PID Controller Design for A Nonlinear Motion Control Based on Modelling the Dynamics of Adept 550 Robot

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1 nenonl ounl o nul Engneeng n Mngeen EM Vol. No. pp. 9-7 Alle onlne hp:// SSN 7-66 onolle egn o A Nonlne Moon onol Be on Moellng he nc o Aep 55 oo en Zhng epen o Mechncl Engneeng echnolog uue Une no ll oo 9 4 Noh n See We ee N 4797 US hhzhng@puue.eu ecee.5.; ee.6.; Accepe.6. Ac he ulple ln oo nonlne e n genel whoe chcec polnol no unque n whoe conol chee epen on pcul openg conon. Aong ll n o conolle ue o oo conol nel 9% conolle n he nul wol no onl ue o plc n eecene u lo o l o copng wh uncene n nonlnee n he e. Snce o o conolle e egne e on l n eo eho o lc-o pln o he pecon oon conol o oo oe ele o egn he conolle e on he hecl oel o he oo. h ppe ece o conolle egn o nonlne oon conol e on he hecl oellng o he nc o Aep 55 oo. he genel elonhp o he conolle egn on he ooc nc n he plnne jeco e ee. he nl n ulon o cloe loop nc nce eecene n n ccue jeco cng. he eul cn e pccll genelze o ohe ce o conolle egn o ohe oo n he nul pplcon. e wo: nonlne oon conol oo conolle. NOUON he ulple ln oo nonlne e n genel whoe chcec polnol no unque n whoe conol chee epen on pcul openg conon. Aong ll n o conolle ue o oo conol nel 9% conolle n he nul wol no onl ue o plc n eecene u lo o unel n el. conolle cn e egne ccong o n unng eho een he hecl oel o he e no lle o uncene n nonlnee wee oun n he e. conolle h l el uneoo phcl enng: he popoonl conol poe eong oce h popoonl o he nnneou eo eween he e pon n he poce le he oen u en up wh e-e eo ue o con g o o; he negl conol conue coece oce h popoonl o he u o ll p eo ulple he own e nel o h he e-e eo cn e elne u cue oehoo o he e epone; ee conol nouce o e he oehoo ue poucng counece oce h popoonl o he e o chnge o eo. Wh hee unenng oen engnee who o no he ecll nng o conol heo cn egn conolle o he nul poce whoe ne uncon e unnown o he. h wh o o conolle e egne e on l n eo eho o lc-o pln. owee o he pecon oon conol o oo he l n eo ppoch no n ecen w. n ecen e oe n oe eeche o egn een pe o conolle e on heoecl nl o el wh nonlne o non-eplce o een pplcon uch noo lp oo go o lne-o-gh e wo wheele uonoou lncng oo pllel npulo ec. [ ]. eone h he heoecll egne conolle cn e opll une o he nee o pecc e o genec o ee peonce hn h he l-n-eo lenng egne conolle h. h ppe ece o eploe heoecll egne conolle o nonlne oon conol on he o he hecl oel o Aep 55 oo. A one o he o coonl ue oo n he nul poucon lne he Aep 55 oo ou SAA oo wh hee oonl jon n one nlonl jon Fg. -. houle eoe wh he oonl jon elow wh he oonl jon n w wh he oonl jon 4. ecl oon ccoplhe wh he nlonl jon. Snce eue ll oon enelope whle pee n plo e elel hgh Aep 55 oo cn e oun n echncl el el EM

2 Zhng hnlng pcgng chne enng cewng n n ohe opeon equng n pece uoon.. E YNAMS OF AE 55 OBO. he n oon n nee nec elonhp Accong o he en eneg - coone he z - n he econ o he jon Aep 55 h he pecl ce o pllel z e connece wh he g nne n oue ln. he jeco o he oo eene he oon o hee wo ln n he w he oonl jon oe ou he z o ju he gppe ngle u no o chnge he jeco. n oe o ocu on he jeco u whou lo genel we ue he w o ngle zeo. heeoe he coone e o ece jeco n ln poon cn e pl peene ollow Fg. : Fgue. Aep 55 oo wh jon locon [] Neele o coplee u o conolle egn e on he hecl oel o Aep 55 enngul o nul pplcon. he geoec enon o Aep 55 e hown n Fg. o oellng n ulon. Fgue. op ew o Aep 55 wh jon oe ngle le. l he - pee o he nne n oue ln. le. - ee n α nne Oue Fo he nne ln n oue ln he coone noon wh oon n nlon coponen ece wh he : A z z α Fgue. Aep 55 enon [] n n α α nα n nα nα α n EM

3 Zhng EM he ple noon o Aep 55 o he e o he gppe ollow: A A n n n n Nocng he elonhp he ngul poon o he oo n he ngle ou peou z o ol o new : he gppe hozonl poon cn e epee : n n Fo Equon he oo ngul poon cn e ee: ± ± n n 4 whee 5. Fow n Bcw Veloc n Acceleon elonhp he ow eloc cn e oun o Equon : 6 whee con n n 7 An he cw eloc cn e ee ollow: o n n n 8 Alo he elonhp o he ow cceleon cn e eene: 9 whee n n he elonhp o he cw cceleon e ollow: n * n n. Moellng n Sulon o he nc o Aep 55 oo Fo he ple ucue o he oo hown n Fg. 4 he nne ln n oue ln e epeene g wh he cenl he cene n he gppe n lo e olze. Ou o eel coonl ue eho o oelng he oo nc gnge eho eploe o eelop he nc oel o Aep 55 oo. he gnge uncon he eence o he

4 Zhng EM ol nec eneg n he ol poenl eneg V.e. V Fgue 4. Sple ucue o Aep 55 oo Fo he ooc ucue hown n Fg. 4 he ol nec eneg epee : pc oon whee c c c pc oon 5 An he ol poenl eneg V gen : V g V png V 6 whee n g g g V g n g g 7 png V 8 hu he nc o Aep 55 oo ece gnge eho ollow: V V 9 Suung Equon 8 no Equon 9 eul n: 7 n g 7 n g enong n coneng png oque png o he nne n oue ln Equon cn e ewen : png whee 7 7 n n g g

5 Zhng png whee coecen. ngul plceen eg png png copoe o he png e e e ec Fgue 5. nc epone: ngul plceen ngul eloc eg/ec eloc o e eloc o e e ec Fgue 6. nc epone: ngul eloce cn e oee h he nc oel o Aep 55 oo hghl nonlne e. he ulon o he oo nc wll e peoe wh A-Bhoh ecue chee whch h een pple o genel open-chn pe npulo n poen o e uch oe ecen n copuonl lo hn he nonecue eho. h epecll he ce when he e hghl nonlne. Fg. 5 n 6 pl he nc epone o ngul plceen n eloce wh he nl conon gen gppe poon. he ulon llue he nc oelng o Aep 55 eelope gnge eho n eone he l o he oo oon. h een oee h he hee he lo he longe e he e o e ele; n when he lo hee hn cen wegh he gppe e ecoe unle..4 Sene o Sc oque n Open oop onol n he open loop conol o Aep 55 oo he ene o ngul plceen o c oque nce how well he gppe cn hol poon. hee ene o ngul plceen o c oque e ollow: g g n n Von o c oque n he open loop wll pouce eo n ngul plceen. A cloe loop poon conol ele o e h ue Fg.7. Fgue 7. oo conol g. OBO ONO AN S SMUAONS. oo nc wh onolle j h g ue h he oo ng he nne n oue ln e he e pe o oo. oneng he B V oo pee nc o he wo ln ece : n j j n j j j 4 EM

6 4 Zhng Snce whee he ge o he wo nc equon o oo ln n ng oo epee n Equon 4 cn e cone no ngle one: e B e V 5 he conol lw o he conolle n oo e he nne o oue ln ollow: V 6 he loc g e on he ne uncon o Equon 5 n 6 o he oo conol hown n Fg. 8. Fgue 8. conolle ooc oon he ne uncon o he cloe loop e : e B e B e e 7 oo ocu whee he nonlne e e ee unce o he e: g g n n 8 lcng he hee pole p ς ωn ± jωn ς o he chcec polnol ono he le hl-plne n egnng ς ω ± jω ς he onn pole n n n p o npule he oo locu el he ollowng elonhp on he conol pee: ω ς ω p ω n n p e n e ς ωn p e Be 9 oo locu nl o he nne ln n oue ln o he une conolle eone n Fg. 9. oo ocu gn A gn A el A el A Fgue 9. oo locu nl o nne ln n oue ln EM

7 Zhng 5 EM Nocng he nc o he nne o oue ln cn e ece e e B Equon cn e ewen n o: whee e e B B e e n n n n g g. jeco lnnng he conolle cn e egne o peo jeco cng o he nl poon o o o he nl poon e. Whou lo o genel he oon n ue wh ollowng conn: o > n conn cceleon n e nel [ ] conn pee n e nel [ ] n conn cceleon n e nel [ ] whee o gen conn pee o he jeco coponen cn e epee ollow: < < o o 4 Fg. pl he ule jeco ece n Equon n 4 o gen e o pee. An he jeco coponen cn lo e epee n he l w. hen he ee ngul plceen eloc n cceleon cn e eene: ± ± n n 5. Sulon o he loe oop onolle oo nc enong [ ] X Equon cn e ewen X X 6 e Equon 5 he jeco ele ce n eco gen Equon cn e eene. hen he cloe loop conolle nc o Aep 55 oo epee n Equon o ung he plnne jeco cn nuecll ule.

8 6 Zhng ee plceen n ee eloc n / e ec e ec ee cceleon n / e ec Fgue. ee jeco plnnng n n oe o e he eecene o he conolle e on nc o Aep 55 oo he ollowng ce gen o ulon: ue he conolle wh ccl p o oh nne ln n oue ln he gppe oe o he nl poon o he nl poon 7 54 whn ec. Fg. how he ulon eul o Equon 6 ecuel nege A Bhoh eho. plceen n plceen n ee cul e ec ee cul e ec Fgue. Sulon o conolle jeco cng cn e oee h he jeco cng poce n le. eluon gen n he ppen. 5. ONUSON he conolle egn o nonlne oon conol e on he hecl oellng o he nc o Aep 55 oo eploe. he genel elonhp o he conolle egn on he ooc nc n he plnne jeco e ee. he nl n ulon o cloe loop nc nce eecene n n ccue jeco cng. he poceue n nl o h eech cn e pccll genelze o ohe ce o conolle egn o ohe oo n he nul pplcon. enngul o opzng he coonl ue conolle whou l-n-eo eng n epecll pon o pecon opeon. Acnowlegeen he uho nceel hn Fo Moo o. o ponong h eech p o Fo Sewhp unng. he helpul cuon wh oeo ell Bu he Une o Aon lo gel ppece. 6. EFEENES [] n.. ee.. n hoh.. -Augene Ape onol o A o Mo o Se An ounl o onol Vol. 4 No. une pp [] Oung.. Zhng W.. n F. X. Wu Nonlne onol o jeco cng wh oneon o he egn o onol Mehoolog oceeng o he EEE nenonl oneence on ooc 8 Auoon Whngon M pp [] wu. o. Yoo M.. n Ohuch A. 5 Moon egn o noo Blp oo wh onolle ounl o ooc n Mechonc Vol. 7 No. 5 pp [4] Su Y.X. Sun. n un B.Y. 5 egn o n enhnce nonlne conolle Mechonc Vol. 5 pp. 5 4 [5] hee O.Y. Shu M. n An Z. 6 egn n eelopen o wo Wheele Auonoou Blncng oo EEE Suen oneence on eech n eelopen Shh Al Selngo Ml une 7-8 pp [6] o.m. Vg E. ooe E. oeo.. n ez.. 6 neuc lne onol o Mnpulo oo he 6 oneence on nc nuenon n onol. Augu -6 Queéo Qo. [7]. wu. Mngw Y. Yoo M. n Ohuch A. 6 lnng o oon conolle o n noo lp oo Acl e n ooc Volue Nue Noee pp [8] Su W. 7 A Moel eeence-be Ape onolle o oo Moon onol o No Eplcl nown Se nenonl ounl o nellgen onol n Se Vol. No. Sepee pp [9] Aep 55 oo nucon noo [] ollech.m. 98 A ecue gngn oulon o npulo nc n cope u o nc oulon cople ncon o he ASME ounl o nc Se Meueen n onol Vol. No. pp EM

9 Zhng 7 Appen: Vlue o e pee n eluon he lue o he e pee o he oo nne n oue ln e le ellow o nuecl ulon: he ne uncon o he nne ln: nnen he ne uncon o he oue ln: Ouen he conolle o he nne ln: 9. N N/. N he conolle o he oue ln:.97 N.97 N/.76 N he poon eo ene e jeco cul houl he ollowng equeen he nl poon: e. 5 he cul eo he nl poon e. 94. he uncon N e e N houl he ollowng equeen oe he ene jeco:.5 he cul uncon.8. EM