Adaptive Nonlinear Control Algorithms for Robotic Manipulators

Transcription

1 Proeedn o e 7 WSES nernaonal Conerene on oaon noraon Caa Croaa Jne -5 pp8-88 dape Nonlnear Conrol lor or Roo Manplaor EUGEN BOBŞU DN POPESCU Deparen o oa Conrol Uner o Craoa Cza Sr No RO-585 Craoa ROMN p://wwwaero ra: - n paper oe adape nonlnear larale ene ed n e onrol o roo anplaor are preened e nonlnear onrol law and ae eedak are ed n aen a lnear npop eaor or e onrolled e For e den o e adape nonlnear onrol e ea eedak np-op lnearzaon and e eod o raden are ed e nonlnear onrol law aee alo deopln Coper laon are nlded o deonrae oe eoreal ape and e perorane o ee onroller or a pal rre o roo anplaor Ke-Word: - Roo ar Nonlnear onrol nearzn onrol dape onrol nrodon e onrol o e roo anplaor an poran area or reear deelopen and anarn we onder oe approaon on e roo dnaal odel we an do a lnear anal o e anplaor onrol prole Wo ee approaon we ae a nonlnear odel e eld o nonlnear onrol eor lare a lo o eod o onrol: e oped ore eod e ro onrol eod e adape onrol eod [] e ore onrol eod e ee [] [] [7] e onrol rere e knowlede o a aeaal odel and o oe or o nellene o a on e odel e odel o a roo oaned ro e a pal law oernn oeen ere are an eod o oan e dnaal odel ee [5] [7] [9]: arane eod Eler eod d'leer eod Kane eod e Here ed e arane eod o oan e dnaal odel or a roo w work n lndral oordnae n e la ear nan adane ae een ade n e deelopen o dea a eedak lnearzn and np-op deopln ene [] [] n paper n e eedak lnearzn ene a larale nonlnear onrol law oaned or a roo anplaor - wdel ded n [] or o onoarale and larale ae n an praal aon oe roo anplaor paraeer are nknown; ereore an adape onrol rae rered n order o anan e perorane o e onrolled e n paper an adape onrol law aed on reerene odel or e eal lnearzed odel alo dened e paper oranzed a ollow: n Seon oe a o e ea lnearzaon eor are preened n Seon aeaal odel o roo anplaor are analed wle n Seon e adape nonlnear onroller are deeloped and Seon 5 nlde oper laon Fnall Seon olle e onlon e Saeen o e Ea nearzaon Prole larale nonlnear e an e dered n ae pae eaon o e ollown knd: j j j n w are oo eor eld e prole o ea lnearzaon a eedak and deoorp on n ranorn a nonlnear e no a lnear one n a ae eedak and a oordnae ranoraon o e e ae e ea eedak lnearzaon eor wdel preened [] Ne oe a rel o eor are preened ee rel are appled n Seon were adape nonlnear onrol law are deeloped or roo anplaor Conder e e derae o a non

2 Proeedn o e 7 WSES nernaonal Conerene on oaon noraon Caa Croaa Jne -5 pp8-88 n : R R alon a eor eld : n Denon larale nonlnear e o e or a a relae deree r r } a a pon : k { j or all j or all or all k r and or n a neorood o e ar r r nonnlar a r r r r < eore e e e nonlnear e o e or Sppoe e ar a rank en e Sae Spae Ea nearzaon Prole olale and onl : or ea n e dron G a onan denon near ; e dron G n a denon n; or ea n e dron G nole Maeaal Model o Roo Manplaor We onder e roo anplaor w ree ae dered n F w dren a d oor onrolled n rren For roo ar w work n lndral oordnae e kne ener : K 5 e poenal ener : P arane eaon o oon or a onerae e are en : d d τ 7 were an n-eor o eneralzed oordnae τ an n-eor o eneralzed ore τ and e aranan e derene eween e kne K and poenal P enere F Srre o a roo anplaor Now we all e arane eaon o dere e eneral roo ar dna e e araerzed a e o ree r order derenal eaon: τ τ 8 τ were repreen e oen o nera o e old w repe o e a z; are e old ae; τ τ τ are e eneralzed ore For e ennn we onder and we noe e ae eaon are e ollown: 9 were ; [ ] and [ ] [ τ τ ] z

3 For e e 9 we onder a op arale e eneralzed oordnae and : n aon e aeaal odel larale and a wo np and wo op e ae eaon are e ollown: [ ] and [ ] τ τ τ 5 n aon e aeaal odel larale and a ree np and ree op dape Nonlnear Conrol aw e aeaal odel n e larale ae o e or 9 were e np are e eneralzed oordnae τ and τ n aon we onder a op arale e eneralzed oordnae and : For e we ae deopln ar 5 and e nonlneare aneln eor Un relaon 5 and e np-op e an e wren n e or: 7 n ea all ow a e ar or aeaal odel o e roo nonnlar and e eor relae deree {r r } { } Beae e deopln ar 5 no nlar pole o den a nonlnear np: 8 a e oaned lnear e a e raner ar: H 9 pon on e lnear e an addonal eedak o e or: re re en e oaned e a a lnear np-op eaor dered e ollown daonal raner non ar H n e larale ae or e e we onder a op arale e eneralzed oordnae and : Proeedn o e 7 WSES nernaonal Conerene on oaon noraon Caa Croaa Jne -5 pp8-88

4 ; For e we ae deopln ar and e nonlneare aneln eor: Un relaon and e np-op e an e wren n e or: 5 n ea all ow a e ar or aeaal odel o e roo nonnlar and e eor relae deree {r r r } { } Beae e deopln ar no nlar pole o den a nonlnear np: a e oaned lnear e a e raner ar: H 7 pon on e lnear e an addonal eedak o e or: re 5 re 8 re e oaned deopled loed-loop e a a dered eaor e pleenaon o e oaned nonlnear onrol law e 8 or e r ae and 8 or e eond ae apered oe o roo paraeer are nknown or arale n e lowl n order o oeroe dadanae an adape onrol law aed on reerene odel approa an e dened For e ne o e adape alor e eod o e raden ed oon e ollown reron [8]: He e Q 9 were e and ar H > e olon o e apno eaon G H H were G a er poe dene ar and reerene odel ar e adape alor wll e: D d d Ψ were D a poe dene ar and Ψ Ψ e raden o Ψ n rappor w paraeer e adapaon law or e onroller paraeer o e or [ ] [ ] d d d d γ γ For e aeaal odel 9 8 and repeel 8 and o onrolled roo anplaor we ooe a a reerene odel a raner non o order wo aoaed w e neral o e Mlpled ole Vale o Error E reron Proeedn o e 7 WSES nernaonal Conerene on oaon noraon Caa Croaa Jne -5 pp8-88

5 Proeedn o e 7 WSES nernaonal Conerene on oaon noraon Caa Croaa Jne -5 pp Slaon Rel wo laon ae were ondered n order o e e perorane o e propoed adape nonlnear onroller e laon wa done or e odel eaon 9 e nonlnear onrol law 8 and e adapaon law e perorane o e onrolled e preened n F F e eolon o anlar poon preened n F and e poon n F e reerene odel op er e real op and e onrol np are preened onl or e r np-op annel n F and F 5 repeel n F e plane rajeor o e roo ar preened nle er reerene deped or e r annel Fnall F 9 ow e onrol np We ded n o laon ae e onerene o e onroller paraeer or e aon wen one or ore paraeer o e proe are arn n e wa reled a kl onerene o ee paraeer Error re [rad] 5-8 e [] F Reerene odel op er e real op 5-5 re [] F nlar poon ae - 8 e [] Poon er reerene 8 e [] F Eolon o e poon ae e laon wa done or e odel eaon e nonlnear onrol law 8 and e adapaon law e perorane o e onrolled e preened n F 7 F 9 F 7 ow e e eolon o e eneralzed oordnae e anle - er reerene n F 8 e reerene odel op er e real op Y a poon [] [N] e [] F 5 Conrol np or e ae 8 Plane rajeor X a poon [] F Plane rajeor ae

6 Proeedn o e 7 WSES nernaonal Conerene on oaon noraon Caa Croaa Jne -5 pp8-88 [N] e o laon ae ow a e oaned perorane ood we ae er all oeroo e eln e are all and e eolon o e oand are aepale re [rad] nle er reerene - 8 e [] F 7 Eolon o e anle ae Erorr e [] F 8 Reerene odel op er e real op e [] F 9 Conrol aon ae Conldn Reark n paper an adape nonlnear lnearzn onrol ene or roo anplaor wa preened e den o e nonlnear onrol law e e ea eedak np-op lnearzaon e odel o roo anplaor are ded n order o pleen o e onrol law Un larale odelln and onrol den ea lnearzn onroller are oaned n adape onrol law aed on reerene odel approa dened n order o oeroe e dadanae o paraer nerane For e ne o e adape alor e eod o e raden ed Coper laon perored n order o e and aldae e propoed adape nonlnear onroller Fro e laon rel an e een a ood eaor o e e 7 knowledeen work wa parall ppored ro e ran no 79 CNCSS Reerene: [] KJ ro dape Feedak Conrol EEE ranaon on oa Conrol Vol75 No 987 pp 85-7 [] E Boaş Nonlnear lor or e Roo Conrol nnal o Uner o Craoa Eleral En Sere no pp - [] J Foard D Norand-Cro See nonlneare Maon Par 99 [] E Frend e Srre o Deopled Non near Se nernaonal Jornal o Conrol Vol no 975 pp -5 [5] B Gorla M Renad Modele de Roo anplaer: plaon a ler oande Cepade- Edon oloe Frane 98 [] dor Nonlnear Conrol Se rd edon Sprner-Verla Berln 995 [7] M ăne ndral Roo Conrol Se and lor Unerara Craoa 99 [8] D anda R ozano M M Saad Dre dape Conrol lor: eor and pplaon Sprner-Verla 988 [9] J R Slln Fndaenal o Roo nal and Conrol Prene Hall 99 [] *** MB Reerene Book e Mawork n Nak M