Tuning of PID Controller for DC Servo Motor using Genetic Algorithm
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1 eriol Jourl of Eergig Techology d Advced Egieerig Weie: (SSN , Volue, ue, Mrch 0) Tuig of D Coroller for DC Servo Moor uig Geeic Algorih Bidu R., Mii. Noohiripd, Depre of Elecricl Egieerig, Fr. C. Rodrigue iue of Techology,(Affilied o Mui Uiveriy) Vhi, Nviui. riducri@gil.co ii_vdhy@yhoo.co.i Arc The poiio corol udy of DC ervo oor i very ipor ice hey re exeively deployed i vriou ervoechi. Norlly D coroller re ued o iprove he rie repoe of DC ervo oor. A pree, o uig ehod re deiged o provide workle iiil vlue, which re he furher ully opiized for pecific requiree. Thi pper pree flexile d f uig ehod ed o geeic lgorih (GA) o deerie he opil preer of he D coroller for he deired ye pecificio. Siulio reul how h wide rge of requiree re ified wih he propoed uig ehod. eyword DC ervooor, Geeic Algorih, Opiizio, D coroller, D Tuig, Trie repoe.. NTRODUCTON Elecricl oor ervo ye re idipele i oder idurie. Servo oor re ued i vriey of pplicio i iduril elecroic d rooic h iclude preciio poiioig well peed corol [9]. Servooor ue feedck coroller o corol he peed or he poiio, or oh. The ic coiuou feedck coroller i D coroller which poee good perforce. However i dpive eough oly wih flexile uig. Alhough y dvced corol echique uch elf-uig corol, odel referece dpive corol, lidig ode corol d fuzzy corol hve ee propoed o iprove ye perforce, he coveiol /D coroller re ill doi i joriy of rel-world ervo ye []. To iplee D coroller he proporiol gi, he iegrl gi d he derivive gi D u e deeried crefully. My pproche hve ee developed o deerie D coroller preer for igle ipu igle oupu (SSO) ye. hi pper geeic lgorih i ued o clcule hee preer. Geeic lgorih i copuiol procedure h iic he url proce of evoluio []. work y evolvig populio of oluio over uer of geerio. For ech geerio, oluio re eleced fro he populio ed o he fie vlue. Thee oluio y croover (ergig previou oluio d y uio (odifyig he oluio geere ew populio. Sice i erche y pek i prllel, he rppig locl ii i voided [6].. SYSTEM MODEL A referece we coider DC ervo oor how i figure. A iple heicl reliohip ewee he hf gulr poiio d volge ipu o he DC oor y e derived fro phyicl lw. he poi of corol ye, DC ervo oor c e coidered SSO pl [5]. Therefore, coplicio reled o uli-ipu ye re dicrded. DC ervo oor hve he field coil i prllel wih he rure. The curre i he field coil d he rure re idepede of oe oher. A reul, hee oor hve excelle peed d poiio corol. E () - R L E () Fig.. Scheic Digr of DC Servo oor - Fixed Field T () θ() 0
2 eriol Jourl of Eergig Techology d Advced Egieerig Weie: (SSN , Volue, ue, Mrch 0) The dyic ehviour of he DC oor i give y he followig equio [8], d c e repreeed y he lock digr how i figure. E ( R ( L ( E ( T ( ( E ( ( T ( ( J D ( where, R =Arure reice i oh, L =Arure iducce i hery, i =Arure curre i pere, e =Arure volge i vol, e =Bck EMF i vol, =Bck EMF co i vol/(rd/ec), =Torque co i N-/Apere, T =Torque developed y he oor i N-, θ()=agulr diplcee of hf i rdi, J=Moe of ieri of he oor d lod i g /rd, D =Friciol co of oor d lod i N- /(rd/ec). θ r( - D ( Fig.. Block Digr repreeio of DC Servo oor wih D coroller. The he overll rfer fucio for uiy feedck ye will e, C( T( c( which c e clculed, θ( E ( - E ( (L R ) (J D θ( T( ( D ) 4 ( ) D Fig.. Block Digr repreeio of DC Servo oor Afer iplificio d kig he rio of (, he E ( rfer fucio will e elow, L J ( R J L D ) (. D CONTROLLER DESGN...() R D ) Coider he rfer fucio of he DC ervo oor,... () By coprig equio () d (), =L J, =R J L D d = R D. Trfer fucio of he D coroller c e wrie, C( D Thu he cul pole locio re he roo of he equio, 4 ( ) 0...( ) D Bu he required pole locio re he roo of he equio, ( w w )( ) 0...(4) D where, d w re he rie preer fro he required rie repoe. Coprig he equio () d (4) we will ge 5 equio for olvig hree ukow,, d D, d hece opiizio i required. Alo he preer deeriio proce u e perfored f poile for he give ye. By he coveiol Ziegler Nichol ehod, uied ocillio i oied y icreig he vlue fro zero o criicl. The eured frequecy d gi of hi ocillio re ued o deerie he D preer [7]. Sice hi echique deped o geeric odel, he deig ojecive will lo lwy o e e. The echique, however, doe provide effecive rig. By coiderig hi he iiil oluio he uer h o opiize he reul [4].
3 eriol Jourl of Eergig Techology d Advced Egieerig Weie: (SSN , Volue, ue, Mrch 0) V. GENETC ALGORTHM The ojecive of he Geeic lgorih (GA), ed o he url proce of evoluio, i o fid he opil oluio o prole. GA work o collecio of everl lerive oluio clled populio. Ech oluio or idividul i he populio i clled chroooe d idividul chrcer i hi i clled gee. To oi eer oluio (populio) fro exiig oe, ew geerio i evolved i ech ierio of he GA [0]. The geerio gp i he frcio of idividul i he populio h re replced fro oe geerio o he ex. Bed o hi, here re wo ic GA pproche, clled iple GA d edy e lgorih. Geerio gp i equl o oe i he iple GA d i le h oe for he oher pproch. Geerio of ew populio ivolve vriou ep. Fir evlue ech idividul of he populio y uer defied fie fucio, which i oppoie o he error fucio. The highly fi idividul re eleced fro he populio for reproducio. Seleced idividul for pir clled pre. Differe operio for reproducio re croover d uio. he croover operio, porio of wo pre re coied o produce wo ew idividul, clled offprig. Thi provide echi for he chroooe o ix d ch heir deirle quliie i forig offprig. For ech pir of pre, croover i perfored wih croover proiliy c. New feure c e iroduced io populio y uio. produce rdo chge i he offprig wih proiliy clled uio proiliy, M. Croover i he i operio o erch he oluio pce, u doe o guree he rechiliy of he eire oluio pce wih fiie populio ize. Muio iprove erch pce y iroducig ew gee io he populio. Wih croover d uio here i high rik h he opiu oluio could e lo here i o guree h hee operor will preerve he fie rig []. To couerc hi, echi i ued i which, he e idividul fro populio i ved i he ew populio. Neighour of he good oluio re lo icluded i he ew geerio o iprove he erch proce. Whe hee eighour oluio of he exiig chroooe re evlued y he lgorih, fer covergece wih fier uig could e chieved. Thu coiderle iprovee i he oluio quliy could e oied. GA he iiil geerio c e rdo or uer pecified. Afer he reproducio, ew geerio will replce he old oe d evolve uil oe oppig crierio i e. V. D TUNNG BY GA The jor ojecive of he GA i o deerie he opil vlue of he D coroller preer o iprove he rie repoe of he ye. To chieve hi, he lgorih coider he xiizio of ojecive fucio. Thi ojecive fucio provide e for evluig he perforce of he D coroller wih he deeried gi preer, o h opiized coroller would e developed y he e idividul. Whe pplied o he D coroller deig prole, he gee re he gi vlue of he coroller,, d D which re o e deeried. Ech chroooe coi coplee e of he gee eeded o defie uiquely ril oluio. The fie of ech chroooe i evlued uig he error crierio, which i ued he i of elecio for he chroooe i he ex geerio []. Durig he opiizio proce, he required pole d he cul cloed loop pole re ued y he geeic lgorih. ech geerio, ccordig o he coroller preer, cloed loop pole re deeried. The uig lgorih erche he opil preer for he D coroller wih he help of hee cloed loop pole. We ue populio ize of 0, d erie he proce fer 00 geerio. he lgorih, igle poi croover proce w eployed. Neighour of he good chroooe re clculed fro he verge of he good oluio. ech geerio, ll oluio i he populio re evlued y fie fucio which c e coidered he ivere of he error fucio. Error E c e clculed y coprig he cul d required cloed loop pole locio. c e foruled, E=α(E OS )β(e T )γ(e Td )δ(e o )λ(e of )..(5) where E o i he error i percege overhoo, E T i he error i elig ie, E Td i he error i pek ie, d E o d E of re he error i he locio of he rel pole. hi fucio, he vrile α, β γ, δ d λ re he weighge fcor. By djuig hee fcor, he o pproprie D coroller preer o chieve he required cloed loop repoe c e oied. Afer he fie evluio, highly fi oluio re eleced d croover operio i perfored o ge offprig. Muio c e doe y odifyig y rdo vlue. Thi cue ior chge i he oluio.
4 eriol Jourl of Eergig Techology d Advced Egieerig Weie: (SSN , Volue, ue, Mrch 0) Afer hee reproducio ehod, replce he eire populio wih he offprig, eighour of good oluio d he e oluio. Now coiue he proce of evluio, reproducio ec, for fixed uer of geerio o ge eer oluio. Algorih c e urized, iilize he populio; while predeeried eriio codiio o ified; { }. Evlue ll hee oluio wih he fie fucio, which c e he ivere of error fucio.. Selec oe highly fi oluio.. ir he pre d perfor croover operio o geere offprig. 4. erfor uio y lighly chgig oe rdo oluio. 5. Geere oe oluio i he eighourhood of good oluio y kig he verge of good oluio. 6. Sve he e oluio. 7. Replce he eire populio wih hee offprig, eighour of good oluio d he e oluio. V. RESULT Opiized gi vlue of D coroller re oied wih he ipleeio of GA ed D coroller i MATLAB. For ipleeio of DC Servooor he followig preer re coidered []. R =.45 oh, L =0.05 H, =. vol/(rd/ec), J=0.0g- /rd, B=0.5*0 - N-/(rd/ec). Thu he overll rfer fucio of he ye i give, Clculed gi vlue of he D coroller re give i Tle. for differe vlue of required repoe. Acul repoe i clculed fro he ep repoe of he copeed ye. i oerved h for wide rge of requiree, uig i doe d cul repoe i foud o e eer h he required repoe. TABLE ARAMETERS OF THE D CONTROLLED SYSTEMS FOR DFFERENT VALUES OF REQURED RESONSE Ser. No. 4 5 Required Repoe Overhoo=0 Tie=0.5 ec ek Tie=0.5ec Overhoo=5 Tie=0.5ec ek Tie=0.5ec Overhoo=0 Tie=0. ec ek Tie=0.5ec Overhoo= Tie=0.ec ek Tie=0.5ec Overhoo=6 Tie=0.ec ek Tie=0.5ec Acul Repoe Overhoo=5.09 Tie=0.04 ec ek Tie=0.54ec Overhoo=. Tie=0.ec ek Tie=0.6ec Overhoo=4.6 Tie=0.79ec ek Tie=0.5ec Overhoo=6.9 Tie=0.98ec ek Tie=0.4ec Overhoo=0 Tie=0.67ec Gi Vlue of D Coroller =0.875 =0.8 D=0.95 =0.5 =0.06 D= =5.644 =0.978 D=0.688 =4.89 =0.85 D=0.094 =6 =0.07 D= ie of hi ye wih uiy feedck i 4.59ec wihou y copeio. c e reduced d hece he required rie repoe c e chieved y uig D coroller. Geeic lgorih for D coroller uig i ipleeed d perfored i MATLAB wih vriou vlue of required repoe. 6 Overhoo= Tie=0.4ec ek Tie=0.5ec Overhoo=0 Tie=0.6ec =0.5 = D =0.0755
5 Apliude Apliude eriol Jourl of Eergig Techology d Advced Egieerig Weie: (SSN , Volue, ue, Mrch 0) The ep repoe for he ucopeed ye d he copeed ye o chieve % overhoo, 0.5 ec. pek ie d 0.4 ec. elig ie i give i figure 4. i ee h elig ie of cul repoe i 0.6 ec. d he perce overhoo i zero Sep Repoe Fig. 4. Sep repoe for he ucopeed ye d copeed ye for % OS=, T p= 0.5 ec d T =0.4ec. Siilrly he ep repoe for he ucopeed ye d he copeed ye o chieve 0% overhoo, 0.5 ec. pek ie d 0.5 ec. elig ie i give i figure Sye: wih_cop Tie (ec): 0.6 Sye: wih_cop ek pliude:.05 Overhoo (%): 5.09 A ie (ec): 0.54 Sye: wih_cop Tie (ec): 0.04 wih_cop wihou_cop Required Repoe Overhoo= ie=0.4 ek Tie= 0.5 Acul Repoe Overhoo=0 ie=0.6 Fig.5.Sep repoe for he ucopeed ye d copeed ye for % OS=0, T p= 0.5 ec d T =0.5ec. Fro hee ep repoe, i i ee h he gi vlue of he D coroller re opiized o chieve he deired repoe. Tie (ec) Required Repoe Overhoo=0 ie=0.5 ek Tie= 0.5 Sep Repoe Acul Repoe Overhoo=5.09 ie=0.04 ek Tie= 0.54 Tie (ec) Sye: wihou_cop Tie (ec): 4.59 wih_cop wihou_cop V. CONCLUSON The geeic lgorih ed D uig provide uch eer reul copred o he coveiol ehod. The coveiol ehod i good for geig he iiil vlue of he D uig which eed o e odified. he deiged D coroller uig wih GA, he cul repoe i foud o e ifyig he required vlue. D coroller gi vlue deped upo he rge eleced for he iiil populio. our ipleeio, vlue re eleced i he rge of 0 o 0, i he rge of 0.00 o 0.55 d he D i he rge of 0.00 o 0.5. i oerved h wihi hi rge uig i doe effecively. The rge of requiree c e wideed y icreig he rge of iiil populio u he uer of geerio required o coverge o opil vlue y icree. REFERENCES [] Guoi Li d i Mig Tg, Cocurre Rely-D Corol for Moor oiio Servo Sye, eriol Jourl of Corol, Auoio, d Sye, vol. 5, o., Jue 007. [] Ayeki Bgi, Deeriio of he D Coroller reer y Modified Geeic Algorih for proved erforce, Jourl of iforio ciece d egieerig, (007). [] Neeu Tho, Dr.. oogodi, oiio Corol of DC Moor Uig Geeic Algorih Bed D Coroller, roceedig of he World Cogre o Egieerig 009 Vol, WCE 009, July, 009. [4] Chuck Lewi, Tuig Servooor, CEO of erforce Moio Device. [5] Dog-Seog Be d Jg-Myug Lee, Ukow reer deifier Deig of Dicree-Tie DC Servo Moor Uig Arificil Neurl Nework, Trcio o Corol, Auoio d Sye Egieerig Vol., No., Sepeer, 000. [6] M. Ge, d R. Cheg, Geeic lgorih d egieerig deig, (Joh Wiley & So, c., 997). [7] rker Hifi, Fudel of Servo Moio Corol, Elecroechicl Auoio Div. / / [8] Nor S. Nie, Corol Sye Egieerig, Wiley di v. Ld., fourh ediio. [9] Whyuggoro, Oy; Sd, Nordi, Evluio of fuzzy-logiced elf-uig coroller d fuzzy-cheduled D coroller for DC ervooor, TSi 008, [0] M. M. i, J. N. Nderu,.. Hig, Adpive D Dc Moor Speed Coroller Wih reer Opiized wih Hyrid Opiizio Sregy, d eriol coferece o Advce i Egieerig d Techology 0. [] Ay A. Aly, D reer Opiizio Uig Geeic Algorih Techique for Elecrohydrulic Servo Corol Sye, ellige Corol d Auoio, 0,, [] Rhul Mlhor, Nrider Sigh, Yduvir Sigh, Geeic Algorih: Cocep, Deig for Opiizio of roce Coroller, Copuer d forio Sciece, Vol. 4, No., Mrch 0.
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