Multi-input Multi-output Fuzzy Logic Controller for ... - ScienceDirect.com

35 downloads 0 Views 372KB Size Report
The robot manipulator is a mechanical system multiYarticulated, in which each ..... e e. G G Gτ and the input and output variables of the Flc are: iN e i. iN e i i. iN.
Available online at www.sciencedirect.com

ScienceDirect Procedia Technology 19 (2015) 607 – 614

F:"@F7D@3F;A@3> A@87D7@57 "@F7D6;E5;B>;@3D;FK;@@9;@77D;@9 "',* '     (5FA47D   ,;D9G &GD7E *A?3@;3

&G>F; ;@BGF ?G>F; AGFBGF 8GLLK >A9;5 5A@FDA>>7D 8AD 5A?B>7J EKEF7? BB>;53F;A@ A@ FIA >;@=E ?3@;BG>3FAD 3F;?303:D339:>;3  %3D4;>43==3>;3 /3EE;@7%3=:3>3 "

0%&-*/("/%*.5-"4*0/0'&$)"/*$"-934&.3"#02"4029#%&-."-&,33""%* /*6&23*49"$5-490'$*&/$&3 ;)"//&$)   &405"/ 020$$0

%&$& ,:7DA4AF?3@;BG>3FAD;E3?75:3@;53>EKEF7??G>F; 3DF;5G>3F76 ;@I:;5:735:3DF;5G>3F;A@;E6D;H7@;@6;H;6G3>>K4K3@7>75FD;5 35FG3FAD ;F ;EF:7?AEFDA4AFGE76;@;@6GEFDK F:;EEKEF7?@7763@788;5;7@F5A@FDA>EFD3F79K EG5:3EGLLK %A9;5 >3I5A@FDA> 4K ?73@E 735: 3DF;5G>3F;A@ ;E 5A@FDA>>76 ;@67B7@67@F>K  F:;E =;@6 A8 5A@FDA> BD7E7@F 3 >AF A8 ;@5A@H7@;7@F EG5: 3E 7DDAD A8 735: 3DF;5G>3F;A@ ;E@QFF3=7@355AG@F;@FAAF:7DE "@ F:;E BD7E7@F IAD= I7 BD7E7@F 3 &G>F; "@BGF&G>F; (GFBGF GLLK 5A@FDA>>7D &"&( FA 7@EGD7F:7 3DF;5G>3F;A@ DA4AF 5A@FDA> EFD3F79K F:7D7EG>FEA4F3;@76BD7E7@FE3F;E835FADK3@6E:AIE5>73D>KF:7788;5;7@5KA8F:7BD7E7@FGLLK &"&(5A@FDA>>7D M 2015   The ,:7GF:ADE )G4>;E:764K>E7H;7D%F6 © Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license +7>75F;A@3@6 ADB77D D7H;7IG@67DD7EBA@E;4;>;FKA8R)7FDG&3;ADS-@;H7DE;FKA8,;D9G&GD7E 35G>FKA8@9;@77D;@9 (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of “Petru Maior” University of Tirgu Mures, Faculty of Engineering &9702%3*A4AF&3@;BG>3FADK@3?;5&A67>;@9 GLLK%A9;5 A@FDA> &"&(

 !&$"'&"! *7E73D5:A@F:76K@3?;5?A67>;@93@65A@FDA>A8F:73D?E ?3@;BG>3FADE:3ED757;H76;@5D73E763FF7@F;A@E;@57 F:7>3EFK73DE6G7FAF:7;D36H3@F397E  DA4AF ?3@;BG>3FAD ;E 3 :;9: EB776 BDA57EE F:3F ;E :;9:>K @A@>;@73D  6K@3?;53>>K 5AGB>76 3@6 A8F7@ ;F ;E @AF 367CG3F7FAGE7>;@73DE7DHA5A@FDA> ;8355GD3F7B7D8AD?3@57;@:;9:43@6I;6F:AB7D3F;A@E;E67E;D76 &3@K788ADFE :3H7477@?367;@67H7>AB;@95A@FDA>E5:7?7FA35:;7H7F:7BD75;E7FD35=;@95A@FDA>A8DA4AF?3@;BG>3FADE

ADD7EBA@6;@93GF:AD ,7>   83J

."*-"%%2&33439:>; 83F;?3L3:D39?3;> 5A?

2212-0173 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of “Petru Maior” University of Tirgu Mures, Faculty of Engineering doi:10.1016/j.protcy.2015.02.086

608

Fatima Zahra Baghli et al. / Procedia Technology 19 (2015) 607 – 614

$@AI>769743E765A@FDA> 7JB7DF5A@FDA>3@6;@F7>>;97@F5A@FDA>3D7EA?7I:3FEK@A@K?AGE3@68GLLK5A@FDA>;E3 B3DF;5G>3DFKB7A8;@F7>>;97@F5A@FDA> GLLK>A9;55A@FDA>:3E39D73FBAF7@F;3>E;@57;F;E34>7FA5A?B7@E3F78ADF:7 G@57DF3;@ @A@>;@73D6K@3?;5E GE;@9F:7BDA9D3??;@953B34;>;FKA8 :G?3@5A@FDA>47:3H;AD ,:7 ?3;@873FGD7EA8 8GLLK5A@FDA>;EF:3F35A@FDA>=@AI>769743E7 ;E3H3;>34>7I;F:;@F:75A@FDA>>7D3@65A@FDA>35F;A@E3D797@7D3F764K 3BB>K;@9 7J;EF;@9 5A@6;F;A@E AD 63F3 FA F:7 =@AI>7697 43E7  ?3=;@9 GE A8 ;@87D7@57 ?75:3@;E? 1 2 >EA  F:7 =@AI>7697 43E7 3@6 ;@87D7@57 ?75:3@;E? 53@ :3@6>7 @A 5D;EB  ;@5A?B>7F7 ;@8AD?3F;A@ F:7 =@AI>7697 ;FE7>8 I;>> ;?BDAH73@67HA>H7F:DAG9:>73D@;@93@6B3EF7JB7D;7@57 12 GLLK>A9;55A@FDA>6A7E@AFD7CG;D735A@H7@F;A@3>?A67>A8F:7BDA57EE I:7D73E?AEF5A@H7@F;A@3>F75:@;CG7E D7CG;D77;F:7D3@3@3>KF;53>?A67>AD3@7JB7D;?7@F3>?A67> GLLK>A9;55A@FDA>;EB3DF;5G>3D>KEG;F34>78AD5A?B>7J 3@6 ;>> 678;@76 BDA57EE ;@ I:;5: 3@3>KF;53> ?A67>;@9 ;E 6;88;5G>F 6G7 FA F:7 835F F:3F F:7 BDA57EE ;E @AF 5A?B>7F7>K =@AI@3@67JB7D;?7@F3>?A67>;67@F;8;53F;A@;E@AF873E;4>74753GE7F:7D7CG;D76;@BGFE3@6AGFBGFA8F:7BDA57EE ?3K@AF47?73EGD34>7 ,:7 ?3;@73D ?G>F; ;@BGF ?G>F; AGFBGF &"&( EKEF7?E ,:75A@FDA>A8F:7E7 EKEF7?E;E?7FI;F:3@G?47DA86;88;5G>F;7E6G7FABDA57EE;@F7D35F;A@E 6736F;?73@6BDA57EE@A@>;@73D;F;7E ,:7 6;887D7@5747FI77@&"&( EKEF7?E5A@FDA>3@6+;@9>7 "@BGF+;@9>7 (GFBGF+"+( EKEF7?E5A@FDA>;E43E76A@3@ 7EF;?3F;A@ 3@6 5A?B7@E3F;A@ A8 F:7 BDA57EE ;@F7D35F;A@ 3?A@9 735: 679D77 A8 8D776A?  "F ;E A4H;AGE F:3F F:7 6;88;5G>FK A8 &"&( EKEF7?E 5A@FDA> ;E :AI FA AH7D5A?7 F:7 5AGB>;@9 78875FE 3?A@9 735: 679D77 A8 8D776A?  ,A A4F3;@ 9AA6 B7D8AD?3@57  5AGB>;@9 78875F 53@@AF 47 @79>75F76  !7@57 +"+( EKEF7? 5A@FDA> E5:7?7 ;E @AF 73EK FA ;?B>7?7@F A@ 5A?B>;53F76 &"&( EKEF7?E  "@ 366;F;A@  F:7 5A@FDA> DG>7E 3@6 5A@FDA>>7D 5A?BGF3F;A@ I;>> 9DAI 7JBA@7@F;3>>K I;F:D7EB75FFA 3@G?47DA85A@E;67D76H3D;34>7E ,:7D78AD7 ;@F7>>;97@F5A@FDA>EFD3F79K;E 9D36G3>>K 6D3I;@93FF7@F;A@ 12 "@ F:;E IAD= 38F7D F:7 EKEF7? ?A67>;@9  E;?G>3F;A@ 3@6 5A@FDA> DA4AF ?3@;BG>3FAD GE;@9 FIA 3DF;5G>3F;A@E 8AD ?AF;A@ GE;@9 &3F%34 +;?G>;@= EA8FI3D7 I7D7 53DD;76  I:7@ F:7 BDABAE76 &"&( GLLK 5A@FDA>>76 ;E GE76 FA ;?BDAH7F:73DF;5G>3F;A@DA4AFEF34;>;FK ,IAFKB7EA85A@FDA>GLLK +"+( 3@6GLLK &"&(I7D7 EFG6;76 3@3>KE76 3@65A?B3D3F;H7EFG6;7EI7D7?367 ,:7D7?;@67DB3B7DI3EEFDG5FGD763E8A>>AIF:7DA4AF?A67>;@9;EBD7E7@F76;@ E75A@6B3DF A8F:;EB3B7D ;@F:7 F:;D6B3DFA8F:;EB3B7D F:7GLLK &"&(;E 67F3;>76 F:7D7EG>FEA4F3;@76BD7E7@FF:7788;5;7@5K3@6F:7DA4GEF@7EEA8 F:7BDABAE765A@FDA>I;F:9AA6B7D8AD?3@57E5A?B3D76I;F:GLLK +"+( " !&'$% ' '& '+ ) )& )+ 0 % % &"&( +E & 

'793F;H7;9 '793F;H7&76;G? '793F;H7+?3>> )AE;F;H7;9 )AE;F;H7&76;G? )AE;F;H7+?3>> 07DA GLLK%A9;5A@FDA>>7D &G>F;;@BGF&G>F;AGFBGFGLLK%A9;5A@FDA>>7D +53>;@935FAD &3;@GLLKA@FDA>>7D AGB>;@9GLLKA@FDA>>7D

 (%" *A4AF &3@;BG>3FADE 3D7 83?;>;3D 7J3?B>7E A8 FD3>34>7 ?75:3@;53> EKEF7?E  !AI7H7D  F:7;D @A@>;@73D6K@3?;5EBD7E7@F35:3>>7@9;@95A@FDA>BDA4>7? E;@57FD36;F;A@3>>;@73D5A@FDA>3BBDA35:7E6A@AF73E;>K 3BB>K

609

Fatima Zahra Baghli et al. / Procedia Technology 19 (2015) 607 – 614

,:7?3@;BG>3FAD GE768ADE;?G>3F;A@;E3FIAD7HA>GF7;76 FA F:7 ?3@;BG>3FAD >GEFD3F76;@ ;9 

9

9 -

9 

-

(

1

8



&

9 1

 

8

8 

8

;9  +FDG5FGD7A8?3@;BG>3FADDA4AFA8FIA679D77A88D776A?

,:76K@3?;53>7CG3F;A@A8?3@;BG>3FADDA4AFA8  EA>;6E3DF;5G>3F7647FI77@GE;E9;H7@4KF:78A>>AI;@9 ?3FD;J 7CG3F;A@12

    1 1   11    1 



I:7D7

 ;EF:7   H75FADA83FAD;@7DF;3?3FD;J  1 1  BD7E7@F F:7   H75FAD A8 AD;A>;E 3@6 57@FD;8G93> 8AD57E 1 ;E F:7   H75FAD A8 9D3H;F3F;A@3> D787D7@57E3@6 1 1 1 3D7BAE;F;A@ H7>A5;FK 3@63557>7D3F;A@A8735:3DF;5G>3F;A@E I:7D7 ,:7 7>7?7@FE A8F:7;@7DF;3?3FD;J 1 ;@F:7F7D?EA8F:7B3D3?7F7DEA8F:7DA4AF?3@;BG>3FAD3D79;H7@4K

 1       .-$  .-$  .-  .--$  $   1      1      .-$  .--$  $   1      .-$ ,:7?3FD;J7>7?7@FE *+ 1 1 * +    57@FD;8G93>3@6 AD;A>;E8AD573D7

 1 1   .--$  1 3  1 1   .--$  3 1  1   1 1   .--$  13  1 1   ;@3>>KF:77>7?7@FEA8F:7H75FADA89D3H;F3F;A@3>FADCG7E C3D79;H7@ 4K

610

Fatima Zahra Baghli et al. / Procedia Technology 19 (2015) 607 – 614

 1  .  .  (-$$  . (-$  $  1  . (-$  $    '))( "!&$"$ %! 7@7D3>>K  F:7 BD;@5;B3> 67E;9@ 7>7?7@FE A8 F:7 GLLK %A9;5 5A@FDA> EKEF7? 3D7 3E 8A>>AIE GLL;8;53F;A@ "@87D7@57?75:3@;E?3@6788GL;8;53F;A@ 12 ,:78;DEFA@75A?BD;E7EF:7BDA57EEA8FD3@E8AD?;@95D;EBH3>G7E;@FA 9D367EA8?7?47DE:;B8AD>;@9G;EF;5F7D?EA88GLLKE7FE ,:78GLLK;@87D7@57EKEF7?:3E477@5A@E;67D76F:7?;@ ?3J?7F:A6&3?63@; I:7D7F:7;?B>;53F;A@:3E477@ 3EEG?76FA?;@3@6F:7399D793F;A@:3E477@5A@E;67D76FA?3J "@366;F;A@ F:7788GL;8;53F;A@?7F:A6:3E477@ 5A@E;67D76 FA F:7 57@FDA;6 ?7F:A6 3@6 F:7 788GL;8;53F;A@ ;E F:7 5A@H7DE;A@ A8 3 8GLLK CG3@F;FK D7BD7E7@F76 4K 3 ?7?47DE:;B8G@5F;A@;@FA3BD75;E7AD5D;EBH3>G7 ,:;E8GLLK5A@FDA>>7D;EFA4767E;9@76FA3GFA?3F7:AI3:G?3@ 7JB7DFI:A;EEG557EE8G>3FF:;EF3E=IAG>65A@FDA>F:7EKEF7? ;DEF F:77JB7DFF7>>EGEF:767E;9@7DEA8F:78GLLK 5A@FDA>>7DI:3F;@8AD?3F;A@E:7AD:7I;>>GE73E;@BGFEFAF:7675;E;A@ ?3=;@9BDA57EE ,:7;9 E:AIEF:7% EFDG5FGD7

% %4

&

&

&

,%&

,&

 &/

&/

  





"@87D7@57 &75:3@;E?E

*5-&"3*3

 



5

5/ ,5

5

;9  GLLK>A9;55A@FDA>>7DEFDG5FGD7

I:7D7   ;EF:7GLL;8;53F;A@BDA57EE3@6  ;EF:7788GL;8;53F;A@BDA57EE "@ F:;E B3B7D F:7 &"&( 8GLLK 5A@FDA> EFD3F79K ;E GE76 FA ?G>F; ?35:;@7E EKEF7? BAE;F;A@ 5A@FDA>  ,:7 4>A5= 6;39D3?A8F:7&"&(8GLLK5A@FDA>E5:7?7;EE:AI@;@ ;9  ,:767E;9@BDA576GD7A8F:78GLLK5A@FDA>EFD3F79K 5A@E;EFE A8 ?3;@ 8GLLK 5A@FDA>>7D & 3@6 5AGB>;@9 8GLLK 5A@FDA>>7D   ,:7 5A@57BF A8 366;@9 5AGB>;@9 5A@FDA>>7D;EFA5A?B7@E3F7F:75AGB>;@9 78875FEA8EKEF7?6K@3?;5E3?A@9735:679D77A88D776A?

&"&( % AGB>;@9GLLK %A9;5A@FDA>>7D

1*

&* 4 

 D? & 3 @ ;B G >3 FA D

& 3;@GLLK %A9;5A@FDA>>7D

;9  >A5=6;39D3?A8F:7&"&(GLLKA@FDA> E5:7?3

1*

611

Fatima Zahra Baghli et al. / Procedia Technology 19 (2015) 607 – 614

@AD6;@3DK8GLLK5A@FDA>>7DF:3FGEG3>>KAB7D3F7EI;F:EKEF7?AGFBGF7DDAD3@67DDAD 5:3@97I3E5:AE7@ 3EF:7?3;@5A@FDA>>7DFA5A@FDA>735:679D77A88D776A?A8F:7&"&(EKEF7?E !7D7 F:7;@BGFH3D;34>7EA8 F:75A@H7@F;A@3>8GLLK5A@FDA>>7D8AD3?A@9735:679D77A88D776A?A83&"&(EKEF7?I7D7678;@76;@6;H;6G3>>K 3E

&* ,   1* ,   1* ,  &*  ,   &*  ,   &*  ,  



I:7D7 &* ,  ;EF:7BAE;F;A@7DDADA8F:7 * 4) 679D77 &*  ,  ;EGE768AD5:3@97;@7DDADA8 F:7 * 4) 679D77 1* ,  ;E F:7D787D7@57;@BGFA8 F:7 * 4) 679D77 3@6 1* ,  D7BD7E7@FEF:7 * 4) BAE;F;A@AGFBGFA8735:679D77A88D776A?A8 F:;E &"&(EKEF7?3FF:7 , 4) E3?B>7 ,:7D7>3F;A@E:;B47FI77@F:7E53>;@9 835FADE &  &   3@6 F:7;@BGF 3@6AGFBGF H3D;34>7EA8F:7% 3D7

&*  & &* &*  & &*  *    *



+7>75F;A@ A8 EG;F34>7 H3>G7E 8AD &  & 3@6  3D7 ?367 43E76 A@ F:7 =@AI>7697 34AGF F:7 BDA57EE FA 47 5A@FDA>>76 3@6 EA?7F;?7E F:DAG9: FD;3> 3@6 7DDAD FA 35:;7H7 F:7 47EF BAEE;4>7 5A@FDA> B7D8AD?3@57  ,:;E ;E EA 4753GE7 G@>;=75A@H7@F;A@3>@A8GLLK5A@FDA>>7DEFA 63F7 F:7D7;E@AI7>> 678;@76?7F:A6 8AD9AA6E7FF;@9A8E53>;@9 835FADQE8AD%QE ,:7+E3D7F:7E;9@;8;53@FB3D3?7F7DEA8%4753GE75:3@9;@9F:7+E5:3@97EF:7@AD?3>;L76 G@;H7DE7 A8 6;E5AGDE7  F:7 6A?3;@E  3@6 F:7 ?7?47DE:;B 8G@5F;A@E A8 ;@BGF AD AGFBGF H3D;34>7E A8 %  >> ?7?47DE:;B 8G@5F;A@E &E 8AD 5A@FDA>>7D ;@BGFE &* &*  3@6 ;@5D7?7@F3> 5:3@97 ;@ 5A@FDA>>7D AGFBGF   *  3D7 678;@76A@F:75A??A@@AD?3>;L76 6A?3;@ 1  .7 GE7EK??7FD;5FD;3@9>7E7J57BFF:7FIA&E3FF:7 7JFD7?77@6E 3EE:AI@ ;@;9  









79D77A8?7?47DE:;B









 





















&7?47DE:;B8G@5F;A@E8AD5A@FDA>>7D;@BGFE3@65A@FDA>>7DAGFBGF

;9  &7?47DE:;B8G@5F;A@EA8 7; O7 ; 3@6 O  ;

,:;E;EF:7 ?AEF@3FGD3>3@6G@4;3E765:A;578AD&E K I3KA8F:734AH767E;9@BDA57EE F:7 35FG3>5A@FDA> ;@BGFFADCG78ADF:7?3;@8GLLK5A@FDA>>7D53@47ID;FF7@3E

 * ,    * ,     * , 



612

Fatima Zahra Baghli et al. / Procedia Technology 19 (2015) 607 – 614

,:78GLLKDG>7 43E7 ;EE:AI@;@ ,34>7  3@6F:7E7DG>7E53@47ID;FF7@;@F:78AD?3FA8" ,!' ,34>7  *G>7E43E7 &

(GFBGF '

&

'

'+

0

)+

)

'

'

'+

'+

0

'+

'

'+

'+

0

)+

0

'+

'+

0

)+

)+

)+

'+

0

)+

)+

)

)

0

)+

)+

)

)

,:78GLLK5A@FDA>DG>7EA8F:75AGB>;@98GLLK5A@FDA>>7D3D7E;?;>3DFAF:7?3;@8GLLK5A@FDA>>7D ,:7AGFBGFA8F:7 5AGB>;@98GLLK5A@FDA>>7D;E5:AE7@6;D75F>K3EF:75AGB>;@95A@FDA> ;@BGFFADCG7 ,:7?3;@D73EA@;EF:3FF:7D7;E3 6;887D7@F 5AGB>;@9 78875F 8AD 735: E3?B>;@9 ;@F7DH3> 3@6 ;F 6A7E @AF :3H7 3@ 355G?G>3F;@9 873FGD7  ,:7 5AGB>;@9 78875F;E;@5ADBAD3F76;@FAF:7?3;@8GLLK5A@FDA>>7D8AD735:EF7BFA;?BDAH7EKEF7?B7D8AD?3@573@6DA4GEF@7EE ;9  ;>>GEFD3F7EF:7EFDG5FGD7A8&"&(8GLLK5A@FDA>E5:7?3 ,:7D78AD7 F:7FAF3>5A@FDA>;@BGF FADCG7 A8F:7&"&( 8GLLK5A@FDA>>7D;ED7BD7E7@F763E

 *  ,    *  ,   * -  , 

* - 



I:7D7 *, 7JBD7EE7E F:7 EKEF7? 5A@FDA> ;@BGF FADCG7 A8 F:7 * 4) 679D77 A8 3 ?3;@ 8GLLK 5A@FDA>>7D ,-* D7BD7E7@FEF:75AGB>;@9 78875F5A@FDA>A8F:7 - 4) 679D77D7>3F;H7FA F:7 * 4) 679D77A8F:75AGB>;@98GLLK5A@FDA>>7D

& 1

-

-

& &  

  *   * 

1

-  -

&    

1

&

&  

& - 

""& !#'&"$

- - 

1 - 

& ;9  +FDG5FGD7A8&"&(8GLLK5A@FDA>E5:7?3

  '&"!$%'&% +"+( 5A@FDA> 43E76 A@ % ?A67> 3@6 ;@F7>>;97@F 5A@FDA> 43E76 A@ &"&( % ?A67> I7D7 F7EF76 FA E;@GE D7EBA@E7 FD33F;A@ 3BB>;76 FA FIA 679D77E A8 8D776A? DA4AF 3D? I3E ;?B>7?7@F76 ;@ &3F>34 +;?G>;@= 3EE:AI@;@;9  3@6;9  )AE;F;A@7DDAD;E 5A?B3D76;@F:7E75A@FDA>>7DE

613

Fatima Zahra Baghli et al. / Procedia Technology 19 (2015) 607 – 614

& 4 

1

  4 

%

1

 D? & 3 @ ;B G >3 FA D

1

1

%   4  

& 4 

;9  D? ?3@;BG>3FADDA4AF% A@FDA>

 &"&( 4 

& 4 

1

%&"&(

1

1

 D? & 3 @ ;B G >3 FA D

1

 &"&( 4 

& 4 

;9  D??3@;BG>3FADDA4AF % &"&(A@FDA>

"@;9   3D7E:AI@7DDADB7D8AD?3@57 4K5A?B3D;@9BAE;F;A@7DDAD8ADF:78;DEF3@6E75A@6>;@= %QE7DDAD;E :;9:7DF:3@% &"&( .753@EG??3D;7E3>>F:7A4F3;@76D7EG>FE;@F:7 ,34>7  % )AE;F;A@7DDA7A8;@=





614

Fatima Zahra Baghli et al. / Procedia Technology 19 (2015) 607 – 614

% )AE;F;A@7DDADA8;@= ,34>7  % 3@6 % &"&(*7EG>FE A@FDA>>7D

%

%;@=E

%;@=

%;@=

%;@=

%;@=

)AE;F;A@7DDAD1D362

















AH7DE:AAF12









% &"&(

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

E363 ! +>AF;@7 ## *A4AF3@3>KE;E3@6A@FDA> '7IKAD=.;>7K  +G?3F:; ) )D75;E7FD35=;@95A@FDA>A8DA4AF ?3@;BG>3FADGE;@98GLLK>A9;5 *! 5A@87D7@57 +7EE;A@ 

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

   12 +G443D3< ) @3@6 )+ &A6;8;76)3DF;5>7+I3D?(BF;?;L76&"&(%8ADA?B>7J"@6GEFD;3>)DA57EE "@)DA5 A8 ""@F> A@87D7@57 A@ A??G@;53F;A@A@FDA>3@6A?BGF;@9,75:@A>A9;7E",   B  

Suggest Documents