Nonlinear PID-based analog neural network control for a two link rigid robot manipulator and determining the maximum load carrying capacity

Transcription

1 Noliar PID-basd aalog ural work corol for a wo lik rigid robo maipulaor ad drmiig h maximum load carryig capaciy Hadi Razmi Aabak Mashhadi Kashiba Absrac A adapiv corollr of oliar PID-basd aalog ural works is dvlopd for h poi o poi ad oriaio-rackig corol of a wo lik rigid robo maipulaor. I ach cas h maximum load carryig capaciy of robo maipulaor subc o accuracy ad acuaors cosrais is obaid. I compariso wih covioal PID mhod h us of ural work corollr ca icras maximum load carryig capaciy of robo maipulaors. A suprb mixur of a covioal PID corollr ad a ural work which has powrful capabiliy of coiuously oli larig adapaio ad acklig oliariy brigs us h ovl oliar PID-basd aalog ural work corollr. Compur simulaios wr carrid ou i wo axs maipulaor ad h ffcivss of h proposd corol algorihm was dmosrad hrough h xprims which suggss is suprior prformac ad icrasig h maximum load carryig capaciy of his maipulaor. Idx rms Aalog ural work Adapiv corol Maximum load carryig capaciy Noliar PID corol. I. INRODUCION Sic h dyamics of robo maipulaors ar highly oliar ad may coai ucrai lms such as fricio may ffors hav b mad i dvlopig corol schms o achiv h prcis rackig corol of robo maipulaors. Covioally may corol chiqus for robo maipulaors rly o proporioal-igral-drivaiv (PID)-yp corollrs i idusrial opraios du o hir simpl corol srucur as of dsig ad low cos [] []. Howvr robo maipulaors hav o fac various ucraiis i pracical applicaios such as payload paramr iral fricio ad xral disurbac [4] [6]. All h ucrai or im-varyig facors could affc h sysm corol prformac sriously. May corol chiqus hav b ivsigad as viabl mas o improv h shorcomigs of h covioal PID-yp corollrs [7] []. Su ad Mills [9] proposd a adapiv-larig corol schm o improv racory prformac ad could guara covrgc i sigl ad rpiiv opraioal mods. Bu h corol schm rquirs h sysm dyamics Mauscrip rcivd Fbruary 8. Hadi Razmi Dparm of Egirig Eas hra Brach Islamic Azad Uivrsiy hra Ira l.: (+98) (-mail: razmi78@yahoo.com). Aabak Mashhadi Kashiba Dparm of Egirig Khamh Brach Islamic Azad Uivrsiy abriz Ira l.: (+98) (-mail: akshiba@gmail.com). i dail. A modl-basd PID corollr was prsd by Li al. [] o achiv h im-varyig rackig corol of a robo maipulaor. Howvr i is difficul o sablish a appropria mahmaical modl for h dsig of a modl-basd corol sysm. hus h gral claim of radiioal illig corol approachs is ha hy ca aua h ffcs of srucurd paramric ucraiy ad usrucurd disurbac usig hir powrful larig abiliy wihou prior kowldg of h corolld pla i h dsig procsss. I h pas dcad h applicaios of illig corol chiqus (fuzzy corol or ural-work corol) o h moio corol for robo maipulaors hav rcivd cosidrabl aio [] []. A corol sysm which compriss PID corol ad ural work corol was prsd by Ch al. [] for improvig h corol prformac of h sysm i ral im. Clifo al. [] ad Misir al. [7] dsigd fuzzy PID corollrs which wr applid o h posiio corol of robo maipulaors. Huag ad L [4] suggsd a sabl slf-orgaizig fuzzy corollr for robo moio corol. his approach has a larig abiliy for rspodig o h im-varyig characrisic of a robo maipulaor. Howvr h fuzzy rul larig schm has a la sabiliy problm. Yoo ad Ham [9] prsd wo kids of adapiv corol schms for robo maipulaor via fuzzy compsaor i ordr o cofro h uprdicabl ucraiis. hough h sabiliy of h whol corol sysm ca b guarad som sric cosraid codiios ad prior sysm kowldg ar rquird i h corol procss. O h ohr had Kim ad Lwis [] dal wih h applicaio of quadraic opimizaio for moio corol of roboic sysms usig crbllar modl arihmic compur ural works. Lwis al. [6] dvlopd a mulilayr ural- corollr for a gral srial-lik rigid robo o guara h rackig prformac. Boh sysm-rackig sabiliy ad rror covrgc ca b guarad i hs ural-basd-corol sysms [] [6]. Howvr h fucioal rcosrucd rror h ural uig wighs ad h high-ordr rm i aylor sris ar assumd o b kow boudd fucios ad som ihr propris of robo maipulaor ar rquird i h dsig procss (.g. skw-symmry propry boudd sysm paramrs ad disurbacs). Barambos ad Exbarria [] proposd a ural schm wih adapiv swichig gai. Hr wo diffr NN archicurs ar proposd o sima h lms of h ukow oliar fucio ad h lms of iria marix. Bhra al. [] 8

2 Noliar PID-basd aalog ural work corol for a wo lik rigid robo maipulaor ad drmiig h maximum load carryig capaciy proposd a uro adapiv hybrid corollr for robo maipulaor rackig corol whr hr mulilayr ural works ar usd o lar h iria marix Coriolis vcor ad h graviaioal orqu vcor rspcivly. I howvr suffrs from compuaioal complxiy. Erugrul ad Kayak [] uilizd wo NNs o raliz h obciv of racory rackig basd o slidig mod corol mhodology. h quival corol ad h swichig corol rms ar h oupus of h wo NNs. I [] Wai prsd a slidig mod ural work corol sysm for posiio corol of roboic maipulaors. For may idusrial applicaios curr roboic maipulaors wih oi lasiciy ar rlaivly slow v wh hy ar o fully loadd. hir spd load carryig capaciy ad hc hir produciviy ar limid by h dflcio of h d-ffcor ad h capabiliy of hir acuaors. Icrasig acuaor siz ad powr is largly slf-dfaig bcaus of icrasd cos ad powr cosumpio of h largr acuaors as wll as icrasd iria of h acuaors hmslvs. A mor succssful approach should maximiz h load carryig capaciy of h flxibl maipulaor subc o h cosrais imposd by acuaor capaciy ad allowabl d-ffcor dviaio for a giv dyamic racory. homas al. [4] usd h load capaciy as a cririo for sizig h acuaors a h dsig sag. I hir work picwis rigid liks ad ois wr assumd. If o rmovs h rigid body assumpio h Dyamic Load Carryig Capaciy (DLCC) drmid usig h acuaor cosrai alo [] would ormally b oo larg. h DLCC for a wo-lik plaar flxibl arm is dal wih for oly a sigl dyamic racory [6]. I [7] a w mhod for drmiig h DLCC for flxibl oi maipulaors subc o boh acuaor ad d-ffcor dflcio cosrais is iroducd. A adapiv corollr of oliar PID-basd aalog ural works is dvlopd for h poi o poi ad oriaio-rackig corol of a wo lik rigid robo maipulaor. I ach cas h maximum load carryig capaciy of robo maipulaor subc o accuracy ad acuaors cosrais is obaid. I compariso wih covioal PID mhod h us of ural work corollr ca icras maximum load carryig capaciy of robo maipulaors. A suprb mixur of a covioal PID corollr ad a ural work which has powrful capabiliy of coiuously oli larig adapaio ad acklig oliariy brigs us h ovl oliar PID-basd aalog ural work corollr. h aims of his rsarch work ar rducig h difficulis of oliar dyamics fas moio corol of robo maipulaors ad comparig h prformacs of h oliar PID-basd aalog ural work ad h covioal PID mhods. h papr is orgaizd as follows: h dyamic modls of robo maipulaors ar dscribd i Scio. h ural work modl for simaio of h appropria PID gais ad adapiv corol sysm ar prsd i Scio. Scio 4 prss h simulaio rsuls obaid by drmiig h maximum load carryig capaciy ad h poi o poi ad h rackig corol of a wo rigid-lik robo maipulaor i various opraig codiios ad compars h prformac of h ural work basd mhod wih ha of covioal PID mhod. Scio cocluds h papr. II. ROBO DYNAMICS Usig h Eulr Lagragia formulaio h dyamics of robo maipulaors wih rigid liks ca b wri as [8]: M ( q) q C( q q ) q G( q) () Whr q displacms corol ipu forcs C dos h vcor of gralizd dos h vcor of gralizd M ( q q ) is h Coriolis marix vcor ad ( q) is h iria marix G ( q) is h graviy dis rprss disurbacs which ar boudd. For h robo dyamic modl giv by () h followig assumpios ar mad. max ) h maximum allowabl orqus for ach oi i for i ar kow. ) h dsird oi racory q di ( ad h highr ordr drivaivs of q di ( ar boudd i.. qdi q di q di L. ) h disurbacs ar boudd so ha dis db. h corol obciv ca b sad as follows: giv dsird racoris q [ q ( q ] drmi a d corol law which is a fucio of posiio oly ad achivs dsirabl rackig prformac i h prsc of ucraiis ad acuaor cosrais which ar giv by max i. i i dis III. ADAPIVE CONROL SYSEM h sragy of PID corol has b o of mos sophisicad ad mos frquly usd mhods i idusry. his is bcaus h PID corollr has a simpl form ad srog robusss i broad opraig codiio. Howvr h rquirm of corol prcisio bcoms highr ad highr i accordac wih h complxiy of plas. h covioal PID corollr wih fixd paramrs may usually driora h corol prformac. Various yps of modifid PID corollrs hav b dvlopd i h xisig liraur. Howvr if svr oliariy is ivolvd i h corolld procss a oliar corol schm will b mor usful paricularly i h cas of high oliariy of -liks robo maipulaors. Nowadays ural works hav b provd o b a promisig approach o solv complx oliar corol problms ad hr ar wo kids of ural works for corol applicaios i.. digial ad aalog ural works. May digial ural works which ar discr larig algorihms hav b prsd owig o h fac ha hy offr svral advaags such as prdicabl accuracy high ois-immuiy as of muliplxig commuicaio ad compuaio availabiliy of wll-sablishd ools for digial dsig ad as of irfacig wih ohr digial sysms. d d 9

3 O h ohr had aalog ural works which ar coiuously larig algorihms hav may advaags such as high spd small siz low cos low powr ad sraighforward irfacig wih h ousid word ha is aalog by aur wh aalog ural circuis ar mad of lcroic lms or chips. Corol sysms hav o rspod i ral im ad hrfor dmad fas compuaio. Currly may promisig dvlopms i roboics ad auomaio ar impracical bcaus of h larg siz cos ad powr cosumpio of h rquird corol sysms. Hc i moivas us o combi a aalog ural work wih PID corol. h combiaio proposd hr will ak advaag of h simpliciy of PID corol ad h aalog ural work s powrful capabiliy of coiuous oli larig adapabiliy ad acklig oliariy. Howvr hr is a liar PID corollr ud usig ANN i liraur bu i may usually driora h corol prformac [8] if svr oliariy is ivolvd i h corolld procss. hrfor h oliar PID corollr ud usig ANN is proposd i his papr ad i ca improv h corol prformac of h oliar sysms. h srucur of h wly proposd corol algorihm of oliar PID-basd aalog ural works is show i Fig.. his corol algorihm has h characrisics such as simpl srucur lil compuaio im ad coiuous auo-uig mhod of h ural work corollr. wo dirc corollrs of h PID-basd aalog ural works ar composd of h oriaio corol of h wo lik robo maipulaor. Robo moio ca b corolld by is oriaio agls ad. Hr h corol goal is o dsig wo ANN corollrs ha forc h rackig rror [ p p ] o zro whr p d p d ad d ad d ar h dsird oriaio agls ad rspcivly. ad ar h oupus of h ANN ad h ANN rspcivly. h work srucur wih a hr layr uro is show i Fig.. d d s /s s /s p d i p d i PID- Basd ANN PID- Basd ANN wo-lik Rigid Robo Maipulaor Fig. Block diagram of h wo rigid-lik robo maipulaor corol sysm. d i kd k ki f ( x) Fig. Block diagram of a oliar PID-basd ural work. Hr k k i ad k d ( ) ar h proporioal igral ad drivaiv gais rspcivly; i ad d ( ) ha ar hr ipus of h ural work ar h sysm rrors bw h dsird oupu ad moio oupu of h mobil robo igral of h sysm rror ad diffrc of h sysm rror rspcivly. A corollr oupu ca b obaid from h followig quaio: f ( x) () whr x is h ipu of sigmoid fucio f (.) ha has a oliar rlaioship as prsd i h followig fucio ax ( ) f ( x) ax () a( ) whr a is a paramr which drmis h shap of sigmoid fucio. h ipu sigal of h sigmoid fucio i h oupu layr bcoms x k ki( i( kd d (4) whr dp( p( d( ( i( p( d d( d dp( p( d ( ( i ( p( d d ( d h Nural works ar raid by h covioal back propagaio algorihm o miimiz h sysm rror bw h oupu of h mobil robo ad dsird oupu dfid by h followig quaio: E ( ) () From h discr algorihm usig h sps dsc mhod [9] h followig quaios ca b drivd: E k k () d k E ki( ki() i d (6) ki E kd kd () d d kd whr i ad d ( ) ar larig ras drmiig h covrgc spd. From () usig h chai rul h followig quaios ar drivd: E E x... k x k E E x... k i x k i E E x... k d x k d f ( x ) f ( x ) i f ( x ) d Ad h followig xprssio ca b drivd from Eq. (): ax f ( x) 4 ax (8) ( ) As do by hah ad Ah [9] for covic w assum ( ). h (6) is xprssd as follows: ax k k () ( ) ( )4 d ax ( ) ax ki( ki() i ( ) ( )4 i d ax ( ) ax kd kd () d 4 d d ax ( ) (7) (9)

4 Joi orqu (N.m) Joi orqu (N.m) Joi Agl (dgr) Joi Agl (dgr) rackig Error (ma) : p (dgr) Noliar PID-basd aalog ural work corol for a wo lik rigid robo maipulaor ad drmiig h maximum load carryig capaciy h ffcivss of h proposd PID-basd ANN corol will b dmosrad hrough simulaios of h moio corol of h wo lik robo maipulaor. IV. SIMULAION RESULS For simpliciy a wo rigid-lik robo maipulaor is uilizd i his sudy o vrify h ffcivss of h proposd corol schm. h dyamic modl of h adopd robo sysm ca b dscribd i h form of () as ( ) ( q q ) ( ) c cos( ) c cos( ) c cos( ) s si( ) M M G A M ( q) G( q) C( q q ) q M M G A m m M ( m ml ) a ( ml ) a ( m m ) a a c L dis m m M M ( ml ) a ( ml ) aac () m M ( ml ) a m m G g( m mload ) ac g( mload ) ac m G g( ml ) ac ( ) m A m m a a s ( m ) a L L as m A ( m ) a L as Whr θ ad θ ar h agl of ois ad ; m ad m ar h mass of liks ad ; a ad a ar h lgh of liks ad ; m L (m load ) is h mass of d-ffcor load; ad g is h graviy acclraio. Morovr h sysm paramrs of h wo rigid-lik robo maipulaor ar slcd as: m m kg kg m/sc a m m. g 9. 8 a h proposd ural work corol is vrifid wih compur simulaio usig MALAB/SIMULINK. Hr h simulaio rsuls obaid by drmiig h maximum load carryig capaciy ad h poi o poi ad h rackig corol of a wo rigid-lik robo maipulaor i various opraig codiios ad comparig h prformac of h ural work basd mhod wih ha of covioal PID mhod. h maximum allowabl orqus for ach oi is max N. m cosidrd as ( ) ad h iiial codiios ar ak as q ( ) ( ) ad q ( ) ( ). A. rackig Corol For h simulaio purpos h dsird oriaio agls ar ak as d si( f ad d cos( f Hz (frqucy of rfrc ipu f. ) [9] Fig. shows h rsuls of compariso bw covioal PID corollr ad oliar PID corollr usig ural work i drmiig of maximum load carryig capaciy of wo rigid-lik robo maipulaor. For a prscribd racory h maximum load carryig capaciy of a oi maipulaor is dfid as h maximum load ha h maipulaor ca carry i xcuig h racory wih a accpabl rackig accuracy. h mai cosrais which boud h maximum load carryig capaciy of maipulaors ar acuaors ad accuracy cosrais. I his papr h avrag of rackig rror is cosidrd as. radia or.4 dgr i h slig im of sc PID Corollr Proposd Corollr. Radia =.44 Dgr mload (kg) Fig. Compariso bw covioal PID corollr ad proposd corollr i drmiig of maximum load carryig capaciy (rackig corol cas) mload =.7 kg Rfrc f =. Hz PID Corollr Proposd Corollr im (s) mload =.7 kg Rfrc f =. Hz PID Corollr Proposd Corollr im (s) mload =.7 kg PID Corollr PID Corollr Proposd Corollr Proposd Corollr im (s) Fig 4. Compariso bw covioal PID corollr ad oliar PID corollr usig ural work (frqucy of rfrc f =. Hz ad m load =.7 Kg ).

5 Joi orqu (N.m) rackig Error : p (dgr) rackig Error : p (dgr) Joi orqu (N.m) kd kd Joi Agl (dgr) ki ki kp kp kd kd Joi Agl (dgr) ki ki kp kp mload =.7 kg Rfrc f =. Hz PID Corollr Proposd Corollr mload =.7 kg 4 mload =.7 kg im (s) 7 im(s) 4 im (s) mload =.7 kg mload =.7 kg 8 6 mload =.7 kg Rfrc f =. Hz - PID Corollr Proposd Corollr im (s) mload =.7 kg PID Corollr Proposd Corollr im(s) Fig 6. Updaig of ach corol paramr ( k p 6 4 mload =.7 kg PID Corollr Proposd Corollr 6 4 im (s) k i ad k d ). mload =.7 kg PID Corollr Proposd Corollr PID Corollr Proposd Corollr im (s) Fig. Compariso bw covioal PID corollr ad oliar PID corollr usig ural work (frqucy of rfrc f =. Hz ad m load =.7 Kg ). h paramrs of wo PID corollrs wr s o b k k ad k 7 ( ). I h i xprims of h wo proposd oliar PID corollrs h iiial valus of k () k () ad k () ( ) ar s i o b h sam as ha of covioal PID corollr. h paramrs of wo ANN corollrs ar chos as p 6 i d 8 p 8 i 6 d 8 ad a.. h paramrs of hs corollrs wr obaid by rial-ad-rror hrough xprims. h maximum load carryig capaciy of h robo is obaid from.7 Kg ad.7 Kg i PID corollr ad proposd corollr rspcivly. I compariso wih covioal PID mhod h us of ural work corollr icrass maximum load carryig capaciy of robo maipulaor (.8 Kg ). Firs h xprims wr carrid ou o vrify h ffcivss of h proposd oliar PID corollr usig ural work wh h frqucy of rfrc ipu was. Hz i full load saus (.7 Kg ad.7 Kg ). d d mload =.7 kg PID Corollr Proposd Corollr im (s) 4 mload =.7 kg PID Corollr Proposd Corollr im (s) Fig 7. Compariso rackig rror bw covioal PID corollr ad proposd corollr. Figs. 4 ad show h xprimal rsuls bw h covioal PID corollr ad h proposd oliar PID corollr wih rspc o Jois ad ad h updaig of ach corol paramr ( k p k i ad k d ) ad h rackig rror wr show i Figs. 6 ad 7 rspcivly. h purpos of h xprim is o show h ffcivss of h adapabiliy of h proposd oliar PID corollr. From Figs. 4 ad 7 i was udrsood ha h sysm rspos of h proposd corollr was i good agrm wih ha of rfrc ipu ad i was dmosrad ha h proposd algorihm was ffciv i rackig problm. B. Poi o Poi Corol I his scio firsly maximum load capaciy of oliar PID corollr usig ural work ad covioal PID corollr ar compard o rach ( d d ) ( / 6 / ) or m m ( x y) (.866. ) poi i s slig im (Fig 8). Maximum load capaciy is drmid cosidrig ha fial

6 Joi orqu (N.m) Joi orqu (N.m) Joi Agl (dgr) Joi orqu (N.m) Joi Agl (dgr) Joi Vlociy (rad/s) Fial Posiio Error (mm) Joi Agl (dgr) Noliar PID-basd aalog ural work corol for a wo lik rigid robo maipulaor ad drmiig h maximum load carryig capaciy poi rror should b lss ha cm. Bcaus of approximaly similar rsuls of wo corollrs i poi o poi mov so oly h rsuls of oliar PID corollr usig ural work ar show. wo diffr simulaios ar do usig oliar PID corollr usig ural work kg i wo o load ad maximum load ( m. 8 ) cass. Fig 9 shows h simulaios rsuls. load 6 4 Proposd Corollr mload = 6 kg qd =.97 Rad Lik.98*qd qd = Rad Lik 4 PID Corollr Proposd Corollr mm = cm im (s) Fig. Liks posiio Proposd Corollr mload = 6 kg Lik Lik mload (kg) Fig 8. Compariso bw covioal PID corollr ad proposd corollr i drmiig of maximum load carryig capaciy (poi o poi corol cas) im (s) Fig. Liks vlociy. Proposd Corollr mload = 6 kg - Lik Lik - qd = dgr Proposd Corollr (No Load) Proposd Corollr (mload =.8 kg) im (s) qd = 6 dgr Proposd Corollr (No Load) Proposd Corollr (mload =.8 kg) im (s) - Proposd Corollr (mload =.8 kg) Proposd Corollr (No Load) Proposd Corollr (No Load) Proposd Corollr (mload =.8 kg) im (s) Fig 9. Rsuls of proposd oliar PID corollr usig ural work i wo o load ad maximum load (m load =.8 Kg ) cass. -.. im (s) Fig. Moors orqu. I his scio iiial codiios ar chos similar o prvious scio bu larig cofficis valus ar chos as p. 6 i. d. 8 p. 8 i.6 ad d. 8. hs valus ar chos wih rial-ad-rror. Ohr simulaios ar do i a poi o poi mov o a wo lik robo maipulaor wih hs paramrs: m m kg kg m / sc.4 a. m 9.8 m g a Mchaical maipulaor mov is do o a horizoal surfac so h graviy acclraio assumd o b zro. max N.m Limid spa of moor orqus ar as blow: ad max N.m 9 ad. Iiial codiios ar assumd as q ( ) ( ) q ( ) ( ). Our dsird is o rach o Rad ( d d ) (.97 ) poi i.4s slig im. Maximum load capaciy is calculad as 6kg i his cas cosidrig ha fial poi rror is lss ha cm. Liks posiio ad vlociy

7 i maximum load cas ar show i Figs ad. Moors orqu ar show i Fig. I his cas iiial valus of slcd PID paramrs ar: k () k () p k () 9 k () k () ad k () 7. d p i d i Larig coffici ad drmiig paramr of sigmoid fucio ar cosidrd o b similar o prvious cas valus. V. CONCLUSION I his papr a adapiv corollr of a oliar PID-basd aalog ural work is proposd for h poi o poi ad oriaio rackig corol of a wo rigid lik robo maipulaor ad h comparisos of corol prformac bw h covioal PID ad h proposd oliar PID corollr ar prformd. A suprb mixur of a covioal PID corollr ad a ural work which has powrful capabiliy of coiuously oli larig adapaio acklig oliariy ad icrasig h maximum load carryig capaciy of robo maipulaor brigs us h ovl oliar PID-basd aalog ural work corollr. Simulaio rsuls dmosra h ffcivss of h proposd corol algorihm br dyamic propry ad srog robusss ad i was suiabl for h corol of a wo rigid lik robo maipulaor. Acually h proposd ural corollr dos o rquir h dyamics modl of robo maipulaors which is dd oly i h simulaio for his papr. I compariso wih covioal PID mhod h us of ural work corollr ca icras maximum load carryig capaciy of robo maipulaor. ACKNOWLEDGMEN his rsarch work has b fiacially suppord by Eas hra Brach Islamic Azad Uivrsiy hra Ira. REFERENCES [] K.J. Asrom ad. Hagglud Auomaic uig of simpl rgulaors wih spcificaio o phas ad ampliud margis Auomaica vol. 984 pp [] K.J. Asrom ad. Hagglud PID Corollr: hory Dsig ad uig. Rsarch riagl Park NC USA 99. [] C.C. Hag K.J. Asrom ad W.K. Ho Rfims of h Ziglr-Nichols uig formula IEE Proc. Corol hory Appl. vol pp. 8. [4] A.J. Koivo Fudamals for Corol of Roboic Maipulaors. Wily Nw York 989. [] F.L. Lwis C.. Abdallah ad D.M. Dawso Corol of Robo Maipulaors. Macmilla Nw York 99. [6] R.J. Schillig Fudamals of Roboics: Aalysis ad Corol. Pric-Hall EglwoodCli4s NJ 998. [7] I. Cha ad C. Ha h auo-uig PID corollr usig h paramr simaio IEEE/RSJ Iraioal Cofrc o Illig Robos ad Sysms Souh Kora 999 p. 46. [8].Y. Kuc ad W.G. Ha Adapiv PID larig of priodic robo moio 7 h IEEE Cofrc o Dcisio ad Corol USA 998 p. 86. [9] D. Su ad J.K. Mills High-accuracy racory rackig of idusrial robo maipulaor usig adapiv-larig schms Amrica Corol Cofrc USA 999 p. 9. [] Y. Li Y.K. Ho ad C.S. Chua Modl-basd PID corol of cosraid robo i a dyamic virom wih ucraiy IEEE Iraioal Cofrc o Corol Applicaios USA p. 74. [] P.C.Y. Ch J.K. Mills ad G. Vukovich Nural work larig ad gralizaio for prformac improvm of idusrial robos Caadia Cofrc o Elcrical ad Compur Egirig Caada 996 p. 66. [] C. Clifo A. Homaifar ad M. Bikdash Dsig of gralizd Sugo corollrs by approximaig hybrid fuzzy-pid corollrs IEEE Iraioal Cofrc o Fuzzy Sysms USA 996 p. 96. [] L.B. Guirrz F.L. Lwis ad J.A. Low Implmaio of a ural work rackig corollr for a sigl flxibl lik: compariso wih PD ad PID corollr IEEE ras. Id. Elcro. Vol pp [4] S.J. Huag ad J.S. L A sabl slf-orgaizig fuzzy corollr for roboic moio corol IEEE ras. Id. Elcro. vol. 47 pp [] Y.H. Kim ad F.L. Lwis Opimal dsig of CMAC ural-work corollr for robo maipulaors IEEE ras. Sysms Ma Cybr. vol. pp.. [6] F.L. Lwis A. Ysildirk ad K. Liu Mulilayr ural- robo corollr wih guarad rackig prformac IEEE ras. Nural Nworks vol pp [7] D. Misir H.A. Malki ad G. Ch Graphical sabiliy aalysis for a fuzzy PID corolldrobo arm modl IEEE Iraioal Cofrc o Fuzzy Sysms USA 998 p. 4. [8] A.. Vmuri ad M.M. Polycarpou Nural-work-basd robus faul diagosis i roboic sysms IEEE ras. Nural Nworks vol pp [9] B.K. Yoo ad W.C. Ham Adapiv corol of robo maipulaor usig fuzzy compsaor IEEE ras. Fuzzy Sysms vol. 8 pp [] O. Barambos ad V. Exbarria Robus ural corol for roboic maipulaors Auomaica vol. 8 pp. 4. [] L. Bhra S. Chaudhury ad M. Gopal Nuro adapiv hybrid corollr for robo maipulaor rackig corol IEE Procdigs D Corol hory ad is Applicaios vol pp [] M. Erugrul ad O. Kayak Nuro slidig mod corol of roboic maipulaors Mcharoics vol. pp [] R. J. Wai rackig corol basd o ural work sragy for robo maipulaors Nurocompuig vol. pp [4] M. homas H.C. Yua-Chou ad D. sar Opimal acuaor sizig for roboic maipulaor basd o local dyamic criria ASME Joural of Mchaisms rasacios ad Auomaio vol pp [] L.. Wag ad B. Ravai Dyamic load carryig capaciy of mchaical maipulaors-par I: problm formulaio rasacios of ASME Joural of dyamic sysm Masurm ad corol vol. 988 pp [6] M.H. Koraym Y. Yao ad A. Basu Load carryig capaciy for a wo-lik plaar flxibl arm Proc. hir Caadia Cogrss of Applid Mchaics vol. Ju 99. [7] M.H. Koraym ad A. Basu Dyamic load carryig capaciy of roboic maipulaors wih oi lasiciy imposig accuracy cosrais Roboics ad Auoomous Sysms vol. 994 pp [8] J. J. Sloi ad W. Li O h adapiv corol of robos maipulaors Iraioal Joural of Roboics Rsarch vol pp [9].D.C. hah ad K.K. Ah Noliar PID corol o improv h corol prformac of axs pumaic arificial muscl maipulaor usig ural work Mcharoics vol. 6 6 pp Hadi Razmi was bor i hra Ira i 98. H rcivd h M.S. dgr i corol girig from Uivrsiy of abriz abriz Ira i. H is currly a Ph.D. sud a h Scic ad Rsarch Brach Islamic Azad Uivrsiy hra Ira. H is a Acadmic Saff of Corol Egirig a Eas hra Brach Islamic Azad Uivrsiy hra Ira. His rsarch irss iclud powr sysm opimizaio ad corol scuriy aalysis ad ural works ad fuzzy sysms applicaios. Aabak Mashhadi kashiba was bor i Orumiyh Ira i 98. H rcivd h M.S. dgr i corol girig from Uivrsiy of abriz abriz Ira i. H is currly a Ph.D. sud a h Scic ad Rsarch Brach Islamic Azad Uivrsiy hra Ira. H is a Acadmic Saff of Corol Egirig a Khamh Brach Islamic Azad Uivrsiy abriz Ira. His rsarch irss iclud powr sysm opimizaio ad corol scuriy aalysis ad ural works ad fuzzy sysms applicaios. 4