Dual adaptive control of mechanical arm
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1 Itatoal Joual of Avac Rsach Comput Egg & chology (IJARCE Volum 6 Issu 9 Sptmb 07 ISSN: Dual aaptv cotol of mchacal am Bgtao Lu Jx Pu Jg Lu Abstact Amg at th fctoal foc a th molg o caus by th chag of mol paamts jot obot cotol systm th sg mtho of ual aaptv cotoll s scuss ths pap. h ucta yamcs caus by th chag of th paamts of th obot mol s compsat by th aaptv cotoll compos of th gsso matx. At th sam tm Aaptv fuzzy cotol algothm s us to ovcom th fcto of obot jots Lyapuov fucto s us to tm th aaptv laws th mtho sus global stablty of th systm h smulato sults show that th cotoll has a goo posto a sp tackg ablty th psc of mol o a fcto tfc. Kywos Robotc mapulato; tajctoy tackg; fuzzy aaptv chattg I. INRODUCION Robot mapulatos play a sgfcat ol automato. hy hav b wly us vaous applcatos wh may tasks qu hgh-sp a hgh-pcso tajctoy tackg. Howv obotc mapulatos gally fac may uctats a xtal stubacs th yamcs such as payloa vaatos fctos xtal stubacs a sso oss. hus th cotol of obot mapulatos s a hot topc th oma of cotol. h tatoal la cotol caot gt th al cotol ffct u to th wak obustss a low cotol pcso so som tllgt cotol statgs a appl to th cotol of th mapulato At pst may ltatus hav stu th cotol of mapulato vaous cotol appoachs that attuat th ffct of obotc uctats hav b popos such as fuzzy cotol obust aaptv cotol slg mo cotol a ual twok cotol. Ltatu [-3] shows th obust cotol of th mchacal am ca guaat th ovall stablty of th systm but t affcts th al-tm gg applcato. Ltatu [4-8] us th uvsal appoxmato fatu of th fuzzy systm to alz th appoxmato of th uctaty; Fuzzy appoxmato s a btt way to al wth uctaty. h mo th pcso of fuzzy appoxmato s th mo fuzzy uls a hfo th poblm of hgh mso of fuzzy systm s vy wspa. Ltatu [9] us aaptv obust cotol mtho to ovcom th ffcts of uctaty; th cotoll has a Mauscpt cv Sp 07. Bgtao Lu Collg of Ifomato Egg Ha Uvsty of Scc a chology Luoyag Cha. Jx pu Collg of Ifomato Egg Ha Uvsty of Scc a chology Luoyag Cha. Jg Lu Collg of Ifomato Egg Ha Uvsty of Scc a chology Luoyag Cha. stog obustss but obust cotol s a vy cosvatv cotoll a ts stablty most cass s guaat by th sacfc of yamc pfomac. I ths pap th ual aaptv cotoll s sg fo th molg o a fcto tfc of th mapulato. Aaptv fuzzy cotol s us to compsat th fluc of fcto o th systm; th aaptv cotol lag algothm bas o th gsso matx to ovcom th molg o caus by th vaato of obot mol paamts. W pov th tal cotol algothm. Fally th smulato sults show th ffctvss of th popos mtho II. PROBLEM DESCRIPION Cosg a -lk obot ts yamc pfomac s scb by th followg sco-o ola fftal quato. D q q C q q q G q F q ( wh q q q R a th jot posto vlocty a acclato vctos spctvly; D( q R s th bou postv-ft ta matx; C( q q R s th matx of cools a ctfugal focs; G( q R s th gavty vcto; F( q R s th tfc tm of fcto Fo obot systms som yamcs chaacts a show blow: Chaact : h tal matx Dq ( s th postv ft matx a bou Chaact : D ( q C( q q s a skw symmtc matx fo ay vcto that hav: R s th vcto of th cotol put fo th obot; ( D ( q C( q q 0 ( Chaact 3; wth th pop slcto of physcal paamts such as lgth mass a ta matx of obot th xsts a paamt vcto pt o th mapulato to mak D( q C( q q a Gq ( satsfy th la latoshp D( q q C( q q q G( q Y( q q q q a (3 Wh Y ( q q q q a s th gsso matx of kow jot vaabl fuctosit s a kow fucto matx of th galz cooats of th obot a ts vatvs. a R s a ukow ft costat paamt vcto scbg th qualty chaactstcs of a obot. hs quato ca b us to spaat th ukow paamts All Rghts Rsv 07 IJARCE 4
2 4 Itatoal Joual of Avac Rsach Comput Egg & chology (IJARCE Volum 6 Issu 9 Sptmb 07 ISSN: th obot yamcs quato a to al wth th ucta paamts of th obot. III. DSIGNE OF CONROL h s posto of th obots jots s f hus th posto tackg o s: Lts q q q q h slg sufac s f as: q q s q q q ( q h cotol momt s sg as Dˆ ( q q Cˆ ( q q q Gˆ ( q Fˆ ( q K S (4 D Wh KD sg( K K 0... If th systm os ot xst xtal mol vato loa a fcto tfc slctg fft cotol ga ca achv th pupos of covgc. But pactcal gg th a vaous ptubatos; som tatoal cotol mthos ca't mt th qumts of cotol accuacy a stablty. h slg mo cotol (SMC s o of th flutal ola cotol mthos that hav b wly appl to cotol both cta a ucta systms. h SMC has th avatags of smpl cotol quck spos asy mplmtato scg o a couplg. hus th SMC s also commoly us to cotol obotc mapulatos. o mak full us of avatags of slg mo cotoll; ths atcl s bas o ths th ucta mol o s compsat by th aaptv cotoll compos of th gsso matx a th fcto of th mapulato s compsat by aaptv fuzzy compsato. Fuzzy cotol ot oly ca alz th appoxmato to abtay o-la fucto also ca gatly uc th chattg of slg mo. q scb asnb NS O PS PB fuzzy cotol uls a: IF q s Wh A HEN s A a B B a fuzzy st Usg th abov fuzzy cotol ul ˆF ca b ajust al tm to alz th fuzzy appoxmato of Fq (. Df th followg vaabls ag m sup F( q F( q ˆ w F( q F( q (4 Wh s th optmal appoxmato paamt s: s th paamt appoxmato o a s th last fuzzy appoxmato o. Fuzzy aaptv law s sg as: s( q (5 V. LYAPUNOV FUNCION DESIGN Cosg th fuzzy appoxmato a stmato paamt oh Lyapuov fucto s f as: V S DS a a (6 Wh a aˆ a a paamt stmato os s th al paamt a s a costat vcto a a gat tha zo; h th vatv of V bcoms V ( t S DS S DS a a V ( t S D( q q S DS a a (7 Applyg ( a (4 to (6 yls; IV. DSIGNE OF FUZZY RULES Sc fcto s oly lat to sp q (.. s us as fuzzy cotol put to f 5 fuzzy sts a th fuzzy systm s sg: ˆ ( F q ( q ˆ ˆ F ( q ( q Fq ( Fˆ ( ( q q Wh ( q s th spctvly: m mso vcto a l... l a l ( q l.. ( l q m m l ( q l l Wh l ( s th mmbshp fucto q a th q put vaabls of th fuzzy cotoll a th output vaabls th substs of th put a output vaabls a V ( t S ( Dq ˆ Cq ˆ Gˆ Fˆ ( q K S C q q ( S q D G q F q Dq S DS a a Lts D Dˆ D C Cˆ C G Gˆ G hus V( t S ( Dq Cq G K S Fˆ ( q F q D C q q S S DS a a Accog to th la atu of th obot: Substtutg (4 to (9 yls (9 (8 V( t S K S S ( Y( q q q q a S ( Fˆ ( q F q D a a (0 I o fo th cotoll to b globally stabl V must satsfy th coto that Vt ( 0 hus lt S ( Y ( q q q q a a a 0 ( Fom ( w ca obta
3 Mmbshp fucto g Itatoal Joual of Avac Rsach Comput Egg & chology (IJARCE Volum 6 Issu 9 Sptmb 07 ISSN: So a Y ( q q q q s ( ˆ D V ( t S K S S ( F( q F q (3 Lt V ( t S ( Fˆ F q hus V ( t S ( Fˆ ( q Fˆ q Fˆ q F q ( ( ( V t S w S Fˆ q Fˆ q V ( t S w ( s ( q (4 Fom (4 w hav V ( t S K S S w 0 (5 D I o to uc th fluc of fuzzy appoxmato o th obust tm s a th cotol law a th symbol fucto s plac by ta-h fucto to wak th chattg caus by slg mo. xp( s xp( s tah( s xp( s xp( s So w sg th followg cotolls: Dˆ ( q q Cˆ ( q q q Gˆ ( q Fˆ ( q K S W tah( s D wh I m l I m l m l I mlc m l l cos( c c c mll c s( H m kg l l 0.5 I / m 3 I c I / 9.8 h s jot tajctos fo tackg a q s( t q s( t h tal valu of th accus objct s: [ q q q q ] [ ] h stmato fcto sgal of th two jots s: F( q 0.5q 0.sg( q 0.5q 0.sg( q akg th followg fv mmbshp fuctos: xp[-((x p/6/(p/4^] NB xp[-((x p//(p/4^] NS xp[-(x /(p/4^] O xp[-((x -p//(p/4^] PS xp[-((x -p/6/(p/4^] PB c VI. SIMULAION EXAMPLES Cos th two-lk mapulatos. h stuctu of th jot mapulato s show fg m x Fg. Mmbshp fucto gaph l q l q m g h smulato sults of oubl aaptv algothm ths pap a as follows. Fgus 3-6 show th posto tackg posto tackg o vlocty tackg a vlocty tackg o of two jots whch show that th popos mtho s ffctv. Fg. two jots mchacal am stuctu h yamcal quato of th mapulatos s: D( q q C( q q q G( q Wh cos( q s( q cos( q s( q Dq ( cos( q s( q ( s( q cos( q q ( s( q cos( q q C( q q ( s( q cos( q q 0 Fg. 3 Posto tackg cuvs of two jots cos( q q s( q q ( cos( q Gq ( cos( q q s( q q All Rghts Rsv 07 IJARCE 43
4 44 Itatoal Joual of Avac Rsach Comput Egg & chology (IJARCE Volum 6 Issu 9 Sptmb 07 ISSN: Fg. 4 Posto tackg o cuvs of two jots Fg. 8 posto tackg o cuvs of two jots Fg. 5 Vlocty tackg cuvs of two jots Fg. 9 Vlocty tackg cuvs of two jots Fg. 6 Cotol put cuvs of two jots o pst th avatags of th popos mtho w compa th sults fgu 3-6 wth th smulato sults of th comput toqu cotol as show fgus 7-0 Fg. 0 Cotol put cuvs of two jots h smulato sults a obvously btt tha th fuzzy aaptv cotol aft th oubl aaptv cotol s aopt ths pap; th posto a vlocty tackg os of th popos mtho ca also mo aply covg to zo h cotol pfomac of th systm s mpov. VII. CONCLUSIION h ual aaptv cotoll s sg ths pap. h latv vaabls of obot stuctu a appoxmatg wth aaptv law a th ola fcto volum of obot s compsat by aaptv fuzzy cotol law. h xpmtal sults show that th ual aaptv cotol law ot oly has a fast covgc sp a tackg accuacy but also ca ffctvly suppss th vbato of th systm so t has btt cotol pfomac. Fg. 7 Posto tackg cuvs of two jots
5 Itatoal Joual of Avac Rsach Comput Egg & chology (IJARCE Volum 6 Issu 9 Sptmb 07 ISSN: REFERENCES [] Zhou J.L Zhag W.H. A obust tackg cotol of obot tajctoy. Cotol Egg vol. 3 pp [] Wag S.X Yu L Xu. J.M. aaptv obust tackg cotol fo obotc mapulato. Cotol Egg vol. o. 05. [3] Basctta. L Rocco. P Rvsg th Robust-Cotol Dsg fo Rg Robot Mapulatos.Robotcs IEEE asactos o. vol. 6 o. pp [4] Ch Y B Y. J Gao J. Aaptv Fuzzy Comput-oqu Cotol fo Robot Mapulato wth Ucta Dyamcs. Itatoal Joual of Avac Robotc Systms vol. 45 o. pp [5] N X Lu Q. Aaptv fuzzy slg mo cotol fo mapulato bas o MIMO systm. Joual of Chs Agcultual Mchazato vol.36 o. pp [6] Baghl F. Z Bakkal L.E Lakhal Y Mult-put Mult-output Fuzzy Logc Cotoll fo Complx Systm: Applcato o wo-lks Mapulato. Poca chology. vol. 9 pp [7] Shao. K Ma Q. Global Fuzzy Slg Mo Cotol fo Mult-jot Robot Mapulatos Bas o Backstoppg. Fouatos of Itllgt Systms. Spg Bl Hlbg pp [8] Al-Dabbagh.R.D Kshl.A Mkhlf. S t al. Systm tfcato a cotol of obot mapulato bas o fuzzy aaptv fftal voluto algothm. Avacs Egg Softwa vol. 78 o C pp [9] Yu.Z. G Sh.Y.M Sog.Z. M. Mchacal am obust aaptv moto cotol. Cotol thoy. vol. 8 o. 7 pp All Rghts Rsv 07 IJARCE 45
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