Design, Modeling and Motion Control of Mechatronics Robot Arm

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1 I.J. Inelligen Sye nd Applicion, 13, 5, Publihed Onle April 13 MECS (hp:// DOI: /iji Deign, Modelg nd Moion Conrol o Mechronic Robo Ar Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk (I). Ahd A. Mhouz Depren o Auoic nd Mechronic Sye, ldiir Se Univeriy, ldiir, RF; Alph Cener or Engeerg Sudie nd Technology Reerche, An, Jordn Eil: hd_llh@yhoo.co Mohed M.. Deign nd producion progr, Depren o Mechnicl Engeerg, Fculy o Engeerg, Ti Univeriy, 888, Ti, Sudi Arbi Eil:.ohed@yhoo.co Frhn A. Sle Mechronic Secion. Depren o Mechnicl Engeerg, Fculy o Engeerg, Ti Univeriy, 888, Ti, Sudi Arbi; Alph Cener or Engeerg Sudie nd Technology Reerche, An, Jordn Eil: le_rh@yhoo.co Abrc The ccure conrol o oion i undenl concern echronic pplicion, where plcg n objec he exc deired locion wih he exc poible oun o orce nd orque he correc exc ie i eenil or eicien ye operion. An ccure odelg, iulion nd dynic nlyi o cuor or echronic oion conrol pplicion i o big concern. The ulie gol o hi pper ddree dieren pproche ued o derive heicl odel, buildg correpondg iulk odel nd dynic nlyi o he bic open loop elecric DC oor ye, ued echronic oion conrol pplicion, priculrly, o deign, conruc nd conrol o echronic robo r wih gle degree o reedo, nd veriicion by MATLAB/Siulk. To ipliy nd ccelere he proce o DC oor izg, elecion, dynic nlyi nd evluion or dieren oion pplicion, dieren heicl odel er o oupu poiion, peed, curren, ccelerion nd orque, well correpondg iulk odel, upporg MATLAB.ile nd generl uncion block odel re o be roduced. The roduced odel were veriied ug MATLAB/ Siulk. Thee odel re ended or reerch purpoe well or he pplicion educionl proce. Thi pper i pr I o wrier' reerch bou echronic oion conrol, he ulie gol o hi reerch ddree deign, odelg, iulion, dynic nlyi nd conroller elecion nd deign iue, o echronic gle jo robo r. where elecric DC oor i ued nd conrol ye i eleced nd deigned o ove Robo r o deired oupu poiion, θ correpondg o pplied pu volge, nd iyg ll required deign peciicion. Index Ter Elecric Moor, PMDC Moor, Seprely Excied Moor, Mheicl Model, Se Spce, Siulion, Repone, MATLAB.ile nd Funcion Block I. Inroducion Mechronic ye oen ue elecric oor o drive heir work lod, where elecric oor re ued o provide rory or ler oion o vriey o elecroechnicl device nd ervo ye [1]. Dependg on pplicion (e.g. robo, elecric vehicle, low-o-ediu power che-ool ec.) nd deired dynic nd edy e perornce, well or oor' perornce nlyi, conroller elecion nd deign, i i o concern o derive heicl odel o elecric DC oor, nd buil correpondg Siulk odel, h cn ipliy nd ccelere he proce o odelg, iulion nd dynic nlyi o DC oor oion conrol or echronic pplicion. Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

2 4 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk Moion conrol ye ke pu volge cuor pu, nd oupu ler or roionl poiion/peed/ ccelerion/ orque, he o ued cuor or oion conrol ye i DC oor. A gle jo robo r i n pplicion exple o n elecroechnicl ye ued duril uoion. Ech degree o reedo (DOF) i jo on Robo r, where r cn roe or rnle, ech DOF require n cuor. When deigng nd buildg robo r i i required o hve ew degree o reedo llowed or given pplicion, gle jo Robo r i ye wih one DOF. In duril uoion, he conrol o oion i undenl concern, pug n objec he correc plce wih he righ oun o orce nd orque he righ ie i eenil or eicien θ() θ nucurg operion []. To ipliy nd ccelere he proce o DC oor izg nd elecion or dieren pplicion, We re o odel, iulion nd nlyze he bic open loop DC oor ye ug dieren ehod nd veriicion by MATLAB/ Siulk, lo o ugge MATLAB.ile nd uncion block odel or purpoe o deign nd nlyi. II. Robo Ar Sye Chrceriic J, F Sgle jo robo r ye coni o hree pr (Fig. 1); r, conneced o cuor hrough ger r wih ger rio, n. Pion M L Lod,( r), orque,t L N1 N pur Lod ngulr poiion, θ er M*g Moor ngulr poiion, θ 1 Moor orque,t θi Z Moor J1, F1 Y Fig. 1: Scheic odel o gle jo (one DOF) robo r driven by n rure-conrolled DC oor X The cuor ued i DC oor hown Fig.. DC oor urn elecricl energy o echnicl energy nd produce he orque required o ove he lod o he deired oupu poiion, θ L, or roe wih he deired oupu ngulr peed, ω L. The produced orque i exered o ccelere he roor nd uliely hi echnicl power will be rnied hrough ger e o robo r, hereore, pr o he orque produced will cue roionl ccelerion o he roor, dependg on i eri, J, nd he oher pr o he energy will be diiped he berg ccordg o i vicou ricion, b nd he roionl peed. III. Modelg he Elecric Moor DC oor (che) coni o one e o curren crryg conducive coil, clled n rure, ide noher e o curren crryg conducive coil or e o pernen gne, clled he or. The pu volge cn be pplied o rure erl (rure curren conrolled DC oor), or o crryg conducive coil erl (ield curren conrolled DC oor). Thi curren will genere le o lux round he rure nd ec he le o lux he ir gp beween wo coil, generg wo gneic ield, he ercion beween hee wo gneic ield (rc nd repel one noher) wih he DC oor, reul orque which end o roe he roor (he roor i he rog eber o he oor). A he roor urn, he curren he wdg i coued o produce conuou orque oupu reulg oion. DC che re chrcerized by heir veriliy. By en o vriou cobion o hun-, erie-, nd eprely-excied ield wdg, hey cn be deigned o diply wide vriey o vol-pere or peed-orque chrceriic or boh dynic nd edy-e operion. Becue o he ee wih which hey cn be conrolled, ye o DC che hve been requenly ued ny pplicion requirg wide rnge o oor peed nd precie oupu oor conrol [3, 4]. The elecion o oor or peciic pplicion i dependen on ny cor, uch he enion o he pplicion, correpondgly llowble vriion peed nd orque nd ee o conrol, ec. Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

3 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, 41 or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk The dynic equion o DC oor cn be derived, ly bed on he Newon lw cobed wih he ircho lw. The undenl ye o elecrogneic equion or ny elecric oor i given by [5,6]: d k u Ri j d d R k u RRiR j( Pb ) R (1) d Li LiR R LRiR Li S k where : he ngulr peed o rog coorde ye (reerence re), Dependg on oor conrucion (AC or DC), he ehod o he upply nd he coorde ye (ionry or rog wih he roor or or lux) he bove enioned odel becoe rnored o he deirble or [7], A deigner cn oen ke ler pproxiion o nonler ye. Ler pproxiion ipliy he nlyi nd deign o ye nd re ued long he reul yield good pproxiion o reliy [8].In odelg DC oor nd order o ob ler odel, he hyerei nd he volge drop cro he oor bruhe i negleced, nd he oor pu volge y be pplied o he ield or rure erl. In hi pper we re o concerned wih rure conrolled nd ield conrolled DC oor. 3.1 Modelg o he Arure Conrolled PMDC Moor The Pernen Mgne DC (PMDC) oor i n exple o elecroechnicl ye wih elecricl nd echnicl coponen, ipliied equivlen repreenion he rure conrolled DC oor' wo coponen re hown Fig.(). ELECTRIC coponen o PMDC oor ye MECHANICAL coponen o PMDC oor ye Elecroechnicl PMDC oor ye Fig. (): Scheic o ipliied equivlen repreenion o he rure conrolled DC oor' elecroechnicl coponen, (PMDC oor) Fig. (b): Scheic o ipliied equivlen repreenion o he ield conrolled DC oor' elecroechnicl coponen Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

4 4 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk 3. Modelg o Moor Dynic, Approch I; The Bic Idel, Ler, PMDC Moor Model 3..1 Elecricl Chrceriic o PMDC Moor Applyg volge o oor coil produce orque he rure, he orque developed by he oor,t i reled o he rure curren, i by orque conn, nd given by he ollowg equion: Moor Torque = T = * i The bck elecrooive orce, EMF volge, e i duced by he roion o he rure wdg he ixed gneic ield, he polriy o EMF volge c oppoiion o he curren h produce he oion. The EMF i reled o he oor h ngulr peed,ω by ler relion given by: d () e () b b d Where: b : EMF conn. Bed on he Newon lw cobed wih he ircho lw, he heicl odel he or o dierenil equion decribg elecric chrceriic o he rure conrolled PMDC oor cn be derived, where he elecricl equivlen o he rure circui, cn be decribed n ducnce, L erie wih reince, R erie wih n duced EMF volge which oppoe he volge ource. Applyg ircho lw round he elecricl loop by ug volge hroughou he R-L circui give: EMF R L 4 Applyg Oh' lw, ubiug nd rerrngg, we ge dierenil equion h decribe he elecricl chrceriic o PMDC oor: di () d() R i () L b d d di d R i L b d d 5 Tkg Lplce rnor nd rerrngg, give: () = R I() + L I() + b θ() (L +R ) I() = () - b θ() Mechnicl chrceriic o PMDC oor. The orque, developed by oor, produce n ngulr velociy, ω = dθ /d, ccordg o he eri J nd dpg ricion, b, o he oor nd lod. Perorg he energy blnce on he PMDC oor ye he heicl odel he or o dierenil 3 equion decribg echnicl chrceriic cn be derived; he u o he orque u equl zero, we hve: T = J *α = J*d θ/d T e T α T ω - T EMF = Subiug he ollowg vlue: T e = *i, T α = J *d θ/d, nd T ω = b *dθ/d, open loop PMDC oor ye wihou lod ched, h i he chnge T oor i zero, give: d d Lod * i T J b d d Tkg Lplce rnor nd rerrngg, give: *I() - J * θ() b * θ() = I () = (J + b ) θ() The elecricl nd echnicl PMDC oor wo coponen re coupled o ech oher hrough n lgebric orque equion given by (1). In ury; icory PMDC oor equion h decribe he elecric nd echnicl chrceriic o prcicl PMDC oor or ny purpoe i given by Eq. (1), (),(5) nd (7). 3.3 Derivg PMDC Moor Open Loop Sye Trner Funcion To derive he PMDC oor rner uncion, we need o rerrnge (6) decribg elecricl chrceriic o PMDC, uch h we hve only I() on he righ ide, hen ubiue hi vlue o I() (7) decribg PMDC echnicl chrceriic, ollow: 1 I ( ) ( ) ( ) b L R 8 The PMDC oor elecric coponen rner uncion relg rure curren, nd volge, i given by: ( ) ( ) L R b 7 I ( ) 1 9 The PMDC oor Mechnicl coponen rner uncion er o oupu orque nd pu roor peed i given by: ( ) 1 1 I ( ) T ( ) J b L Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

5 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, 43 or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk In ce, no lod ched, T lod =, we hve: ( ) 1 I ( ) J b Now, Subiug (8) (7), give: 1 b ( ) ( ) L R J b ( ) ( ) Rerrngg (11), nd knowg h he elecricl nd echnicl PMDC oor coponen re coupled o ech oher hrough n lgebric orque equion given by Eq. (1), we ob he PMDC oor open loop rner uncion wihou ny lod ched relg he pu volge, (), o he oor h oupu ngle, θ (), given by: ngle ngle () () () () () () L R J b B 3 L J ( R J b L ) ( Rb b) The PMDC oor open loop rner uncion relg he pu volge, (), o he oor h oupu ngulr velociy, ω (), given by: peed peed () () () () () () L R J b b L J ( R J b L ) ( Rb b) Here noe h he rner uncion ngle () cn be expreed : ngle () = peed () *(1/). Thi cn be obed ug MATLAB, by he ollowg, code: >> _ngle = (1,[1,] )* _peed Where: runng (1,[1,] ), will reurn 1/ The open loop PMDC oor rner uncion relg he orque developed by he oor, T () nd he oupu oor h ngle θ (), i obed by rerrngg Eq.(6), o give: ( ) 1 T J b ( ) 14 The open loop PMDC oor rner uncion relg he rure volge, (), o he rure curren, I (), direcly ollow: 1 L I ( ) L J ( ) R b Rb b L J LJ LJ M Modelg o Moor dynic, pproch II : The rure, i curren cn be ound by rerrngg he orque equion given by (1), rerrngg nd kg Lplce rnor, give: ( ) T ( ) I To d he rner uncion o he PMDC oor, er o pu volge nd oupu ngulr poiion θ, we ir ubiue (3), nd (16), (5) nd kg Lplce rnor, hi give: L R T ( ) ( ) b( ) The orque developed by he oor, T (), er o oupu ngle θ (), i given by (14), ubiug (17), nd nipulg, give: L R J b ( ) ( ) b( ) Mnipulg nd Rerrngg give: R J b ( ) b ( ) L R J b b ( ) ( ) Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

6 44 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk ngle () () () 3 L J ( R J b L ) ( Rb b) Arure ducnce, L i low copred o he rure reince, R (dicued ler). Neglecg oor ducnce by ug, (L =), nipulg nd give: ( ) RJ ( ) 1 b b J R Modelg o Moor Dynic, Approch III : The orque i given by: T= j d θ/d = J dω/d Alo orque i given by (), equg hee wo equion, eprg rure curren i, kg Lplce rnor, give: *i = J d θ/d 19 I J Subiug (19) (6), nd rerrngg give: J L R b J J L R + b ngle ( ) ( ) 3 ( ) LJ RJ b To wrie rner uncion er o oupu peed ω, we rewrie he orque Eq.(19) er o oupu peed *i = J dω /d, nd repe previou ep. 3.6 Sipliicion o Open Loop PMDC Moor Sye Trner Funcion Model Bed on he c h, he PMDC oor repone i doed by he low echnicl ie conn, where he elecric ie conn i uch er (e.g. en ie) hn he echnicl ie conn, hi cn oive u o ue h he rure ducnce, L i low copred o he rure reince, R. neglecg oor ducnce, (L =), will reul he ollowg ipliied ir order or o PMDC oor rner uncion er pu volge, () nd oupu peed, ω () given by: peed () () () R J Rb b Rerrngg hi ir order equion o ndrd ir order rner uncion or, yield: peed () () () b Rb b B RJ 1 1 Rb b A ipliied ir order or o PMDC oor rner uncion er o oupu ngle, cn i lo be obed by ubiug (L =), nd given by: ngle () () () RJ M 1 b b J R Eq.(1) cn be ipliied by ubiug,(l =), o hve ny o he ollowg wo or, where he econd or given by () cn be ipliied o econd order ye, given by: ngle () () () R J ( Rb b) ( ) Alo () by ubiug,(l =), cn be ipliied o econd order ye relg pu volge nd oupu ngle, well equion relg pu volge nd oupu peed, o be given by: 1 3 Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

7 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, 45 or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk ngle peed () () () ( R J ) () () () b ( R J ) b 3.7 Nonler Model o PMDC Moor Mechnicl conrol ye re uppoed o opere wih high ccurcy nd peed depie dvere eec o ye nonleriie nd uncerie. Thi robune propery i o gre ipornce i he ye i pr o roboic or ervo ye, which require eniiviy o unodeled dynic [11,1]. The idel ipliied PMDC oor odel rrely ccure copred wih cul reul nd eureen, ce noe ll cor re conidered. To ob he ull ye odel, jor echnicl nd elecricl nonleriie uch urion, coulob ricion nd bcklh u be cluded he odel. Here we will derive ore n cul equion o PMDC oor, ideniyg ll poible preer, (cul iulk odel i hown Fig.7). Coulob ricion i non-ler eleen which orce end o ppoe he oion o bodie conc echnicl ye, i c diurbnce orque eedbck or he echnicl ye, Coulob ricion i conidered o be conn rerdg orce bu i diconuou over zero crog, h i, when DC oor revere direcion i u coe o op which po Coulob ricion drop o zero nd hen oppoe he revered direcion. In eec Coulob ricion i conn when roionl velociy i no zero [3]. Inroducg Eq.(6),Coulob ricion nd ded zone ricion, where (T lod =), we hve: 4 5 *i = T α + T ω + T lod + T *I() - J * θ() b * θ() - T = A edy e condiion, d/d =, give: *i = - b*ω T T = *i - b*ω 6 I. PMDC Moor Model Repreenion, Siulion nd Anlyi 4.1 PMDC Moor Model Repreenion Ug Block Digr Applyg volge,, o oor coil produce orque he rure. The produced orque produce n ngulr h velociy, ω= dθ/d, ccordg o he eri J nd vicou ricion b, he rure will roe peed nd direcion dependen on he pplied volge nd polriy. Theoreiclly, reul o pplied volge he oor h hould conue o ccelere o higher nd higher peed unle here i orce h work oppoiion o he pplied volge, hi orce i bck elecrooive orce, EMF, e b., where becue he roion o he PMDC oor' rure wdg he ixed gneic ield genere, EMF, h oppoe he pplied volge. Ug hi we cn build he block digr odel o he open loop PMDC oor ye. The PMDC oor elecric coponen rner uncion relg pu rure curren, i nd volge, i given by (9), he DC oor echnicl coponen rner uncion relg oupu orque nd pu roor peed i given by (1), lo he elecricl nd echnicl PMDC oor coponen re coupled o ech oher hrough n lgebric orque equion given by (), ug hee relion we cn build he block digr odel o he open loop PMDC oor ye hown Fig.3, block digr odel how he eedbck cion he open loop PMDC oor ye, lo how h he elecricl nd echnicl PMDC oor coponen re coupled o ech oher hrough orque conn. Angulr Oupu olge () velociy Curren Torque Moor ngle ()-EMF 1 I() T ()- 1 ω() + 1 θ() L + R + n - J + b er rio Arure, elecric pr b() Bck e b TL Lod orque Lod, echn. pr Fig. 3: The block digr repreenion o open loop PMDC oor ye Oupu Lod ngle Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

8 46 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk 4. The Feedbck Acion o he Open Loop DC Moor Sye Biclly he DC oor i n open-loop ye, o conn rure oupu ngulr velociy, (n creg ngle conn vlue) he DC oor exhibi peed eedbck, hi peed eedbck i chieved by oor' buil- velociy eedbck cor b, (The bck-emf conn), hi cloed loop i ccoplihed ollow; I he lod on he oor cree due o n cree vicou ricion, b hen he edy e ngulr velociy o he oor will reduce, hi cn be hown by equion *i = b *ω. Rerrngg, o ob ngulr velociy we hve, equion ω = *i /b. Thi equion en n cree vicou ricion, b will reul reducion edy e ngulr velociy o he oor. A reducion edy e ngulr velociy produce reducion he bck EMF, hi i cn be een ro (3). Thi chnge reul n cree rure curren which cree he developed orque, hi i cn be een ro () h cloe he loop o conn rure oupu ngulr velociy. x x x ' 1 ' ' 3 d x d d d i b T d d J J J L di R i d L L L b Subiug e vrible, or elecric nd echnicl pr equion rerrngg give: x d x d ' 1 b x x x T ' 3 J J R 1 x x x ' b 3 3 L L L l. Se Spce Repreenion o PMDC Open Loop Sye The e vrible (long wih he pu uncion) ued equion decribg he dynic o ye, provide he uure e o he ye. Mheiclly, he e o he ye i decribed by e o ir-order dierenil equion er o e vrible. The e pce odel ke he ollowg or [9]: dx Ax Bu d y CX Du Rerrngg (5) nd (6) o hve he below wo ir order equion, relg he ngulr peed nd rure curren: d i b T d J J J L di R i d L L L b Lookg he DC oor oupu h poiion θ, nd choog he e vrible o be he oor h oupu poiion θ, velociy ω nd rure curren i : x x x 1 d d i Lookg DC oor peed, beg he oupu, he ollowg e pce odel obed: The e pce odel re he bi or buildg he iulk odel o open loop DC odel. 9 9 Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

9 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, 47 or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk I. Siulion nd Anlyi o PMDC Moor Open Loop Sye Ug Siulk Ug derived PMDC oor odel, he ollowg iulk odel or Speed/ie, Torque/ie, Poiion/ie nd Curren/ie curve cn be obed, hee curve cn be ued o evlued, e nd vlide given DC oor. Runng ny o he uggeed iulk odel wih priculr DC oor' preer deed, will reurn curve hown Fig.9, here noice h, dependg on pplicion, dieren equion w derived; ipliied nd ccure. The ollowg nol vlue or he vriou preer o PMDC oor ued: =1 ol; J =. kg ²; b =.3; =.3 N-/A; b =.3 -/rd; R =1 Oh ; L =.3 Henry; T L = ( no lod ched). 6.1 Siulion nd nlyi o PMDC oor open loop ye bed e pce repreenion given by (9),i hown hree uggeed odel Fig.4()(b)(c), runng ny o hee odel will reurn Torque/ie, Speed/ie, Angle/ie nd Curren/ie curve or 1 ep pu hown Fig.9 Fig. 4(): iulk odel bed on e pce repreenion Fig. 4(b): iulk odel bed on e pce repreenion Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

10 48 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk Fig. 4(c): iulk odel bed on e pce repreenion 6. Siulion nd nlyi o PMDC oor open loop ye bed on rner uncion odel given by equion (1) nd (13), i hown Fig.5. Fig. 5: PMDC oor iulk odel bed on rner uncion odel given by (11) 6.3 Block digr repreenion o ipliied heicl odel iulk o PMDC oor given by equion (1) nd (), ug L =, i hown Fig. 6. Fig. 6: Siulk odel bed on ipliied heicl odel Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

11 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, 49 or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk Fig. 7: uggeed ull block digr odel o PMDC oor open loop ye wih roduced urion nd coulob ricion 6.4 Suggeed Funcion Block wih I Funcion Block Preer Wdow To ipliy nd ccelere he proce o DC oor izg nd elecion or dieren pplicion, he ollowg wo ipliied nd ccure uncion block wih i uncion block preer wdow re roduced below, hee odel cn be ued by deg preer, correpondg block or runng.ile wih hee preer deed nd runng he odel, will reul correpondg Torque/ie, peed/ie, poiion/ie nd curren/ie curve or given ep pu vole Sipliied uncion block bed on block digr odel, hown Fig.8(), i hown Fig.8(b)(c), runng hi wih nol vlue, will reurn repone curve hown Fig. 9 well ngulr ccelerion/ie curve Accure uncion block bed on iulk odel, given Fig.8(c), i hown Fig.8(d). Runng hi wih nol vlue, will reurn repone curve hown Fig. 9, well ngulr ccelerion/ie curve, here noe h he curren/ie curve will dier ro h Fig. 9() nd i hown Fig.9(b), hi i becue o (L=) ipliicion. Fig. 8(): Sipliied PMDC oor ub ye Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

12 5 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk Fig. 8(b): Sipliied PMDC uncion block PMDC oor ub ye Fig. 8(c): Sipliied PMDC oor ubye Fig. 8(d): Accure uncion block wih i preer wdow or open loop DC oor perornce veriicion nd nlyi Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

13 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, 51 or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk 6.5 Modelg nd Anlyi Ug MATLAB. The rner uncion cn be deed nd enered MATLAB nuber o dieren wy ; by deg he vrible he rner uncion, h re:, R, l,, b,j, b polynoil coeicien or, hen deg nueror nd denoor, or we cn eprely ener rner uncion decribg echnicl nd elecric DC oor chrceriic,hen cobe he erie, nd lly ug MATLAB uncion eedbck o cree eedbck connecion o wo rner uncion, progr.ile cn be wrien o ipliy nlyi proce, he ollowg.ile cn be ued o reurn he rner uncion relion ngle (), peed (), θ ()/ T (), I ()/ (),ipliied peed (), ipliied ngle () well heir repone o ep pu ignl, hown Fig. 1 clc, cloe ll, cler ll = 1;J=. ;b =.3; =.3; b =.3; R =1 ; L=.3; TL= ; % J = pu(' Ener oen o eri o he roor, (J) ='); % b = pu(' Ener dpg conn o he echnicl ye,(b)='); % = pu(' Ener orque conn, ='); % b = pu(' Ener elecrooive orce conn, b='); % R = pu('ener elecric reince o he oor rure (oh), R ='); % L =pu(' Ener elecric ducnce o he oor rure (Henry), L='); % = pu(' Ener pplied pu volge, ='); nu1 = [1]; den1= [L,R]; nu = [1]; den= [J,b]; A = conv( [L,R], [J,b]); TF1 =(, A); dip('dc oor elecric pr Trner uncion,oupu curren: ') _elecric=(nu1,den1) dip('dc oor echnicl pr Trner uncion o,oupu peed: ') _echnicl=(nu1,den) dip('dc oor ye open loop Trner uncion,oupu ngle ') _peed= eedbck(tf1,b) dip('dc oor ye open loop Trner uncion,oupu peed ') _ngle=(1,[1,] )*_peed dip('trner uncion relg orque developed by he oor, T() nd h ngle?(),') _orque_ngle=(1,[j,b,]) dip(' Trner uncion relg orque developed by he oor, T() nd h peed, ') _orque_peed=(1,[j,b]) dip('trner uncion relg pu ()nd oupu curren I() : ') _Curren=([1/L,1/J], [1,((R/L)+(b/J)),((R*b)/(L*J))+((b*)/(L *J)) ]) dip(' Sipliied Trner uncion relg pu ()nd oupu ngle: ') _ngle_ipl=(,[r*j,(r*b + *b),]) dip(' Sipliied Trner uncion relg pu ()nd oupu peed :') _peed_ipl=(,[r*j,(r*b + *b)]) ubplo(4,,1), ep(*_ngle),ile('sep repone, oupu ngle ') ubplo(4,,), ep(*_peed),ile('sep repone, oupu peed ') ubplo(4,,3), ep(*_orque_ngle),ile('sep repone, pu oor orque oupu ngle') ubplo(4,,4),ep(*_curren), ile('sep repone, oupu curren') ubplo(4,,5),ep(_ngle_ipl),ile('sipliied repone, oupu ngle ') ubplo(4,,6),ep(*_peed_ipl),ile('sipli ied repone, oupu peed ') % e pce nu = ; den_peed = [(J*L),(J*R)+(L*b),(R*b)+(*b )]; den_ngle = [(J*L),(J*R)+(L*b),(R*b)+(*b ),]; _peed=(nu,den_peed); _nle=(1,[1,] )*_peed; dip('se rix, oupu ngle: ') [A1,B1,C1,D1]=(nu,den_ngle) ubplo(4,,7), ep(a1, B1, C1, D1), ile('e pce repone,oupu ngle') dip('se rix, oupu peed : ') [A,B,C,D]=(nu,den_peed) ubplo(4,,8), ep(*a, *B, *C, *D), ile('e pce repone, oupu peed ') % edy e clculion : % or velociy edy e vlue =:.1:1; y=ep(1* _peed,); peed_edy_e_vlue=y(lengh()); pr(' Oupu edy e peed, OMEA= % rd/ec \n ',peed_edy_e_vlue) % or ngle edy e vlue y=ep(1* _ngle,); ngle_edy_e_vlue=y(lengh()); pr('oupu edy e ngle or given ie rnge, THETA= % rdin \n ',ngle_edy_e_vlue) II. Modelg o Seprely Excied DC Moor 7.1 Modelg o he ield curren conrolled DC oor, wih i () held conn Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

14 5 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk A ipliied equivlen repreenion o he ield conrolled DC oor' wo coponen re hown Fig.(b). i coni o dependen wo circui, rure circui nd ield circui, which lod re conneced o he rure circui The volge i pplied o boh o ield nd rure erl, hown, here re wo curren, iled curren, i () nd rure curren, i () order o hve ler ye, one o hee wo curren o held conn. In he ield curren conrolled DC oor, he rure curren u ed conn i () = i = conn, nd he ield curren, i vrie wih ie,, hi yield: The ir-gp lux, Φ i proporionl o he ield curren nd given by: * i 3 The bck EMF volge i given by: EMF * * - I R The orque developed by he oor i reled lerly o ir-gp lux, Φ nd he rure curren i (), nd given by: Moor Torque T * * ( ) 1 i 31 Subiug (3) (31), we hve: T * * ( )* ( ) 1 i i The rure curren u ed conn i () = i = conn, yield: T ( * * i )* i ( ) * i ( ) 1 Where : he oor conn. Bed on he Newon lw cobed wih he ircho lw, we ob he heicl odel. Applyg ircho lw, Oh' lw, nd Lplce rnor o he or ield yield heicl odel decribg he elecricl chrceriic o ield conrolled DC oor nd given by: _ ield R_ ield L_ ield Applyg Oh' lw, ubiug nd rerrngg, we ge dierenil equion h decribe he elecricl chrceriic, given by: di () _ ield R i L d Tkg Lplce rnor nd rerrngg, give: _ield () = (L +R ) I () I _ ield L R Where: L, or ducnce, R,or reince The Mechnicl chrceriic o iled conrolled DC oor; perorg he energy blnce on he DC oor ye; he u o he orque u equl zero, we hve: T = J *α = J*d θ/d T T α T ω = The oor orque i reled o he lod orque, by: T T ω = J*d θ/d i b * ( ) * J * Subiug (3) nd rerrngg, give: R * b J L _ ield Rerrngg Eq.(33), he elecricl nd echnicl ield curren conrolled DC oor coponen re coupled o ech oher hrough n lgebric he oor conn,, we ob he rner uncion relg pu iled volge _ield (), nd oor oupu ngle θ (), nd given by: ngle ( ) ( ) _ iled ( ) L R J b The iulk odel o he iled curren conrolled DC oor i hown Fig. (11), here noe h he rure conrolled DC oor i nure cloed loop ye, while iled curren conrolled DC oor i open loop. 7. Modelg o eprely excied DC oor, wih vryg boh i () nd i () Perorg he energy blnce on he DC oor ye (Fig.(b)); he u o he orque u equl zero, we hve: T = J *α = J*d θ/d T e T α T ω - T EMF = Seg, Te * * i i, ubiug, give: d d Lod * i * i T J b d d 3 33 Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

15 Ap N/ Ap Rd/ Rd Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, 53 or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk Tkg Lplce rnor nd rerrngg, give: *I ()* I () T lod - J * θ() b * θ() = *I ()* I () - T lod = (J + b ) θ() 34 ( ) 1 * I ( ) * I ( ) T ( ) J b L ( ) * I ( )* I ( ) T ( ) L J b 35 Applyg ircho lw round he ield elecricl loop by ug volge hroughou he R-L circui give: di () R i () L d Tkg Lplce rnor, rerrngg o epre he ield curren, i give: R I () L I I ( ) R L Applyg ircho lw round he rure elecricl loop by ug volge hroughou he R-L circui, kg Lplce rnor, give: EMF R L Seg, EMF * * ( ) / b i d d, give: di () d() R i ( ) L b * i * d d 1 * i * ( ) * i * ( ) T L R b lod J b ( ) ( ) Rerrngg, he rner uncion relg pu rure volge o oupu oor ngulr peed given by: () () rure I RR b L b ield J L J 1 Rb R b R R b Ug hee equion, he iulk odel hown Fig.1(), o eprely excied DC oor, cn be buil. Anoher odiied ro iulk odel ro [16] i hown Fig.1(b), hi odel he couple reig, uul ducnce nd coeicien o ricion re roduced Ti (ec) Torque Tie Angulr peed S ie 4 6 Ti (ec) Ti (ec) Curren Tie ngle Tie 4 6 Tie (ec) Fig. 9(): Torque/ie, Speed/ie, Poiion/ie nd Curren/ie curve or 1 ep pu () = R I() + L I() + b * i * θ() 8 Angulr ccelerion S ie Angulr ccelerion Curren S ie S ie Rerrngg o epre he rure curren, i give: 1 I ( ) ( ) b * i * ( ) L R Subiug (43).(43), give: Rd/ Ti (ec) Rd/ Ti Ti (ec) (ec) Fig. 9(b): Angulr ccelerion/ie curve, nd ipliied odel curren/ie curve,boh or 1 ep pu Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

16 T The Oeg The Oeg The Oeg 54 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk 4 x 15 Sep oupu Angle 1 Sep oupu peed 1 3 e (ec) x x 14 pce repone, oupu ngle e pce repone, (ec) oupu peed x 14 Sipliied, Tie ep (ec) oupu ngle x Sipliied, ep (ec) oupu peed 1 3 x 17 Sep T (ec). ngle x Sep repone Tie, (ec). curren The (ec) x 1 4 I (ec) Fig. 1: Repone curve obed by runng uggeed.ile Fig. 11: Siulk odel o he iled curren conrolled DC oor Fig. 1() Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

17 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, 55 or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk Fig. 1(b) Fig. 1()(b): Siulk odel o eprely excied DC oor III. Concluion To ipliy nd ccelere he proce o elecion, odelg, iulion nd dynic nlyi o elecric DC oor or peciic echronic pplicion, hi pper preen odelg, iulion nd nlyi o he bic open loop DC oor ye, ug dieren pproche nd veriicion ug MATLAB/iulk owre, or dieren pplicion, dieren heicl nd iulk odel, well, MATLAB.ile nd uncion block odel re derived, buil nd roduced, hee odel ended or reerch purpoe well or he pplicion educionl proce, obed repone curve er o oupu orque/ie, ngulr peed/ie, ngulr poiion/ie, ngulr ccelerion/ie nd curren/ ie or 1 ep pu or ued DC oor, relec he ccurcy nd pplicbiliy o derived odel or reerch purpoe elecion, perornce nlyi nd conrol o elecric oor, well or reerch purpoe nd pplicion educionl proce. Reerence [1] M. S. RUSU, nd L. r, The Deign o DC Moor Speed Conroller, Fcicle o Mngeen nd Tech. Eng., ol. II (XII), 8, pp [] Chun Hoo Aung, h Thndr Lw, nd Y Mon My, Modelg Moion Conrol Sye or Moorized Robo Ar ug MATLAB, World Acdey o Science, Engeerg nd Technology 4 8. [3] Hlil A., Éude de che àcourn conu, MS Thei, Univeriy o LAAL, (Tex French), My 1. [4] Cpolo. A., Cirrcione., Cirrcione M., Heno H., riel R., Digil ignl proceg or elecricl che, Inernionl Conerence on Elecricl Mche nd Power Elecronic, udi (Turkey), pp.11-19, 1. [5] M.P.zierkowki, H.Tuni "Auoic Conrol o Converer-Fed Drive", Wrzw Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

18 56 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk [6] R.D. Doncker, D.W.J. Pulle, nd A. eln. Advnced Elecri-cl Drive: Anlyi, Modelg, Conrol. Sprger, 11. [7] rzegorz SIELUCI,Anlyi o he Trner- Funcion Model o Elecric Drive wih Conrolled olge Source PRZEL AD ELETROTECHNICZNY (Elecricl Review), ISSN 33-97, R.88NR7/1. [8] Richrd C. Dor nd Rober H. Bihop. Modern Conrol Sye. Nh Ediion, Prenice-Hll Inc., New Jerey, 1. [9] Norn S. Nie, Conrol ye engeerg, ixh ediion, John Wiley & Son, Inc, 11. [1] P. Wol, X.Q. Chen, J.. Che, W. Peigrew, C.E. Hnn1, Anlyi o PM DC Moor Model or Applicion Feedbck Deign or Elecric Powered Mobiliy ehicle. [11] Sloe E, Li W. Applied nonler conrol. USA: Prenice Hll Inc.; [1] Fber MN, Eig he uncery eie o roo en qure error o predicion: Applicion o deerg he ize o n deque e e ulivrie clibrion. Cheoer Inel Lb 1999;49(1): [13] The MhWork ( Conrol Sye Toolbox docuenion erion 5. (R9b). [14] uhiko Og, Modern conrol engeerg, hird ediion, Prenice Hll, [15] Bouediene Allu, Abdellh Loui, Brhi ASBAOUI, Abdelh NASRI nd Abdel Abdelrhni Inelligen Conroller Deign or DC Moor Speed Conrol bed on Fuzzy Logic- eneicalgorihopiizion.hp://lj.cdeic direc. org/ A13/9_1.h Appendix I: Tble-Noenclure Sybol Quniy UNIT, or The pplied pu volge,(moor erl volge) ole, _ield() Inpu iled volge ole, R Arure reince,( erl reince) Oh,Ω R Sor reince Oh,Ω L L Φ Sor ducnce Arure ducnce Air-gp lux, i Arure curren Apere, A I Field curren Moor orque conn N./A e Moor bck-elecrooive orce con. /(rd/) The oor conn ω Moor h ngulr velociy rd/ T Torque produced by he oor N. J Moor rure oen o eri kg. J ol Tol eri=j+jlod kg. L Arure ducnce Henry, H b icou dpg, ricion coeicien N./rd. e,emf: The bck elecrooive orce, EMF = bdθ/d e,emf: θ Moor h oupu ngulr poiion rdin ω Moor h oupu ngulr peed rd/ec R = R*i The volge cro he reior olge L=Ldi/d The volge cro he ducor olge T lod Torque o he echnicl lod T lod Tα Torque du o roionl ccelerion Tα Tω Torque du o roionl velociy Tω T EMF The elecrogneic orque. TEMF Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57

19 Modelg, Siulion nd Dynic Anlyi Iue o Elecric Moor, 57 or Mechronic Applicion, Ug Dieren Approche nd eriicion by MATLAB/Siulk Auhor Proile Ahd A. Mhouz: B.Sc. nd M.Sc; Bri Univeriy, Ily nd Mocow e Acdey. Now, He Auoic nd Mechronic Sye, ldiir Se Univeriy nd he direcor o lph cener or engeerg udie nd echnology reerche. Mjor cdeic nd reerch ere: Deign, odelg nd nlyi o priry Mechronic Mche Conrol Sye, Roboic, Elecronic, Microconroller, nd Quniy Surveyg. Mohed M.. W born en, Egyp, He received he B.Sc. nd M.SC. degree Producion Engeerg nd Deign dep. ro El-Mi univeriy Egyp, 9 nd 96 repecively. He received he Ph.D degree Mechnicl Engeerg Hnnover univeriy erny, 4. ce 1He i workg n Aocie Proeor he Depren o, Producion Engeerg nd Deign dep. El-Mi,. He i currenly n Aocie Proeor he Depren o Mechnicl Engeerg, Fculy o Engeerg, Ti Univeriy, Sudi Arbi, hi publicion bou ory reerch he ield o non-convenionl chg (ECM,WJ nd AWJ) nd Tribology. Frhn Allh Sle: B.Sc., M.Sc nd Ph.D., Mechronic o producion ye, Mocow e Acdey. Now he i. Proeor Ti Univeriy, Mechronic progr, Dep. o Mechnicl Engeerg nd gen-direcor o lph cener or engeerg udie nd echnology reerche. Reerch Inere; Deign, odelg nd nlyi o priry Mechronic Mche, Conrol elecion, deign nd nlyi or Mechronic ye. Roor Dynic nd Deign or Mechronic pplicion Copyrigh 13 MECS I.J. Inelligen Sye nd Applicion, 13, 5, 39-57