Figure 10, he resonses ecome fser. The resonses now rech he sedy se in 0.4 ime uni nd 0. ime uni resecively. The resuls show h s he vlue of is incresing, he resonse re is incresing. Figure 10: Resonse of he moor o uni se inu,. 0 Figure 11: Resonse of he moor o n imulse inu, Figure 1: Resonse of he moor o n imulse inu, 0. 3 Figure 8: Resonse of he moor o uni se inu, Figure 9: Resonse of he moor o uni se inu, 1. 0 Figure 13: Resonse of he moor o n imulse inu, 0. 1 In order o furher evlue he erformnce of he modeled moor, is erformnce ISSN: Pge 4

7 SSRG Inernionl Journl of Elecricl nd Elecronics Engineering (SSRG-IJEEE) volume Issue 3 Mrch 015 ws lso exmined using imulse signl differen vlues of. The resonses oined were shown in Figures The grhs show he shes oined for he hree vlues of were similr exce h i ook he resonses differen ime unis o reurn o ero. For insnce, while i kes ou 0.5 ime unis in Figure 11 when , i kes infiniesiml ime uni in Figure 1 when while he resonse in Figures 13 reurns o ero immediely when he vlue of On he siliy of he moor, he seed of he moor when sujeced o disurnce differen vlues of were oserved. The resuls oined resened grhiclly ove show h he seed of he moor is direcly roorionl o he vlue of. The resuls lso show h he iniil inroducion of he disurnce cuses dro in he seed of he moor. The resul furher shows h disurnce does ffec he seed of moor. [5] M. Adus Slm, Fundmenls of elecricl mchines, Nros Pulishing House, New Delhi, 005. [6] B.M. Chen, Personl Course Wesie EG1108 Elecricl Engineering Pr - Cher 4: DC Moors, 011, Online [Aville]: h://vl.ee.nus.edu.sg/~mchen/courses/eg1108_dcmoors. df. Accessed on 3 rd Mrch, 015. [7] S.L. Alerich, nd W.N. Hermn, Indusril moor conrol, Delmr Pulishers, Fourh Ediion, [8] H.A. Toliy, nd G.B. limn, Hndook of Elecric Moors, CRC Press, USA, 004. [9] B.L. Therj, nd A.. Therj, A Texook of Elecricl Technology, S. Chnd nd Comny Ld, Tweny- Third Ediion, 01. [10] I.J. Ngrh, nd M. Gol, Conrol Sysems Engineering, New Age Inernionl Pulisher, New Delhi, Fifh Ediion, 011. V. CONCLUSION In his er, he simulion model of n rmure conrolled DC moor ws develoed using MATLAB/Simulink. The nlysis nd erformnce evluion of he develoed moor show h he simuled moor correcly redics he effec of rmure volge on he rmure volge-seed chrcerisics nd orque-seed chrcerisics of he rmure conrolled dc moor. Furhermore, he resuls of he sudy show h he seed of he DC moor is direcly roorionl o he rmure volge. REFERENCES [1] A. Mri, Inroducion o modeling nd simulion sudies, Proc. of he 1997 Winer Simulion Conf. Aln, GA, Dec. 7-10, 1997, Online [Aville]: h://im.cqnoes.com/achmens/whie%0per%0inr oducion%0o%0modeling%0nd%0simulion%0y% 0Anu%0Mri.df. Accessed on 6 h Ferury, 015. [].B.T.M. hlil, PI conrol of DC moor drive, B.Sc. diss. Universii Teknikl, Melk, Mlysi, 007. Online [Aville]: h://lirry.uem.edu.my/index.h?oion=com_docmn& sk=doc_view&gid=5008&iemid=08. Accessed on 5 h Ferury, 015. [3] L.Y. Hui, nd.h. Seok, Digil conroller design o conrol he direc curren moor sysem, Inernionl Journl of Conrol nd Auomion, Vol.7, No. 9, 004, [4] D. Bnsl, D.J. Evns, nd B. Jones, A rel-ime redicive minennce sysem for mchine sysems, Inernionl Journl of Mchine Tools & Mnufcure, Vol. 44, 004, ISSN: Pge 5