Cross Standard Form for generalized inverse problem: application to lateral flight control of a highly flexible aircraft

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(19) •. ÚÓÔ$ÝÁû/Û!ÚhÑ&Ø½æ:áFÐ:Õ×ÁÚWá½ÚhÐ:àÑÔ Ý§Ñ\Õæê½Ð:Ú²Ö¨ÝÁÐ/ÛWÑ$ÐÕÕ¨ÖàÝ§á½ß Ù<àØ<ì Ð/Ü<ÓÓÚ5ê½Ô&Ð/à¨àÚhàÔFÑOÓÐ/ÝÁÐ:Û5ÕÚJÔ$ãÑ½û ú)Ý¬Õ¨êÚÐBÝÁû/àÚhÚÑ&ÕæÐ/Ô ×§á½ÚJàÚÝÁÝÁÑSû/ÚhàÑ&ØHæÚhÐ/Ó ×§á<ÚhàhÜeàÜFØHÕÚhê<Ó Ð:Õ)Ý´àÜ àØHÚhÓ ÝÁàÕ¨ê½Ú!àÚÕ²Ô ëì ç \áÓ¨êàá<Ù<àØÐ/ÓÚJàÐ/ÖÚUÚhÐ/àÝÁ×§ÒOÓÔ$Û5Ø<áFÕÚJãSá<àÝÁÑ½û FÓ¨ê\á½ÖãFÚhÓÔ/Û!ØHÔ$àÝ¬Õ¨Ý§Ô$Ñ<à Ôú)ÓÔ$Mê½Û!ÕÚhê½ÖØ½Ú²Ú áFÛWÕÚÐÕ¨Õ¨ê½ÖÝ§ÚUß àÔ$×§áFÕ¨ç Ý§Ð:Ô$Ñ<Ñ ã ëì . . A. •. A + BDK C BK C. U2 ∈ RnK ×n. U1 ∈ Rn×n Acl. (Γn ). 2n. ·. . n. BCk Ak. ¸·. U1 U2. ¸. =. . (A). (Acl ) ¸ U1 Γn , U2. ·. I. 5. I. ;. T = U2 U1−1 .. . . Youla parameter e.

(20). + +u -. +. +. . x. y. +. . -. . Plant. + +. +. . . ^ x. . State estimator. ^ x. State feedback. "!$#&%')(+*&,.-0/2143&57698:';8:<+(>=)(>'?!A@B8C=?!$DFEHGI!$=?JLK.MONQPR=?')%9ST=)%'?(FU. VEW=?J(+E(>XY=ZPR(BST=)!ADFE4[\=?J(+!AE&=?(>'?(BPR=ODF]^DF_`PR(B')aF(B'Rbc_98FP)(Bde')(B8FfA!$@g8C=)!ADFE`PhDF]^#F!AaF(>EiS>DF<+6j(>E`P)8:=)DF';Pk!APOJ!A#FJfA!A#FJ&=?(Bd7]DF' 6fl8:EY=mPR=?8:=)(O<+DFE9!n=?DF'?!$E9#9U oqprots&uRu)vhw&xyz"x{|~}Luz}^xw&xz x|~}h{x|y9{R}m qJ(O<+Dd(Bf\D:].8fl8:%9E9S?J(B'q_j(>=G^(B(>E=?J(OY8gG8:E#&fA(. ψ. 8:E9dH=)J9(STD&<+<+8FE9d. 8:696')DX!$<8:=)(BdH_Y0=?J(P)(BSTD&E9dHD&'?d(>'=)';8:E`P](B']%E9ST=)!ADFE4,. G(s) =. s2. β . =)J9')%9PR=)(B'md(T9(gS=?!$D&E`SB8:E_j(O'?DF%9#FJfA. 1 −1. 8FP?P)DST!l8C=)(gd0GI!$=)J=?J(P=;8C=)(>bP)698&ST(')(g8:fA!$@g8C=?!$D&E4,.   ψ˙ 0  ψ¨  =  1 1 ψ . K4(>=I%`PIS>DFE9P)!Ad(>'=?J(O]DFfAfADGI!AE#P=;8:_!Af$!A@>!AE#STD&<6j(BE9P?8C=)D&'. . K(s) = − PR=?8C=?(PR6`8FST(O'?(B8:fA!A@B8:=)!ADFE . 1 0 0 .   ψ 0 1   ψ˙  . 0 β. *g& . 6jD&P)!$=)!AaF(](>(gd_98FS;,. s2 + 27s + 26 . s2 + 7s + 18. STDF<+698FE!ADFE]DF'?<D:] =?J!APmS>DF<+6j(>E9P?8C=?DF'q'?(B8Fd9P>,.   0 x˙1  x˙2  =  −18 β −8 . 1 −7 −20.   0 x1 1   x2  . −1 ψ. qJ(8:66fA!lS>8:=)!ADFEDF] =)J(6'?(>a!ADF%9Pq6'?DST(Bd%')(69')DCa!Ad(gP^=?J(O]DFfAf$DCGI!AE#698F'?8F<(>=)(B')!A@B8C=?!ADFE4,. Kc = [3. 3]; Kf = [4. 5]T ; Q = −1 .. . *&*g.

(21) 1. 0.5. 0.5. 0. 0. Rd − Rd/s. Rd − Rd/s. 1. −0.5. −0.5. −1. −1 attitude angle: ψ attitude rate: dψ/dt compensator: x1 compensator: x. −1.5. attitude angle: ψ attitude rate: dψ/dt estimated attitude angle estimated attitude rate. −1.5. 2. −2. 0. 2. 4. 6. 8. 10. 12. −2. 14. 0. 2. 4. 6. Time (s). 8. 10. 12. èMë ÚJÝ§é&û$á<á½ÐÖ¨ÚÕ¨Ý§Ô$Ñë)ý/Úhý àØHÔ/äQÑÔ/àÑBÚJàÕ¨ê½Õ¨ÔÚ²ÖÝÁÑ½ÝÁû/Ý§Õê&Ý´Õ Ð:r×Ô$ÓÙ<Ô/àÑ<Úã½Ö¨Ý¬æ/Õ¨ÚÝ§Ô$ÖäpÑ<Ù<àUÐ/àÔ$ÚhÑ(ãx×ÁÖÐ/ÚJá½Ð:Ñ<×ÁÝ ÓJê½ÐÚÕÖ5ÝÁÔ$àÑxÕÐÔ ÕÚJà²äÔ/Ñ(ëDÚhÕé&ê½á<ÚxÐ×ÁÕ¨Ú ÝÁðÔ/Õ ÑYWëÓý Ô$Û!Ø<ç Ð:Ñ½ÝÁÔ/Ñ(ÖÚJÐ:×ÁÝ JÐÕ¨Ý§Ô$ÑÔ ìì ìì @ê½ÚhÑ£ÜFÕê½Ú²Ô$Ù<àÚhÖæ/ÚhÖäµÙ<Ð/àÚhãÖ¨ÚhÐ/×§Ý hÐ:ÕÝÁÔ/ÑBÔ Ö¨ÚhÐ/ã<à K . LK. . /. . 14. Time (s). . . QK. K(s). /. Q. . K(s). K. K(s).  ˙   ψˆ −4 1  ˆ˙    ψ˙  = −6 −3 −2 −3 β.  4  4  −1. ëý ì.  ψˆ ˆ  ψ˙  ψ. . /Ð à¨àÔFèMÓÝÁÝ´û/Ðá½ÕÚJÖ¨Úhãà ú)@Ý§Ø<ÕêO×§Ô/Õ¿Õ¨ê½ÕÚ²ê½ÚÚhàÓÕ×ÁÝÁÔ&Û!àÚhÐ:ãFÕäpÚJ×ÁãOÔ\Ô/àØ²Õ¨ÐàÕ¨Õ¨ÚÐ:Õæ/ÚQÚhÖ¨ÓÚhÕàÔ$ØHÖ Ô$Ñ<àÚhàwëD×´Ð:á½Ñ<Óê½ç ÚÖMÐ/Ñ<ãUÓÔ/Û!ØHÚhÑ<àÐ:ÕÔ$Ö ÕÔ ÝÁÑ½Ý§ÕÝ´Ð:×\ÓÔ/Ñ<ã½Ý¬Õ¨Ý§Ô$Ñ<à¿Ô/ÑU×ÁÐ/á½Ñ<Óê½ÚÖ àFÕ¨ç Ö¨ÐÝ§Õ¨û$Úhê$àhÕçQÝ´èMàÝ§û$Ô/á½ÙFÖÕÚ Ð:ÝÁFÑ½ç Úh×§Ú ãðÕú)Ý´Ý§à)ÕêÔ/ÙFÕ¨Õê½Ð:ÚWÝÁÑ½Ô/ÚhÙ<ãOàÚú)Ö¨ê½æ/ÚÚÑSÖäpÙ<Õê½Ð/Ú²àÚJô<ãÖ¨àÖ¨Õ ÚhÐ/Ó×§Ô$Ý hÛ5Ð:ÕØHÝÁÚhÔ/Ñ<Ñà¨ÐëDÚhÕÔ$é&Ö@á<ÐÖ¨Õ¨ÚhÝ§Ð:Ô$×ÁÑÝ hÐëÕ¨ý Ý§Ô$ÑçWë ÚJè½é$Ô$áì ÖÐÕÙHÝÁÔ/Ô/Ñ(ÕêYëý$àÝ§ý Ûaìì á½×´ÝÁÐà)Õ¨á<Ý§Ô$àÑ<ÚhãOàÕú)ê½ê½ÚWÝÁ×Á×ÁÚUÐ/á½èMÑ<Ý§û$Óê½á½ÚÖ¨ÚÖ àÓÕ¨Ô$ÐÛ!Õ¨Ú²ØHÚÖ¨Ñ<Úhàà¨ØHÐÕÔ/Ô$Ñ<Ö£àÚhÝÁà¿à)ÝÁÐ/Ñ<ÖãFÚÚØHÕê<ÚhÚaÑ<ãFàÚÐ/Ñ&Û!ÕMÚUÔ FÐ/Ý§à@Õ¨à¿Õ¨ê½Ö¨ÚhÚUÐ/ÝÁ×§Ñ½Ý hÝ§ÕÐ:Ý´ÕÐ:ÝÁ×Ô/Ñ£ÓÔ$ç Ñ<áãFFÝ§ÕÕhÝÁÜÔ/Ô/Ñ<Ñ½à ÚQÐ:ÓhÖ¨Ð:ÚÑUÕ¨àê½ÚÚaÚwà¨ÝÁÑaÐ:Û!èÚUÝÁû/Ð:á<ÑÖìÚ ãSì ½Ð/ç ×Áà)Ú ðÕÕ¿ê½ÕÚUêÝÁÐÑ½Õ¿Ø½ÕáFê<ÕÚäpÖ¨Ô$ÚwáFÝ´Õà£Ø<Ñ½áFÔÕàÙHÕ¨ÚÖ¨ê<Ð/Ð±Ý§û$æ\ê$Ý§Ô$Õ Ö)Ô/ÔÖ¨úrÐ:Õê½Ö¨ãÚ Ö¨ÓÚÔ$×´Û!ÐÕØHÝÁÔ/ÚÑÑ<à¨ÐÙHÕÚÔ$ÕÖ)úàÚhÕÚÐÑÎÕÚJÓà@Ô/Ô Û!ØHÕ¨Úhê½Ñ<Ú²àÔ/Ð:ÙÕÔ$àÖBÚhÖæ/àÕ¨ÚhÐÖÕ¨äpÙÚhàOÐ:àÐ/ÚhÑ<ããÖ¨Úh×ÁÐ/Ð/×§á½Ý hÑ<Ð:Ó¨Õê<ÝÁÔ/ÚÖSÑBàÐ/ÕÖÐÚÕ¨Úhû/àÔ\Ô½ë ãÚJÐ:àÕ¨ÑÝ§ãÛWÐÕ¨Úhì ãOú)Ô ê½MÝ§×Á×´ÚÐ:á½èMÑ<ÝÁÓû/ê½á½ÚhÖ¨ÖÚ àÕFÐç ÖÕÝÁÚJû/à)ê&Ð:ÕBÑ<ê½ãSÝÁû/Óê½Ð:×ÁÑOÝ§û$ÙHê$Ú²Õàxá<Õàê½Úhã Ú ÕÐ:ÔOÖ¨Ú Û!Û!Ô/ÚhÑ½Ð/Ý§ÕÑ½Ô$ÝÁÑ½Öû ×ÁÐ/á½á½×eÑ<æÓÐ/ê½ÖÚÝ´ÖÐ:Ù<à×§Õ¨ÚJÐ:à ÕÚ ë Ô/ÖÔ äµÐ/×§Ñ<ÝÁÑ½ã Ú5Ô/ÖÝ§Ñ½äp×ÁÝ§Ñ<Ú5Ü\Ð/Ô$Ñ<Ñ½Ð:Ú×ÁÒFÓÐ/àÝ´ÑBà;Ð:ë ×´DàÐ:Ô;ÝÁ×§á½ÓÔ/Ö¨Ú!Ñ<ÓãF×§á<ÝÁÐ/ã½û/Ú Ñ½Ô&Õê<àÝ´Ð:à ÕÕÔ/ê½ÖÚÝ§Ñ<àÕ¨àÐ:Õ¨Ð/ÕÚ Ñ<ÓÚhÚ Úhì ãFçaÙ<ÿ Ð$àÓ WÕê½û$Ú!Ð/Ý§Ø½Ñ ×ÁÐ/Ñ$Õ²ê<àÕ¨Ð/Ð:àÕÐÚ ØÔ/½Ùê\àÒ\Óàá½Ý´ÓÖÐ:Ú$×eç ãFÝÁÛ!ÚÑ<àÝÁÔ/Ñ ú)ê½ÝÁì ×ÁÚ Õ¨ê½ÚãFÝ§Û!ÚhÑ<àÝÁÔ/ÑxÔ Õ¨ê½ÚæÐ/ÖÝÁÔ/á<àÓÔ/Û!ØHÔ$Ñ½ÚÑ&Õ¨àÔ ¿Ö¨ÚhÐ/×§Ý hÐ:ÕÝÁÔ/Ñëý/ý ì @Å2Í +3$%J1#&'5(& ( 38 @ @ê½Ú ¿ÚÕWFèá<àWúÓÚÔ/ãFÑ<ÚàÕ¨ÝÁã½Ð/Ý§Ú×<ÖWÝ§Ñ!ÐÕàê½ÒFÝ´ààQÕàÚhÚJÛ Ó¥ÕÝÁÔ/Ñ!Ý´àfÙ<ãFÐ/Úô<àÚhÑ½ã5ÚhãÔ/Ñ5Ù\ÕÒ ê½ÚÚhé&Ø½á<Ö¨Ð:Úæ\ÕÝÁÝÁÔ/Ô/ÑÎá<àrëÔ$ý Ù<àÐ:ÚÑ<Ö¨æ/ã ÚÖrÕ¨ê½Ù<ÚÐ$ààÚJÕ¨ã;Ð/Ñ<Ö¨Úhã½Ð/Ð:×§ÖÝ hã Ð:ÕØ½ÝÁÖ¨Ô/Ô/Ñ;Ù<Ô ×§ÚheÛ Ðû/ÝÁæ/ÚÑWÓÔ$ÓÐ/Û5×§×ÁØHÚhÚhã Ñ<à¨rÐíÕî±Ô$õÖhõ ç ì. :í ¿î:í ë Fè ì ÜÐ/à¨àÔ½ÓÝ´ÐÕÚJãú)Ý§ÕêOÕê<ÝÁààÒFàÕ¨ÚÛ ëý ì ú)àØHê½ÚhÚhÓÖÝ§ÚôÓÐ:ÕÝÁÔ/ÚÑ<Õ àÙ&ÒWÐ/Ð;ÖÚ àá½Ö¨Ý¬ÚhÕàÐ:ØHÙ½Úh×ÁÓÚ ÕÕÝÁæ/ÚJÚÓ¨ê½×ÁÒ!Ñ<ÝÁÐ;é&á½àÕÚ!ÐÕë Û!Ú ÔFÚhã½ÚhÐ/ãF×nÙ<Ü Ð$Ó W5û$Ð:ÜHÝÁÑxçÁç§ç Ð:'ç Ñ<FãxÐ;Úàú)ÕÝÁÐ×§Õ¨× Ú Ð:×´ÚJààÔ;Õ¨Ý§Ð/ÛWà¨àÐ:á<ÕÝÁÛ5Ô/ÑÚ Õû&ê<Ð:Ð:ÝÁÑxÕ àÒ\Ñ&Õê½ÚJàÝ ÚJÚã!Õ Õ¨Ô;Û5ÚhÚÕ)àÔ$Ð:Û5Ö¨ÚÚ ì àÕ¨Ð:Ù<×§Ú$ç +. . ˆ˙ T ˆ ψ] x ˆ = [ψ,. . . . . . . )K. . . . 4. ,. ψ˙. ψ. . ψ (rd) Kc = [3. rd/rd. Q. . ψ˙ (rd/s) 3. s]. . .

(22) . . . G9I. . =@?A B? DB. >F. G9I. G(s).   x˙ A Pp (s) :  z  =  Kc y C. Kc. Kf. . - + . . -. . . Kc. . Pp (s). K. . D. Kf 0 Ip.   B x Im   w  D u. Q. . A − BKc. A − Kf C.

(23) QöHíî:øh÷ $ù ½ùí ù õ ±Wõ ¨î @ù ö põ÷ î:ï nï÷Dî îí!õ FñÁ÷ õîö õpî÷ ï" p:÷Dïî Oõ¨ î÷ ½ù÷ õ$ùù¥õ õ)(f÷ í¥í¥÷Dù!½ù+î*- ,/.î î ½ùWníî:õ ïðï§ùí Hí î!µùöH1íî0 ï§ù.

(24) H ?A B H %= F ? 2 B 6A -B B

(25) =! ∞?F " = A$#&%' 2 /B A K ?A%B K ?A%B -?CB &0. /Fù ÷ðï eBù î. c. %= F ? A= :<-? = A < A < B =. = A = >=@?A%BC? DB 8< A = A = MB. x ˆ˙ u. ¸. =. ·. . K. :. Kf 0. A − BKC − Kf C + Kf DKc −Kc. @ê<ÚàÕÐÕ¨ÚäµàØ<Ü½Ð$ÓÖÚhÚ Ð$Ö¨ã½Úà Ø<ÖÚhàÚÑ&Õ¨Ð:ÕÝÁÔ/ÑÔ £Õ¨ê½ÚàÕ¨Ð/Ñ<ã½Ð/Ö¨ã Ô/Ö¨Û . Fl (Pp (s), KLQG (s)). .   x˙ A  x ˆ˙  =  Kf C Kc z . Pp (s). . ¸·. .

(26) . . . x x ˆ. ¸. Pp (s) KLQG (s). =M. x ε. ¸. M= K. Fl (Pp (s), KLQG (s))    A − BKc BKc x˙  ε˙  =  0 A − Kf C z 0 Kc. ·. In In. 0 −In. KLQG (s). ë ý ì Ð$ààÔFÓÝ´ÐÕ¨Úhã ú)Ý§ÕêÕ¨ê½Ú ëý ì 0. ε = x−x ˆ ¸. ë ý ì Üe÷#ðù9# L. ..   x Kf ˆ  . Kf   x 0 w. −BKc A − BKc − Kf C −Kc. ·. ¸. M. K. ·. x ˆ y. Úhã\äµÙ<Ð/Ó WÙ&ÒWÕê½Ú²ÓÔ$Ñ$ÕÖ¨Ô/×Á×ÁÚÖ. £; ÚÕB<>á= àB?+ÓhÐ:@BAÖ¨ÖôÒ×¬Õ¨Ô/Úá½Ö ÕxÕê<ÚÝÁÑ$Õ¨ÚÖ¨Ñ<Ð:×àÕÐÕ¨ÚÛ!Ð/Ø½Ø½ÝÁÑ½û^á<àÝ§Ñ<û Õê½ÚÚhàÕ¨Ý§ÛWÐÕ¨Ý§Ô$ÑÚÖ¨ÖÔ$Ö ú)Ý¬Õ¨ê @ê½ÚhÑ£ÜFÕê½Ú²Ñ½ÚhújÖ¨ÚØ½Ö¨ÚhàÚÑ$ÕÐÕ¨Ý§Ô$ÑxÔ ÖÚJÐ/ã½à. F. f. ·. 3 46587. MB =. Q2. .. ë ý ì FÚ5ÓhÐ:ÑÑ½Ô:Õ¨ÝÁÓÚaÕê<Ð:ÕÕ¨ê½Ú!àÕÐÕÚJà Ð/à¨àÔFÓÝ´ÐÕÚJãSú)Ý§ÕêÕê½Ú5ÚhàÕÝÁÛWÐÕ¨Ý§Ô$ÑÚhÖÖ¨Ô/ÖÐ/ÖÚaá<Ñ<ÓÔ/Ñ&ÕÖ¨Ô/×Á×´Ð:Ù½×ÁÚaÙ&Ò Ð:Ñ<ãÕêÐÕÕê½Ú àÕ¨ÐÕ¨Úhà Ô Õê½Ú²Ø<×ÁÐ/Ñ$Õ Ð:Ö¨Úá½Ñ½Ô$Ù<àÚhÖæ:Ð:Ù½×ÁÚÙ&Ò ç @ê½ÚÕ¨Ö¨Ð/Ñ<à ðÚhÖ@ÙHÚÕúÚÚÑ Ð/Ñ<ã ÝÁà@Õê½ÚhÖÚ Ô/Ö¨ÚÑ\á½×§× ëý ì Ð:Ñã Ü½ÓÔ/Ñ<àÚhé&á½ÚhÑ$Õ×ÁÒ ëý ì @ê½Ý´à)ÓÔ/Ñ&ÕÖ¨Ô/×Á×§ÚhÖÝ´à@Õê&áà@Õê½Ú²Ô$ØFÕÝÁÛWÐ:×£àÔ/×ÁáFÕ¨Ý§Ô$ÑxÕ¨Ô5Õê<ÝÁààÕ¨Ð/Ñ<ã½Ð:ÖãxØ½Ö¨Ô/Ù½×ÁÚÛ¶ë ì ÁÝ Ñ Ð/Ñ<ã Ñ½Ô/Ö¨Û àÚÑ<àÚ/ç x. ε. . z. 6.   Kf x 0  ε  . 0 w. N. w. 3. . z. K. w. L5. Fl (Pp (s), KLQG (s)) = 0. OK. Q;. kFl (Pp (s), KLQG (s))k2 = kFl (Pp (s), KLQG (s))k∞ = 0. . Pp (s). H2. H∞. \Û!Ñ½Ý§ÔÑ<@ú)Ý§Û!ê<ÑSÝÝÁhàÐ/ÐàCÖÕ¨ÚJÝ§àÔ$*-á½Ñx,×§Õ@Ö¨ÚhÓ÷ <àÐ/ÕøÑxÔ$ùÖÙíÚõÚù)ÐaÓÖÔ$û$Ð:Ñ<Ý§Ý´æ/ààÚhÚhÝ´ÑBãFãBÚhàÝ§ÖÕÑSÚJÐãÕ¨Õê½Ú Ð/Ú àÚ\ÐaÚJÝ§ãFß&û/Ù<ÚÕ¨Ð/Ý§Ñ½ÚJÓ ÚhàeÖ¨Ð/Ð:ç ×§Ñ@Ý hã ê½Ð:Ý´FÕà ÝÁÚÔ/æ/Ñ£Ú½Ü Ñ&èYÕÔ/ÝÁÚhÖ á<ààÚhÐ/ãBÑ<ãOÐ:Ð/Ñàú)ã àê½á<Ý´ÓÓ¨êxêÝ´ÓàÓÔ/Ö¨Ñ½Ñ<Ý¬Õ¨Ô:àÚÕ@Ý´Ö¨àÕ¨ÝÁÔ Ð<ÚhÜ$ãBÝ§ÔÑ&ÝÁ£ÕÑOÚÕÖ¨ê½ô<ÚhÚÑ<àÕ@ã½àÝ§Ô/àÑ½×ÁÝÁáFÑ<ûWÕÓÕÝÁÚÔ/ê½ÑÝ¬Ú Õ)ÕÝÁÔaàÑ½Õ¨ê½ÚhÓÚÓÔ$ÚhàØ½à¨Õ)Öàú)Ô$Ð/ÖÙ½ê<Ò;×ÁÔ$ÚÕ¨ÛàÔÚ \ØHÑ½ÚÑ<ÔúÎà¨ÐÕ¨ÕÔ/ê½ÖJÚaç û&Ð:ÑOÝÁÑ<Õ¨à ê½ÚUÔ:Õ¨Ð:ê½ÑÚã ÖêÐ:Ñ<ã ÕÔ Ü Ö¨Ô$Ô/ÖÛ ÛWÐÐWÕ àÕÕê½ÐÚ5Õ¨Ú àÕÚÐ:ÚJÑ<ãFã½Ù<Ð/Ð/Ö¨ÓãSØ½Ö¨Ô/Ù½à¨×ÁÚÐÛ Õ¨ÝÁà Ò\Ý§Ñ½ûàÐ:Ô/Ñ<Û!ãSÚÕÕÔÝÁÛ5ô<Ñ<Úaãã½Ô/ô<ÛWÑ<Ð:Ð:×ÁÝÁ×ÁÑÒBàÕØHê½ÚJÚ;ÓÝ§Ý§ôÑ<Ý¬ÓÕ¨Ð:ÝÁÕÐ/ÝÁ× Ô/Ñ<à)ÖÚh×ÁÐ:ÓÕÔ/ÝÁÛ5Ñ½û ä ÕÓÔxÔ$Û!ØØ½Ð:Ö×§ÚÕÕÝ´ÓÚJá½ãa×´Ð:Ù&ÖÒaàãFÕ¨Ò\ÐÑ<Õ¨ÚhÐ/à Û5Ô Ý´rÓÕ¨úê½ÚÚ5ÝÁû/àê$ÒFÕ¨àÝ§ÕÑ<Úhû$ÛOàÜÕÔÕ¨ê½ÕÚ Ð /Ú½ÝÁÑ$è9Õ¨ÔÓÐ:Ð$ÑÓÓÙHÔ$Úaá½Ñ$æ/ÕfÚhÖàÒOÔ/Û!á<Ú@àÚ ÓÔ/á½Û!×Õ¨Ø½Ôx×ÁÚÝ§Û!Ñ<Ý¬ÚhÕ¨Ñ$ÝÁÐ/Õ¨×§Ð/Ý ÖÒÚ;ÐxÖ¨Úhàé&Õ¨á½Ð/Ñ<ÚÑã½ÓÐ:ÒUÖãã½Ô/àÚÛWÕäµÐ:á½ÝÁÑ5Øàú)ØHê½ÚhÓÝ´Ó¨Ý¬ôHêÓú)ÐÕ¨Ý§Ý§×ÁÔ$×MÑ<ÙHàhÚ ç @ Å ED GF EÆ HD

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