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Some results on feedback stabilization of a one-link flexible arm

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(1)Some results on feedback stabilization of a one-link flexible arm Sylvie Icart, Juliette Leblond, Claude Samson. To cite this version: Sylvie Icart, Juliette Leblond, Claude Samson. Some results on feedback stabilization of a one-link flexible arm. [Research Report] RR-1682, INRIA. 1992. �inria-00076905�. HAL Id: inria-00076905 https://hal.inria.fr/inria-00076905 Submitted on 29 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(47) A|u #v„3‚ €/~@|7~8<~@|& ‚ ()F* , “ , | ~‡€€&) v |7s7~@‘„3‚ €&~{|7~8 vP<v'3~{|7vƒo~@| ~‡€€/~ ~{x‡†s|7‚ † „3‚ €/~@|7~8 vb<~‡†W‚d3†x cv <~‡€/|€8† t#~{| †s$^ Z*†|us7~, ) €/t3‘ *|7 3†Q|F& 6 ) i , | ) 6 ) i , |   ) j ) i ,  ) \ . e ) i , 6 ) i , e )  j ) i ,  :~@|7 qe )  6 ) i , |  )  69pu l vM|t3€y„#su‚8 v |u #~‰€:„3‚W~@<|z=*~@*<t3‘’|u~{‚dK†!K‘’‚W |7s †

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(54)  )F*-,  e ) OA M‹ R. O iA ŠNR O iA (R ^. 6 )i , ) e )  ) ,i ^ ,  )i ) “. O iA /NR. npoLq&q9rts. k Ž.su‚

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(57) k Ž.su‚

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(61) > V , :~{|u >   x , >R , T OU€ \) e ) O:@ R@R,O'4r o#z= †W€7€&t  „#|u~{‚d R“ l vM| t3 €_#‚A~@<P |us7‚)<t.‘’v €/

(62) ‚  vš„3‚ƒ€/~{|u,~ 8 v t#3‘|7~{‚d3€?|7 3†Q|:~@x{x:z3v t3€&v|7‚  ‚ds$ † l9 †„#t#‚8)> x{~, v  t#3‘|7~{‚d ‚Ws|7 #vw&€ €/|uv K“ + %  ‹ Qp  . 3 2 „ „)4 \ ()F* , . 3 2 „ „)4  3 )\ 6 ) 3 ) o + % ~‰€`|u #v|7‚d|†x]v #vM$s 6 ‚  |7 #vw&€ €/|uv Ko + ,  ‹ Qp D„u )\  ) „u )  u )\  ) j ) u ) /:~{|u  )   = )F, * , l8@:mnpc > f > V , RhghghghR )  †!  ) t + |  ‹ Qp= N O 2 ` > V ,

(63) > e ) OA@OM)‹ R u ) OA@ R R |  $~. k Ž.su‚

(64) . O p<“@‹)Ro 8v 3†8 v. k Ž.su‚

(65) . O i<“ /NR &. &. l +  l r ,. l +  l r % ) `O t > e > V ,

(66) . . 2„ $. . ) :O @GM‹)R„u ) AO @ R R $. .

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(68) ) lr l l r. +. . Op2 „. ` t. ).  3†Q|7v8 vMs,|7 #vw~{#~@|7~‰†Qx)‘‚W*<~@|7~@‚W3€†Q||7~ v/rb r o|u #v# t3‘’|7~@‚W +"~‡€y|7 t3€a vQ‘’s7vˆ†W€/~@ #“g| €y|7~ v> <vMsu,~ 8d†|u,~ 8 vz3vM~{ _z3‚Wt* <v  O €/~{.‘’v|7 #vwz‚dt#*<v<<#vQ€u€y‚,+ <~@vMx.#€|7 #vwz3‚Wt#* v<#vQ€u€y‚ 2 †! 3 ) o †!  o~@*|7t#su]o#|7 #vz3‚Wt* <v <vQ€7€:‚ 8†Qx{x <vMs7~ 8d†|7~ 8 vQ€‚  2 †Q*7u ) Ro w  + |7vM!#€U|u‚bMvMsu‚#“  ‚ '3#~‡€/ K|u #v?„#s7‚ ‚ uo 8v?‚W#x K#vMv  |u‚ €& #‚ o]=z †„#„#x@~‰‘M†Q|7~@‚WK‚ Ul]w †W€u†x{x@Dv : €—)s7~@3‘’~@„#x{v  l]l o|7 3†Q|Mo t#*  vMsy|u #vw‘’‚W.€/|7s †~@<| w  +  r<o#|u #vw&€ €/|7cv  Op “{)‹ R .†W€:‚W#x ‚W#vh€/‚dx{t#|u~{‚W' &,O 2  r  3 )  r R“. w k Ž.su‚

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(70) , 0 Q  |u #v‚W|7 vMs: 3†!  !o  su

(71) ‚  O p<“@)‹ R &. ()+*-, 7O ‹YM‹)R 2 0  () 7O ‹R \ 3 0 )  $   t3€’o3z= t3€&~{  |7 #v]<v '3#~{|u~{‚d i “ ŠB‚  u ) †! šs7v x‰†|u~{‚d i “{‹ p5& = , t) i , $ 2 0   )+*-, > V , l > e ) O:@O )‹ R u 0 ) O:@ R ()+*-, Ou‹M‹R  : #vMsuvkl > ~‡€y|7 vB~  ‘’‚

(72)  „3‚d#vM |y‚ |7 #Pv  ~‰† d‚W3†Qex *†Q|7s7~ j ) “,R– vMx@~, ~@3†|u~{  2 0 z3vM|7`vMv  †!'Oi “{‹(R & ) $ t O >  = , l > i , ROe ) OA@OM‹ R u ) O:@ Rv  0  )F*-, ( )F*-, O7‹YM)‹ R >V , †! oz)*‘’‚6_z~{#~@  |7 #~‡€`s7vMx‡†|7~@‚W  :~{|u *s7vMx‡†|7~@‚W Oi “ / R & ) ) ‹ t O > l >  = , ROe ) OA@OM‹ RUu ) O:@ R   = , t O >  = , l > i , RGe ) O:@GM)‹ R | . $  )F* ,  )F* , > V ,  )+*-, ()F* , O7‹ ‹)R >V , . Oi {‹ qNR. Oi {‹ ŠNR Oi {‹(R Oi “{‹ ŠNR Oi {‹/NR . `y~21 v s7vM |7~‡†|7~@ z3‚W|u  v z3vMs€ ‚]|u #v:„#s7vc8<~@‚Wt3€)s7v x‰†|u~{‚d?|&:~‡‘’vT:~{|u ?s7vQ€&„3vQ‘’|)|u‚B|7~ v o8v:‚Wz#| †~{]& . )\ u 0 )  . r

(73) . Oi {‹ ˜NR.

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(76) ‚  + v  #‚ :x{v =dvB‚ `|u #v?7€ #€&|7v  : €`3†Q|7t#s †x vM~ WvM=  ‚d$s *€)~‡€ |u <t.€#vM<v <v  “$Ž.su

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(78)  ‹r 0   r :~@|7

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(80) Ž#‚Wswv#† „#x@v o- " MA  €/ #‚€ |u #v?v8 ‚dx{t#|u~{‚WK‚|7 #v €7#€&|7v : €y|u‚W|†QxvM#vMs?

(81)  ‚ds?†*€&€/|uv :~@|7 I+ i "3v ~{zx{v5 ‚)<vQ€o t##~@|†Qs$B †W€7€o]†! ‘’‚d3€/| † |w€/|7~21#vQ€7€ =<+qWr<o(†Q*  ‚ds]<~ 1vMsuvM<|U8d†x@t#vQ€ ‚

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(83) N [: €T ~‰€7€&~{„3†Q|7~@‚W*~{3‘s7vQ†d€/vQ€R:~@|7

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(91) rD g<|us7‚)<t.‘’vK|7 #vy~@x{z3vMs7| €/„.†W‘’vQ€ 

(92) | O r M‹)R †! +  , O r M‹)RTO |7 #v;j ‚Wz3‚dx{v8 €/„3†d‘’v ‚

(93) |  t#3‘|7~{‚d3€T:~‰‘ *†

(94) = ~{|

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(98) =  '+ O =  R 7O ‹)R  UO =  R7O rNR  r f  . . k.

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(102)  > |  r_z3v?|7 #v?vM~WvM)8d†x@t#vQ€:†W€u€/‚ ‘’~‡†|uv :~@|7  > “\`yv'3~{  u| #vMK|u #vB„3‚ €&~{|u~,8 vBz~{x{~@#vQ†Qs  ‚W?s m d‚ '++z= %m O$ # R    $ #    .   #  + ‚Wv?‘M†Q €&vM|:|7  v  ‚dx{x@‚ :~@  ?x{cv *† & c  > f 476AE&:tCWO <>R< 4 ! + ]p4F>VUM?<b6CW<'AL> >E    " ! #Mc RA)NN  j UW< \  :4FO 8  , %m OR > @  > R  # =* > | l&5 > |  % ^ npoLq&q9r*s  #vv 3 t3†x@~{7| †z3‚ 8 v~‰€‚d=z 8 ~{‚dt3€’o#~@<|uv Ws †|u~{  w=z „.†s7| €’“”y‚ L ‚Ws:v 8 v $s c f > f o]‹ +@ + o ‚WvB 3†d€ &  J N! V , f >  > ` f   | , # , = O t f >  > ` f R | &l  v= N O t f >  > Or R ` f Or R R | % , +  ‹ # O t f > = > `= f R | l& v= N O t f >  > Or R%` f O rNR R | % , + OU= N  ‹ R # O t f > OU= > R ` O= f R R | l&šz)*— ‚W~@3‘M†Qs vDS : €~{v3!t.†x{~@|7~@vQ€ % , + OU= N  ‹ R # O t f > > |  >` O= f R R | l& % + OU= N  ‹ R  J f > > |  > ` , OU= f R   | . . U.

(103) ) W‚ suvM‚8 vMsMo9 ‚dsBv8 vMs? f  O!Ro% f  ^ , O= f R  †* €/~{.‘’v7c >Af_~‰€w‘’‚

(104)  „#x{vM|uvB~@ oH ‚Ws v8 vMs? ( r<o#|7 vMs7vv ~‰€&|€bc n > f o]‹ +@ + o3/€ t.‘ *|7 .†|Mo ! | t n >  > ` ‹ O= f R    (   NV , yvM.‘’v o z)=|7 #v ~@#v3 t3†x@~{|7K†Qz3‚8 vƒo  ‚Ws?vc8 vMs$ 1O= N  , R ( o)|7 #v s7v v ~‰€&|€ c f > f o f >   { o)€/t.‘   z{ |7 .†| &  J N! V , f &> !>` f   | + O= N  ‹ R  J f > >|  >` , OU= f R   | : ) j ~@3‘’v O(R~‰T € <vM.€/v~{#  +?o#|u #~‰€`v * #€`|7 v „s7‚ ‚ u“ ". 32  hi % A)Mj  *‚W.€/~. vMsy‚ |7 #vw‘’‚d<|us7‚Wx &€ €/|uv Op “ i Ro Op “ & Rb&   ,O =     R O ` r G:O rS= R  R `b $ O r7r

(105) R  O =  R 7O ‹GrSR  r

(106)  †!š|7 v v #vMs$6 ‚ |7 #vw€/‚dx{t#|u~{‚d3€`‚ O & “ (R W~8 vM*z=]& , , - sO r7R  p‹ #    | l&  # = | l& = N  | O rNR  %. =v .†<8 vk&. O &  iNR. %. A)F A)N  S <> c > f5` <  \   : 4FO 8 ER\_<@4 P < ! \9Y ! A@>4BE ! 6XER\>BUW<  Y > E ! E&:E&Y6698 6@><@: 

(107) m []^U-4BAU # c C ?bE&G94 # <b6 k`  69476ER\ m S <> = N K = ƒ K ` <C-E694F>4BG<'K "! # O <> nX'+ 96 Y AU[>VU  > n:O7‹R  r "! ,. O # :n O Rb ( > O  R l& R) > O rNR. % j UW< !ac  4  j UW<AE ! > ?bEO O  ]   m   c. + `dn:Or R >| OrNR. $ O 7r R. .%@0 rD. , , ` = N O KO r Or7R%` # :n O R  O  GrSR l& _ R ` = ƒ O  O r Or7R%` # n:O R   OOr7R l& % %. O & & R. R. 6@> &` 4FO 4 <b6 V> UW<ALO E6 < # &O E ELC698 6@><@: 

(108) m   m  4B4 F\ n r C$ ` <@4 !P  ` E&Y ! #" ?L8 \ < < #&`  A K 698 6@><@: 

(109) m  =476Y ! 4 \9E&?L:lO 8k<bJC-E ! < ! > 4  OFO 8X6@> &` OF<"m •:v*†s?;|7 3†Q|š|u #v=‘’‚6 „3†|u~{z#~@x{~@|& ‘’‚W* ~{|7~@‚W O & “ & R zv |&8vMvM_n †! c > f=‚w|7 vM‚Wsuv p~‰€ |u #v ‘’‚d<|u~{ t#‚Wt3€(v3!t~,8d†x@vM<|(‚|u #v†W€u€/t  „|7~{‚d?‚ |7 #vM‚ds7v‹:~{?|u #vT ~‰€7‘s7vM|uv:‘M†d€/v “   ~@|7 ?|7 v`#‚d|†|u~{‚d € n; l o3‘’‚d*<~{|u~{‚d'O & “ & R8‘M†Q v3 t#~,8d†Qx{vM |7x?zv5:su~{|7|uvM †W€/&. #. %. ,. € O  R  > O R &l   > O rNR

(110)  , € L >.   > O rNRr.  . @pr

(111) . g<|us7‚)<t.‘’~{  %  ‹

(112) n:O rNRo3|7 vB‘x{‚ €&v=> x{‚ ‚d„K‘’‚d<|us7‚Wx]x‡† O p<“ q R *† Q† x‰€&‚_z3v5:s7~@|7|7v  †d€ & , , $ O Sr R# `/= N  % KO r O7r R  # € O R OO7r R &l  `=?ƒ  %   O r Or7R #  € O  R   O  GrSR l&  % % . &. O &  qNR.

(113) ‚Wsv3 t#~,8d†Qx{vM |7x o. . , €   $ sO r7R a` =      O r O  7 r R  % N. #vh‘’x{‚ƒ€/v!kƒx{‚ ‚d„K&€ €/|uv  d~,8 vM z)#O & “ i R8†*    ` O =  O=  R7Ou‹O7r R .  .  %   O r Or7R  , €      . `=?ƒ. O & “ ŠNR~‡€U|u #vMX&. O &  ŠNR. R  r

(114)  = N  % KO r Or7R  , € Osr7R    v= ƒ  %   Or Or7R  , € T Osr7R     O &  (R. rD g|7 v4 ‚dx{x@‚:~@ #o`v*†d€7€&t  v#O & “ ( R O ‚Ws O & “ i R R|u‚Kz3v 8vMx{x k „3‚ €&v&+ ‚Ws?vc8 vMs$ ~{#~@|7~‰†Qx8‘’‚W* ~{|7~@‚W O %  , R  +~; o|7 #vMsuv*v<~‡€/| €B†Kt##~.3 t#v*€&‚Wx@t#|7~@‚W O KO r7RD  O r7R R_ + ; ‚?O & “ (Rw€/t.‘ ;|7 .†| OOr RD  Or R R 1O  %  , R “  #vM€  r O ‚ds n  rNR o)|7 #~‡€B†d€7€/t „#|7~@‚W=~‰€„#s7‚8 vK|7‚Kz3v |us7t#v ~@ †„„v *<~, mB“  #v € A e r o |u #v`v x{x kƒ„3‚ €/v<<#vQ€u€ ‚ O & “ (R ~@ +~; s7v †~{.€y|7‚ zv &t3€/|u~ '3v“  ‚ |7 #vh†t#|u #‚Ws €: <#‚:x@v=Wvƒo~@|: 3†W€y‚d#x,*z3vMvM s7vQ‘vM<|ux, vQ€/| †z#x@~‰€& #v ~{ |7 #vh‘M†W€&vB‚†  vMv<z.†W‘$ ~{)8 ‚Wx8<~@ ?† €/~@ Wx@v5<~‡€/|7su~{z#t|7v |7v s$A~@ „3‚ €/~@|7~@‚W O Ž`“ * ‚Ws†

(115) o„#su~,8d†|uvw‘’‚

(116)  t##~‡‘’†Q|7~@‚W R “.   O=  R7O r Or7R.  #+v  ‚dx{x{‚ :~@ ?‚8|7 ~‰€€/vQ‘’|u~{‚d ~‰€T v8 ‚W|uvš|u‚_|u #vB„#su‚ ‚‚|u #vM‚Wsuv p<“ =vBt3€&vB|7 vB#‚d|†|u~{‚d3€y‚ v3 t3†|u~{‚d3€!O & “ (R“  ‚ vQ€/| †z#x@~‰€& š„.†s7| O ~ Ro 8v'.s€/|:vc< #~@z#~{|† l9 †„t##‚89: €V t#3‘’|u~{‚d  ‚Ws:|u #v?€7#€&|7v O & “ ( R`~@ €&vQ‘’|u~{‚W & “ p “{‹w†**†Q„#„#x, l]†W€7†Qx{x@vD: €:~{)8d†s7~‡†3‘v„#s7~@3‘’~@„#x{v~{ €/vˆ‘’|7~@‚W & “ p<“ p “—)†su|O ~@~ R)|u #vM  ‚Wx@x{‚ R€  s7

(117) ‚  †Bz‚dt#* <<v <#vQ€u€y„#s7‚d„3vMs77| ‚ - O Sr R O€&vQ‘’|7~@‚W & “ p<“ & R“.   

(118)    "!$#&%'( ) ~,8 vM O %  , R) + ;& o3x{v |O KO rSR O rSR@R*+ ;&. |7 vM ~@<|us7‚)<t3‘v|7 #va ‚dx{x{‚:~@ ?„3‚ €/~@|7~8 v t3‘’|7~@‚W3€`‚. + % O r7R p‹ 7O ‹Y O rSR@R |. –`t#| o †! j ‚o. lA+ % lr lA+ > lr . . O & “ (R o! ‚dsbr)cr “l vM|t3€. . ‹ ‹ m OR >:Osr7R@Rd @ c‹ > O 7r R  ‹ OR :> T  O r7R R |  p p >|. + Q #v 3†W€/&. z3vw|7 #vh€/‚Wx@t#|7~@‚WK‚ r“. Ou‹  R  O7‹T  R  O.  7O ‹T R   ‹ , O =  R. O &  /NR .  `O&‹Y R  $ sO r7R. . >  R  O  >  7 R   , %m OR >  R Km O >  R %@ c‹L  {z. m% OR > %R    > = %, `   >  , O =  R.   > O rNR $ O r7R%` O

(119)  >    R(]  . , m OR > T R  W=* >   %, ` # OU=* > R 0Yl&5 % Al + >  OR > T R   > O rNR $ O r7R lr Q† . > | O  >  R . .

(120)  3†Q #€|7‚*|7 vQ€/vb t#3‘’|u~{‚d3€’oH`vP v'3#v #‚"†*l9 †„t##‚8B t#3‘’|u~{‚d‘’‚6 „3‚ €&v ‚|7 #suvMv ‘’‚

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(124)  .'r r  O & {‹ Nq R g*|7 #~‡€:‘M†W€&v o#|7 #vw‘’‚d<|us7‚dx]x‰†  $ ~‡€:‘’‚W3€&|†Q<| & :$ Os7r R 1$ O Nr R 1= N   %  % Or R O€   % R

(125)  z m€bc  >:fw~‰€:†B‚Wsu|7 #‚d#‚W?s *†x]z.†W€/~‡€U‚ ' O x@v *†w)‹ Ro3‚WvB‘ † €/vM|/& OO7r R  t  > Os7r R > O R :~@|7  > Os7r R  OL  > R   > % R ~{v .x #€ &  #vw~{##v s`„#su)‚ <t3‘’|‚  O & “@‹ & R0:~{|u5  7    Z$ Os7 r R' Or R r

(126)  O & {‹ NŠ R : #vMsuv d | ~‰€`|u #vvM,~ dvM= 8d†Qx{t#v†d€7€&‚ ‘’~‰†Q|7v :~{|75 ’“  vB€&‚Wx@t#|7~@‚W ‚ )|u #vw†z3‚ 8 vBv 3 t3†Q|7~{‚d*~‰€b& ‹  OrNRI€/~@ r% # , ‹ $ Osr7Rb7Or R €/~@  O ` r7R l   Osr7R  7Or R&‘’‚ƒ€ r% . . . . .  #vh‘’‚W |7su‚Wx]x‰† . . . %. . . . $ zv {~   ’‘ ‚d3€/| † |Mo#‚d#vB 3†d€ & , # ‹  $ Osr7Rb7Or R €/~@  O  ` rSR l   ` $ O r R  > Or R ‹ `; ‘’‚ | €  r  % #vM o#v8 vMs$ €/‚dx{t#|u~{‚d ‚  O & “{‹ & R€7†|u~‰Y€  <~@   O & “{‹Mq R`~‡R€ W~ 8 vM*=z <& OO7r R% t . F> Or R ‘’‚ƒ€ %>Cr   >  Or R €/~@ > > r `_$ Or R > Or R ‹d`; ‘’‚ | € > r  4 ! > O R  > > % . †!. $ Or R > O rNR R€/~@ > r > O rNR‘’‚ € > r  > O . `O  > O rNR >   4 > > % ”y‚o#|7 vB‘‚W3€&|7s†Q~{ |O & “{‹Mq R`x@vQ

(127) † €`|7‚<& t . `O  > OrNR >  $ Or R > Or R R‘’‚ € > r  >  Or R:‘‚ € > r ; O  %  > Or R  , € L  >  4 >. > %.  OOr7R  t. . . R R  rD O & {‹(R.

(128) –R#O & “ q R o3€&~{3‘’v  %  r?†*5!> Or RN e r<o#‚WvB 3†d€ &  %  > OrNR  , € L >    e r  .%@0 r

(129)  †!  o †d€ cQ€&~{ %>Cr  ‘’‚ € %> rQf~‰€:‘’6‚  „#x@vM|7v~{

(130) | O r g • Ro:O & “{‹)( R`~ „#x@~{vQ€)|7 .†|MoZ. @  r<o   > ONr R >  , $ O Nr R > O rNR r

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(135)   .     #&%' #  %% #  =v „s7‚8 v|7 #v„3†Qs7|O ~@~ R‚)|u #vM‚Wsuv pB~@š|u #vw‘M†W€&v‚8‘’‚d3€/| † |  †W€7€8†* €/|u~ 1#vQ€u€ <~‡€/|us7~{zt#|7~@‚W3€“ Ž#‚Ws,† dvM#vMs †x]„#su‚ ‚ ‚  O ~@~ R-:~{|7 *#‚d<k ‘‚W3€&|† |  t#.‘’|7~@‚W3€d †*q=_~@ €/t#~@|†zx{vw€/„3†d‘’vQ€o `vs7v v s |7‚  *8l " “. ‹ †Q* =  ‹Wo†Q*c‘’‚d3€/~g<vMs*|7 #v=z3‚Wt#!#†s? ‘’‚W |7su‚Wxx‰†  t3€’ow†W€u€/t  vK|u 3†|]   ` = N KO r Or7R'`= ƒ  O r Or7R “`jD#€&|7v1O & “ ( R`3z vQ‘’‚6 vQ€ &.     O `$r GrS R    = N r  Or Or7R= ƒ   O r Or7R  7O ‹GrSR  r. †!š|7 v v #vMs$6 ‚ ~{|€:€&‚Wx@t#|7~@‚W3€b&. ‹ # ,  | l& $# ,  | l& =  | OrNR . N p %  %  #v5 ‚Wx{x@‚:~{ ?x@v † ~‡€`„#s7‚8 v ~{ †„#„3vM! <~, –o<t.€/~{ t#x{|u~{„#x@~ vMs)|7vˆ‘ #~.3 t#vQ€’“ r 69YZAUX>VU  > RA)NN  j UW<@?<l<bJ;476@>B6  AE ! 6@> "! > # \ -?Osr7R lr*+ - Or Rt. r. -?Osr7R. . $ sO r7RX. O &  pdrNR O &  p ‹)R. . . %. =v‘M†Q4|u #vM <v<<t3‘’v=†Q4t#„„v s7z3‚Wt#!  ‚ds*|7 #v/<vˆ‘M† s†Q|7v=‚h|7 #vKvMvMs$6 “"g*<vMv< o†W€.- ~‰€ <vQ‘s7vQ†d€/~{ #o#x{vc*†i?~, „x{~{vˆ€

(136) &  -?O R + - O rNR R– *‘ #‚ ‚ €&~{  o ,p & - O  R + p‹ -?Or R ~“ v “  ‚dsycv 8 vM$s ~{ |7v dvMs   r<o - O   R+ p ‹ N - O Nr R –`t#| !o  ‚ds†x@x r cr<o|7 #vMsuvBv  ~‰€&|€†_„3‚ €&~{|7~ 8 v~{ |7v dvMs  €/t3‘ |u 3†|   + r  O   )‹ R  o†*  |u #vM - O r7R + - O   R “`l vM| ‹ 

(137) p  x{‚6`p r

(138)  †! šs7cv *†?s _|u 3†|~   c‹Wo#‚d#vB 3†d€ & ‹ x@‚

(139) pNR vc<„:OO`  x{‚6:pNR+v „ OG`   p  #vMsuv  ‚Wsukv & - O r7R + p ‹ N - O rNR*+  i PWN *-, T \ -?Or R +  i  -?OrNR  “ " ‚ds7vM‚ 8 vMs Ho `v*‘M†Q(  W~ 8 v*† t#„#„3vMs?z3‚Wt#! _ ‚dsB|u # v <vQ‘ <†  #~‡€B„#s7‚ 8 vQ€„3†Qs7| O ~@~ R‚ |u #vM‚ds7v  p<# s†Q|7v “8m‘’|ut3†x@,x o |u #vw†W€7€& t  „#|u~{‚d  , p o#~  „#x{~@vQ

(140) € & + x@

(141) ‚ 8p  . . . :~{|u |u #vw‘’‚W3€&|†Q<| . d~,8 vM z)#O –“ ˜NR “. &. . . .

(142) ,B7HJ K>@,. =v€&|7t*<~@vB #vMsuv:|7 #v,€/| †z#~@x{~M~{ ,„#s7‚d„v s7|7~@vQ€ ‚(†  vMv<z.†W‘?‘’‚d<|us7‚Wxx‰†  ‚ds`† "3vc<~@z#x{v8|7‚Ws 3!tv†Qs$K“  #~‡€  vMv  z3†W‘ Bx‡<† ™s7v 3 t#~@s7vQ€ ‚d#,x †s7v  t3‘’v + #‚:x{v)Wv‚(|7 v€7#€&|7vKod†!_|7 #vU vQ†d€/t#suv vM |]‚ † ‚Wt#|u„#t#T | : #~‡‘  *† ?z3vw† †suz#~{|us†Qs7~{x 7€ *†x@x „3†Qs7|:‚ )|u #5 v : #‚Wx@v€/| †|7vƒ“  #~‡€`~‰€8† dt3†s † |7vMv‚ |7 vBs7‚dz#t3€&|7#vQ€u€y‚ 8|u #v„#s7‚d„‚ƒ€/v =‘’‚d<|us7‚Wx(€u‘ v  a v :~@|7 suvQ€/„3vQ‘|y|u‚_t#.‘’vMs7| †~@<|u~{vQ€:‘’‚d3‘’vMsu#~{ _|u #v &€ €/|uv K“$gI|:~‡€:†x‡€/‚ #vQ‘’vQ€u€7†Q$s  su

(143) ‚  †Q ,~  „#x{v  vM | †|7~@‚W „3‚W~{ |:‚  8<~@v “  #~‡€ ‘’‚d<|us7‚dx<x‡<† = 3†d€ z3vMvMw†„#„x{~{<v  |u‚yz3‚d|7 U† <~‰€u‘’s7vM|uv  )‚ <vMxd‚ 3|u #v8†$s  oW†QB‚Ws <~{.†$s ]<2~ 1vMs7vM |7~‡†x &€ €/|uv Ko$†* ;†K‘’‚d<|u~{ t#‚Wt35€  )‚ <vMx8‘’‚d3€/~‡€/|u~{   ‚  †K— “ `w“ }:“(Ž.‚ds?|7 #vˆ€/v 7| `X ‚  )‚ <vMx‡€’o$†K€/At P ‘’~{v <| ‘’‚d* <~{|u~{‚d  ‚ds:€/| †z#~@x{~@&| h‘’‚W.€/~‰€&|€)‚ $†w‘’

(144) ‚  „3†|u~{z#~@x{~{7| ‘‚W3€&|7s†Q~{ |zv &| 8vMvM?|u #v ƒ†~@ ~{) 8 ‚Wx 8 v  ~@_|u #v <~‡€/|7su~{z#t|7v ?„3†su|‚ ]|u #v‘’‚d<|us7‚Wx†Q*  |u #vvM,~ dvM=  t#3‘|7~{‚d3€ ‚ ]|7 v†t#|u‚W#6‚  ‚Wt3€8&€ €/|uv &(~{|)suv 3!t~{s7vˆ€ |7 .†|*|7 #~‡ €  †Q~{ †W‘’| € 7„3‚ƒ€/~{|u,~ 8 vMx =‚W|7 vKvM,~ dvM=  t#3‘|7~{‚d3€’o€&‚ †d€ |7 ‚ <~‡€7€&~{„3†Q|7vKvM#‚d t W vM#v $s 

(145) ƒ“ j ~ _t#x‡†|u~{‚W.€ ~@x{x@t3€/|us†|uv €&

(146) ‚  v „‚ƒ€7€&~{z#x@v*‘ ‚W~‰‘vQ €  ‚dsB|7 ~‰+ €  †Q~{™†!  |u #v*€&t#„3vMs7~@‚WsB„3vM7s  ‚W?s  vM3‘’v ‚   — ` !j :#&| „3vw‘’‚W |7su‚Wx]‚ 8 vMs:€&,~  „x{v,V— ` z3‚Wt#* †$s  vMv <z.†W‘  “  ‚=‘’

(147) ‚  „x{vM|uv?|7 #~‡€ 8‚W?s  o)~@| suv *†Q~{3€|7‚ vQ€/| †z#x@~‰€& |7 #v v <„3‚d#vM |7~‰†Qx8€/|†Qz#~{x@~{7| ‚ |u #v ‘’‚W |7~@<t#‚dt3€  )‚ <v xo :~{|7 #‚d<k ‘’‚d3€/| † | *†W€u€)†* P<vM.€/~{7| a t#3‘|7~{‚d3€’odt#* <vMs$|7 #v:v 1vQ‘|)‚ |7 Tv : #‚Wx@Rv  vMv <z3†dI‘  x‰†  O ~@3‘’x{!t <~{  w|7 #v,v 1vQ‘’|`‚ )|u #] v <~‰€&|7su~{z#t#|uv _„3†Qs7| R“m:|`|7 ~‰€`€&|† Wv o3† €/|u*t = ‚ $|7 #vvM#v $s 

(148) Z<vQ‘ <† s†Q|7] v :~{|7 *suvQ€/„3vQ‘’|:|u‚?|7 #5 v 8d†su~{‚dt3€ ƒ†~@K‘’‚ Qv P ‘’~@vM<| V€ :~@x{x z3v‚  ~{ |7vMsuvQ€/| “  #v?suvQ€/t#x@|€y„s7vQ€&vM<|uv š vMs7vh†„#„#x †x‰€&‚*|7‚*†Q=†$s  : #~‰‘ ~‡€ ".v <~@z#x{v~@=‘’

(149) ‚  „s7vQ€u€/~{‚d]o€/~{.‘’vB|u #v v3 t3†|u~{‚d3€U| †  v|7 vB€u†  U v  ‚W$s  “  #vM~@s:v  |7vM3€&~{‚d |7‚ z3vM* <~@   ".v <~@z#~{x@~{7| Bsuv *†Q~{3€|7‚?z3b v <‚d#v “ my#‚d|7 #v s_„3vMs €/„3vQ‘’|u,~ 8 v ‚ |7 #~‡€ 8‚W?s ~‰€B~@|b € WvM#v s†x@,~ Q†Q|7~@‚W;|7‚=|7 #v €&|†z~{x{~ Q†|u~{‚d ‚ 5 t#x{|u~ k x@~{  dv  s7‚dz3‚W|€o]†x@|7 #‚d t W |7 #~‡R€ :~{x@x ~{! <t3‘’v#‚d<k x@~{#vQ†Qs7~@|7~{vˆ€~{*|u #5 v  )‚ <vMx‡€’“ g5 | :~{x{x$†x‡€/‚ zv?~  „3‚Wsu|† ||u‚ €&|7*t )Ks7‚Wzt3€/|u#vQ€7€w†W€&„vˆ‘’|a € :~{|u suvQ€/„3vQ‘||7 ‚ 8d†su~{‚Wt.€ „3vMsu|7t#z.†|7~@‚W3€ O  †W€7€:†Q|y‚d#vv  |7s7cv  ~{7| oD vMx‰† †|‚Wz3€&vM$s 8d†|u~{‚d]“{“@“ R“. B C  I .  mJ" 3j “mysu~, ‚d|7‚#o3Ž8“ " ~ †Q†<~ o > &` 4FO 4F>8 "!# ?'E ` Y 6@> ! <b66 ER\  AE ! >?'EO \9E&??bE ` E>*: "! 4 C Y  O  > E&?b6]p4F>BU 6 < ! 69E&?L8IA  C &` 4FO 4F> 8 o—)s7‚ ‘d“3Ž ~{s €/|g<| “jD) „]“ ‚W •:‚Wz3‚W|u~‰‘M€•Uvˆ€/vQ†Qs‘ ]o#–`suvM|7|uvM  ‚ ‚)#€’o(‹M˜ /Wi o "Kg  — suvQ€7€o ‹ ˜/ & “ =  –,"'* ,. mB“ "“<–`x@‚ ‘ o#”B“ B  “ "K‘)*x‰† s7‚ ‘ ]o E ! >?'EO3ER\

(150) <'AU "! 4BA  O  8 6@><@: 6 ]p4F>VU O  6694BA  O E !  !. ! U-EO E E&:4BA E 6@> ?  4 ! >B6 o —)s7‚ ‘W“:‚h|7 #v p/Q|7 g&}}} *‚W)u“U‚d `vQ‘’~‰€&~{‚dc†Q* *‚d<|us7‚dxo –. *.  † „.†<o#Ž(x{‚Wsu~.#† o#„#„]“3pdr<‹> pWrdq<o)‹ ˜/d˜<“ B“–`s7v ~‰€’o! O 8"6 <p\9E ! AL> 4BE !! <O OF< cj U@< E&?@4 <<>  C&CWO 4BA  > 4BE ! 6 o "K†d€7€/‚d]o(‹M˜/di. ) “ * #vM]o E ! > ?bEO "!# 6@> &` 4FO 4  >4BE ! \9E&? >VUW<)]  G < < "Y  > 4BE ! 4 !  ` E&Y ! # < #$# E&:  4 !<o j g&m ".  “*‚W |7sM“ Q #„ |M“@o ‹( Ou‹M˜N(ˆ˜NR o„#„ “3ŠWŠ> /<‹d“  *8l " Ž`“*‚W#s †

(151)  o  “Ql vMz#x{‚d* o  “ — “"K†s$ ‚Ws†Q|Mo E&Y !#" ?@8NAE ! > ?bEO "!# 6@> &` 4FO 4  >4BE ! ER\>VUW< E ! <  # 4B:=< ! 694BE ! Op]  G< < "Y  >4BE ! o— su‚ ‘W“]g&Ž)g&— `‚ds$€/ #‚d„ –`‚dt#*#†Qs$=‘’‚d<|us7‚Wx$†! z‚dt#*#†Qs$ 8d†su~‰†Q|7~{‚d3€  o j ‚W„ #~‰†Mk my |7~@„‚dx{~‡€’o#‚ ‘’| “]‹M˜W˜dr<“  *8— Ž`“*‚W#s †

(152)  o"“]—)~{v s7s7vƒo > &` 4FO 4  > 4BE ! ER\ Y OF<?  <@? ! E&Y O O 4 ` <  : ` 8 ! E ! O 4 ! <  ? ` E&Y !#" ?@8 \ << #&`  A o•y†Q„#„3‚Ws7|<vw•UvQ‘ #vMs ‘ vg&”•g&m  z=‹MpWidq<o)‹ ˜W˜dr<“  * 

(153) •“ *‚Wt#s † |Moe`w“  ~{x{z3vMsu|Mo

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