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1 7ZA8$ I B y q strs{$btr Bt VZB8s${ ]Bt Bj 7sA$j$k sti VRk8}B${ _ PB 8st{ VtsjkR$R BP s ]jsrr BP i R ]Bt Bj 7kR 8R +$st ]Y t G OBRR$ ]Ys$ sti ]z <BjjB VZZR 1((( VAR s{ BI :R s$tt}ysr js$btry$} }js{ R s Ys I j$8$s$bt Bt } PB 8st{ si B&R $t j$t s $8 T$t%s $st P IAs{, {Bt Bj RkR 8R y YsR jbt A t RZ R I Ys R {Bt Bj YsR Y }B t$sj B $8} B% Y$R R$Zs$Bt i { t -} $8 tsj RZI$ R RZ}}B Y$R {js$8 qy$r }s} PB{ZR R Bt Y stsjkr$r BP RZ{Y R {Bt Bj RkR 8R by${y YsR A t 8$RR$t $t Y$R }sr bb, 7} {$h{sjjk b $% RZjR Bt ABZtI IT$t}Z ABZtI IT BZ}Z RsA$j$k srk8}b${ RsA$j$k sti R siktrs } PB 8st{ qy R RZjR s s}}j$ I B st -} $8 tsj I 8BtR s$bt BP R {Bt Bj BP s 4 -$Aj 8 {Yst$R8 qy$r 8s $sj $R AsR I Z}Bt bb, RZ}}B I Ak Y Ws$Btsj 7{$ t{ BZtIs$Bt ZtI p st WB]7T M((Ed1 G y * }s 8 t =t$% R$k BP srrs{yzr R V8Y R V (d((n {Y to {RZ8sRR IZ y * }s 8 t =t$% R$k BP srrs{yzr R V8Y R V (d((n {Ys$o {RZ8sRR IZ ] * }s 8 t =t$% R$k BP srrs{yzr R V8Y R V (d((n YBjjBo {RZ8sRR IZ

2 d yt BIZ{$Bt y $R b jjts}} {$s I Ys BI :R s$tt}ysr js$btry$} >dh }js{ R s Ys I j$8$s$bt Bt } PB 8st{ si B&R $t j$t s $8 T$t%s $st wnqyd P IAs{, {Bt Bj RkR 8R 7} {$h{sjjk Y t I B 8$t$8$9 Y B} ttjbb} Y$YTP JZ t{k s$t BP t {B8} R b$y JZ$ I Y$Y j % jr BP jbbtp JZ t{k jbb} s$tr sti }YsR 8s $t ABZtIR!Z PB{ZR Bt R {Bt Bj RkR 8R $R 8B$%s I Ak $R }B t$sj B $8} B% Y$R R$Zs$Bt sr I 8BtR s I YB ${sjjk $t >1H d sti Ak R$8Zjs$BtR sti -} $8 tr >nht>eh qy AsR${ {Bt{ } $t R {Bt Bj $R B R Y Rs BP s j$t s {Bt Bjj B 9 B by t % $R $t}z 8 R s Y RYBjI qk}${sj R {Bt Bjj R $t{jzi Y RBT{sjj I ]j $t sb >H sti h RTB I R j 8 t w!id >nh qy PB 8 $R s j$t s $t sb bybr BZ}Z R R B 9 B by t $R $t}z { BRR R 9 B qy js t sj$9 R Y ]j {Bt{ } B s h RTB I js hj yt >H Y ]j $t sb bsr RYBbt B Ys% s I R{ $A$t PZt{$Bt R$8$js B Y P JZ t{k R}BtR BP s j$t s $t sb AZ b$y Btjk nmd H }YsR js V!i bsr RYBbt B Ys% R$8$js P sz by$j } B%$I$t s PZ Y I R$t P IB8 by t {B8}s I b$y ]j T$t sb w>;h sti >EHD yt BZ RZIk b sib} Y!i R 8 {Yst$R8 $t P IAs{, $t {Btt {$Bt b$y s j$t s RkR 8 B BAs$t Y RBT{sjj I R {Bt Bj RkR 8 RYBbt $t $Z d qy R$tsjR, r,, z sti Q $t $Z d } R t P t{ $t}z BZ}Z B R$tsj R trb tb$r sti I$RZ Ast{ R} {$% jk sti UwXD I tb R Y j$t s jbb} {BtR$R$t BP Y }jst sti stk j$t s {B8} trs$bt 1 r _ FORE L(s) d y n $Z du qy {jsrr BP R {Bt Bj RkR 8R {BtR$I I $t Y$R }s} qy BA` {$% BP Y$R }s} $R B } B%$I s j % j BP stsjkr$r 8$RR$t $t }sr bb, Bt R {Bt Bj qy stsjkr$r $t >H bsr j$8$ I B I R{ $A$t PZt{$BtR by$j >nh sti >;H $tb I RsA$j$k $RRZ R sjb Y Vt s}}j${s$bt BP R8sjj s$t $t >xh s}} s R BB {BtR %s$% sti {BZjI tb %sj$is Y BAR % I -} $8 tsj } PB 8st{ $t >EH B$%s I Ak Y$R js{, BP RZjR Y$R }s} {Bt$tZ R BZ { t bb, }B I $t s R JZ t{ BP {BtP t{ }s} R >MH >H sti >d(h yt Y$R }s} b $t BIZ{ s {BtI$$Bt {sjj I Y # }BR$$% T sj {BtI$$Bt by${y by t Rs$Rh I sjjbbr Bt B srr y! sti srk8}b${ RsA$j$k BP Y R {Bt Bj RkR 8 =ti Y$R {BtI$$Bt b b$jj sjrb RYBb Ys Y R {Bt Bj RkR 8 $ty $R Y R siktrs s{,$t } B} $ R BP st ZtI jk$t j$t s {Bt Bj RkR 8 z k $8}B stjk d qy$r bb, } B%$I R st -s8}j BP {Bt Bj R} {$h{s$btr Ys {st A s{y$ % I Ak R {Bt Bj sti tb Ak j$t s P IAs{, 1 qy I R$t BP Y R {Bt Bj RkR 8 $t $Z d $t%bj% R Y R j {$Bt BP ABY Y!i:R }Bj sti RB8 j$t s {B8} trs$bt $t UwXD qy$rb$jja I$R{ZRR I $t7 {$Btx d

3 b b$jj RYBb Ys Y # }BR$$% T sj {BtI$$Bt $R Rs$Rh I PB Y -} $8 t {BtR$I I $t >EH YZR {Bth 8$t Y BAR % I RsA$j$k sr b jj sr I 8BtR s$t Y s}}j${sa$j$k BP BZ RZjR i R {Bt Bj s{$bt R 8Aj R s tz8a BP }B}Zjs tbtj$t s {Bt Bj R s $ R $t{jzi$t jsk {Bt Bj >ddh Rj$I$t 8BI {Bt Bj >d1h sti Rb${Y$t {Bt Bj >dnh V {B88Bt P sz B Y R $R Y ZR BP s Rb${Y$t RZ Ps{ B $ {Yst $t {Bt Bj R$tsj *$R$t{$% jk R {Bt Bj 8}jBkR Y Rs8 wj$t s D {Bt Bj jsb Bt ABY R$I R BP Y Rb${Y$t RZ Ps{ i R $t B{{Z R by t Y RkR 8 s` {B k $8}s{R Y$R RZ Ps{ qy$r R s{$bt {st A sj ts$% jk %$ b I sr Y $t` {$Bt BP `ZI${$BZRjkT$8 I Rs TI } ti t $8}ZjR R $tb st BY b$r Nqy P IAs{, RkR 8 qy$r stsjbk $R %$I t $t Y }s} by b ZR $8}ZjR$% I$& t$sj JZs$BtR R >d;h sti >dxh B 8BI j Ikts8${R * R}$ Y$R js$btry$} b PBZtI -$R$t Y B k Bt $8}ZjR I$& t$sj JZs$BtR B A $Y BB t sj B A BsI B A BP $88 I$s sti I$ { ZR $tsjjk Y$R {Btt {$Bt B $8}ZjR$% {Bt Bj Y j}r B I sb {B8}s $RBt B s ABIk BP {Bt Bj bb, >deh by $8}ZjR R b $t BIZ{ I $t st B} ttjbb} PsRY$Bt B JZsRY BR{$jjs$BtR $t %$A sb k RkR 8R qy }s} $R B st$9 I sr PBjjBbR yt 7 {$Bt 1 b R TZ} s 8BI j B I R{ $A Y R {Bt Bj RkR 8 $t $Z d sti $I t$pk s, k ZtI jk$t j$t s {Bt Bj RkR 8 by${y b P B sr Y AsR Tj$t s RkR 8 7 {$Bt n $R { t sj y $t BIZ{ R Y$R tb$bt BP # }BR$$% T sjt RR sti j$t,r $ B y! RsA$j$k yt 7 {$Bt ; b ss$t ZR Y # }BR$$% T sj {BtI$$Bt B RYBb Ys Y AsR Tj$t s RkR 8 }srr RTBt $R R siktrs } PB 8st{ } B} $ R B Y R {Bt Bj RkR 8 yt 7 {$Bt x b s}}jk Y R RZjR B st -} $8 tsj RkR 8 $t%bj%$t R} I {Bt Bj BP s 4 -$Aj 8 {Yst$R8 by${y b$jj I 8BtR s Y tbtt $%$sj s}}j${sa$j$k BP BZ stsjk${sj RZjR y sjrb } B%$I R stby $ti } ti t sti Ps%B saj {B8}s $RBt BP R B Nqy {Bt Bj 1 7 T=} yt Y$R }s} b PB{ZR Bt Y R {Bt Bj RkR 8 $t $Z d by Y h RTB I R j 8 t w!id $R I R{ $A I Ak Y $8}ZjR$% I$& t$sj JZs$Bt >d;hu? W wd ) K? W wd L wd wd W) (? W w L D ) ( wd )( by? W $R $R Rs $R Y RkR 8 B sti K Y!i:R }Bj R >nh qb s%b$i I t T s$bt B s Nqy RkR 8 b srrz8 Ys Y!i {Bt$tZsjjk R R G {Bjj { Y R R $8 R $t Y ZtABZtI I R { ) \ 7 / D )(, 7 k 7d L, k (, 7)d, 1,, i by b srrz8 Ys si`s{ t R $8 R s tb {jbr Yst qy$r srrz8}$bt $R {Yt$T {sjjk 8B$%s I Ak s I R$ B Ys% {jbr ITjBB} RBjZ$BtR {Bt$tZsAj B% >(, D AZ $R 8 by t!i $R I$$sjjk $8}j 8 t I sti Y Rs8}j$t } $BI $R s jbb ABZtI B 1

4 V Rs TR}s{ I R{ $}$Bt BP Y R {Bt Bj RkR 8 $RU? wd ) \? wdl4? W wd? W wd ) g? wd K? W wdljwd b; {? W w L D ) ( ; { rwd ) g? wdlqwd wdd by \\, 4, gi I tb R s 8$t$8sj sj$9s$bt BP UwXD? wd ;_ z sti jwd ) P wd zwd QwD $R Y s s $t}z R$tsj p$% t w? w(d,? W w(dd Y RBjZ$Bt B wdd $R }$ { b$r j PT {Bt$tZBZR Bt Y $t %sjr, 7Ld H yt Y sar t{ BP R $t wdd IZ{ R B Y PBjjBb$t j$t s RkR 8U ^ ^ ^ ^ ^? q wd P)? q wd (? \q L q w(d? ) w(d w1d? Wq wd? Wq wd jwd? Wq w(d? W w(d by ^ \ q ) \ 4 g K G P B Y$R sr Y AsR Tj$t s RkR 8 sti $t Y R JZ j b b$jj RYBb Ys $ {st }srr Bt RB8 BP $R } B} $ R RZ{Y sr RsA$j$k sti srk8}b${ } PB 8st{ B $R srrb{$s I R {Bt Bj RkR 8 n y! 7sA$j$k VtsjkR$R yt Y$R R {$Bt b stsjk9 Y y! RsA$j$k BP wdd by${y JZ$ R % k ABZtI I $t}z n j B } BIZ{ s ABZtI I BZ}Z r qb A $t Y$R stsjkr$r b s}}jk Y strpb 8s$Bt F wd F W wd )? wd? q wd )? W wd? Wq wd wnd B wdd B BAs$tU F wd ) \F wd L 4F W wd F W wd ) gf wd KF W wd b; { F W w L D )? 7 Wq D ; { w;d VR st $t 8 I$s R } b RYBb Ys ABZtI It RR BP F $8}j$ R Ys r $R ABZtI I N 88s du VRRZ8 \ q $R srk8}b${sjjk RsAj sti Q sti z s ABZtI I yp F $R ABZtI I Y t BZ}Z r $R ABZtI I n V R$tsj F $R Rs$I B ABZtI I $P Y -$RR s {BtRst - RZ{Y Ys /FwD/ c- PB sjj n

5 _ BBPU G Ys% /rwd/ ) /g? wdlqwd/ /gf wd/ L /g? q wd/ L /QwD/ 7$t{ \ q $R RsAj sti j $R ABZtI I Y t? q $R ABZtI I!Z}Z r $R YZR ABZtI I ( PB b } R t BZ 8s$t RZj Bt y! RsA$j$k b t I Y PBjjBb$t j 88sR N 88s 1U yp \ q $R srk8}b${sjjk RsAj sti j $R ABZtI I Y -$RR {BtRstR - d sti - 1 RZ{Y Ys /F W w L D/ c- 7 d sti /gf D/ c- 1 PB 7 )d, 1,, _ BBPU {szr \ q $R srk8}b${sjjk RsAj sti j Y t? Wq sti? q s ABZtI I B8 w;d F W w L 7 D )? Wq D qy PB Y -$RR st - d RZ{Y Ys /F W w L 7 D/ c - d PB 7 ) d, 1,, k I ht$$bt gf D ) j D g? q D 7$t{ j sti? q s ABZtI I Y t Y -$RR st - 1 RZ{Y Ys /gf D/ c- 1 PB 7 )d, 1,, ( qy t - $R Y b jjt,tbbt k T sj8sttos,zab%${y N 88s >dh N 88s nu N.wXD ) _wx{ BD d / A s R{sjs strp PZt{$Bt by I $R srk8}bt ${sjjk RsAj yp.wxd $R R ${jk }BR$$% T sj ; Y t Y -$R s Rk88 ${ }BR$$% TI ht$ 8s $- h s% {B R sti s }BR$$% {BtRst RZ{Y Ys B x h L hb ) R x R h h/ ) _ x!z t - I ht$$bt $t BIZ{ R s }BR$$% T sj {BtI$$Bt Ys $R, k $t RsAj$RY$t Y RZjR BP Y$R }s} * ht$$bt du qy R {Bt Bj RkR 8 wdd $R Rs$I B Rs$RPk Y # }BR$$% T sj {BtI$$Bt $P Y -$RR s # ;_RZ{Y Ys _wxd P )>#g dhwx{ \ q D d >( NNN (dh x $R R ${jk }BR$$% T sj wxd G tbb Rs s 8s$t RZjU qy B 8 du qy R {Bt Bj RkR 8 wdd $R y! RsAj $P Y # }BR$$% T sj {BtI$$Bt wxd $R Rs$Rh I _ BBPU 7$t{ _wxd $t wxd $R R ${jk }BR$$% T sj Y t P B8 N 88s n Y -$RR s }BR$$% TI ht$ 8s $- h s % {B R sti s }BR$$% {BtRst RZ{Y Ys h\ q L \ x h ) R h q Rx h >( NNN (dh x ) >#g dh x wed ; V strp PZt{$Bt wxd $R Rs$I B A R ${jk }BR$$% sj $PU w$d wxd $R srk8}b${sjjk RsAj sti w$$d i > widh k (, ( ;

6 < t{ h {st A b $ t sr h ) ^ hd #g x #g d by h d ;_ zz $R }BR$$% TI ht$ VjBt Y }$ { b$r j PT{Bt$tZBZR RBjZ$BtR BP w;d b I ht ~ wd ) >F x wd,f WwDHh >F x wd,f WwDH x ) F x wdh df wd L1#gF wdf W wd LF 1 W wd B% ;, 7Ld H V Y R $trstr ) 7 b Y t Ys% ~ w L 7 D ) Fx w 7Dh d F D L1#gF DF W w L 7 D L F1 W wl 7 D ) ~ D L1#gF DF W w L 7 D L F1 W wl 7 D 1#gF DF W D F 1 w W 7D 7$t{ 1#gF DF W D F 1 w W 7D w#gf DD 1, ~ w L 7 D ~ D L1#gF DF W w L 7 D L F1 W wl 7 D L w#gf DD 1 ) ~ D L>F W w L 7 D L #gf DH 1 wd {szr j $R ABZtI I $ PBjjBbR P B8 N 88s 1 Ys Y -$RR s {BtRst - k (RZ{Y Ys >F W w L 7 D L #gf DH 1 - PB 7 )d, 1,, qyzr P B8 wdu ~ w L 7 D ~ D L -, 7 )d, 1,, *$& t$s$t ~ wd sjbt RBjZ$BtR B w;d b ZR wed B BAs$t ~ wd ) >F x wd,f WwDHwh\ q L \ x q h D>Fx wd,f WwDH x ) >F x wd,f WwDHwR x R h D>F x wd,f W wdh x >F x wd,f W wdhh >F x wd,f W wdh x ) ~ wd PB sjj ;, 7Ld H qy tbttt s$%$k BP ~ wd $8}j$ R ~ wd w7d ~ w L 7 D wmd by t % ;, 7Ld H 7$t{ 7Ld 7 k ~ Ld D Ld 7D ~ w L 7 D ~ w L 7 D >~ D L - H ]B8A$t$t Y$R b$y wmd $% R ~ wd w 7D > w7dd ~ w(d L - L - L L w7dd -H wd x

7 PB sjj ;, 7Ld H 7$t{ ~ w(d ) ( ~ wd -bwd D qy PB ~ $R ABZtI I {szr h $R }BR$$% TI ht$ $ PBjjBbR Ys F $R ABZtI I $tsjjk P B8 N 88s d r $R ABZtI I qy$r {B8}j R Y } BBP i 8s,RU w$d GY$j Y # }BR$$% T sj {BtI$$Bt $R Btjk RZ^{$ t PB y! RsA$j$k $ s}} s R Ys $ 8sk A s}}j${saj B tbtt $%$sj R$Zs$BtR B -s8}j $t 7 {$Bt x b RYBb Ys Y$R {BtI$$Bt $R Rs$Rh I PB s R {Bt Bj RkR 8 Ys%$t d1 _ TB I UwXD 7$8$js jk $t >dmh Y -} $8 tsj R TZ} $t >EH $R RYBbt B Rs$RPk Y # }BR$$% T sj {BtI$$Bt wxd w$$d qy -$RR st $8}B st {jsrr BP R {Bt Bj RkR 8R Ys Rs$RPk Y # }BR$$% T sj {BtI$$Bt sti Y t{ s y! RsAj qb I R{ $A Y 8 {BtR$I Y R {Bt Bj RkR 8R $t $Z d b$y UwXD ) wx L KD1 z XwX L1 z D by K $R Y }Bj BP!i sti, z k ( qy$r {jsrr bsr $t BIZ{ I $t >nh sti $R AsR Tj$t s RkR 8 YsR RstIs I R {BtITB I strp PZt{$Bt ( 1 z X 1 L1 z X L 1 z qy$r {jsrr BP R {Bt Bj RkR 8R Rs$Rh R Y # }BR$$% T sj {BtI$$Bt wxd PB sjj {B8A$ts$Bt BP }BR$$% }s s8 R K sti z R >H qy PB P B8 qy B 8 d Y R R {Bt Bj RkR 8R s y! RsAj w$$$d y $R }BRR$Aj Ys s R {Bt Bj RkR 8 $R ZtRsAj % t YBZY $R AsR Tj$t s RkR 8 $R RsAj sti I R{ $A$tTPZt{$Bt stsjkr$r IB R tb } I${ s j$8$t{k{j 7Z{Y st -s8}j $R $% t $t >MH nd ibazrt RR B y8}j 8 ts$bt B R yt wdd b $8}j${$jk srrz8 I Ys Y R } B{ RR $R $I sj Ys $R Y Rs BP!i R R -s{jk B 9 B s Y } {$R $trst by t $R $t}z wd $R 9 B!P {BZ R Y$R R jib8 Ys}} tr sr - 8}j$h I Ak Y I$$sj $8}j 8 ts$bt BP R j 8 tr by RZ{Y B R B{{Z IZ B ht$ Rs8}j$t s R sti R$tsj JZst$9s$Bt qb s{{bzt PB RZ{Y $ts{{z s{$ R b 8BI$Pk Y 8BI j BP R {Bt Bj s{{b I$tjk BU? wd ) \? wd L 4? W wd? W wd ) g? wd K? W wd L jwd b; {? W w L D ) 6 d wd ; { { ) \ U g? wd ) jwd L 6 1 wd, 7Ld 7 k,k(,7)d, 1, i, wd(d by 6 d sti 6 1 s ABZtI I R$tsjR 8BI j$t $8}j 8 ts$bt B R qy ABZtI It RR BP 6 1 $R t { RRs k PB r B A ABZtI I qy PBjjBb$t {B Bjjs k Rs R Ys Y y! RsA$j$k {BtI$$Bt $t qy B 8 d 8s$tR %sj$i % t $t Y Ps{ BP Y R $8}j 8 ts$bt B R E

8 ]B Bjjs k du qy R {Bt Bj RkR 8 wd(d $R y! RsAj $P $ Rs$Rh R Y # }BR$$% T sj {BtI$$Bt wxd _ BBPU qy } BBP PBjjBbR sjbt Y Rs8 j$t R sr Ys $t qy B 8 d VP ZR$t Y Rs strpb 8s$Bt wnd RkR 8 wd(d A {B8 RU F wd ) \F wdl4f W wd F W wd ) gf wd KF W wd b; { F W w L 7 D )? Wq DL6 d wd ; { 7$t{ 6 d $R ABZtI I $ $R R s$ypb bs I B RYBb Ys N 88s d sti N 88s 1 s R$jj $t & { qs,$t Y Rs8 ~ sti PBjjBb$t Y BZY Y } BBP BP qy B 8 d k$ jir ABZtI I ~ F sti htsjjk ABZtI I r qy$r {B8}j R Y } BBP ( ; VRk8}B${ VtsjkR$R yt Y$R R {$Bt b RYBb Ys Rs$RPs{$Bt BP Y # }BR$$% T sj {BtI$$Bt wxd k$ jir 8B Yst y! RsA$j$k G$Y $ b {st PZ Y RYBb Ys Y R {Bt Bj RkR 8 wdd $R srk8}b${sjjk RsAj sti Ys $ $ty $R Y srk8}b${ s{,$t } B} $ R BP $R AsR Tj$t s RkR 8 yt Y R JZ j b I tb Y s{,$t B $t Y R {Bt Bj RkR 8 sti $R AsR T j$t s RkR 8 Ak wd ) jwd g? wd q wd ) jwd g? q wd, R} {$% jk G h R t I Y PBjjBb$t {Yt${sj j 88sR N 88s ;U yp j$8 q wd )( Y t _ BBPU B8 Y I ht$$bt BP 7, sr 7 B8 w1d b Ys% j$8 gf D ) ( sti j$8 7 F Ww L D)( 7 gf D ) j D g? q D (,? Wq wd ) K? Wq wd g? q wd L jwd 7$t{ j$8 q wd ) ( sti Kk(, Y t j$8? Wq wd )( B8 w;d F W w L 7 Ys j$8 7 F W w L D )( 7 D )? Wq D RB ( N 88s xu yp Y # }BR$$% T sj {BtI$$Bt wxd $R Rs$Rh I sti j$8 q wd )(, Y t j$8 X^? wd? W wd ^? q wd? Wq wd ~ )(

9 _ BBPU qs, ~ wd sr $t Y } BBP BP qy B 8 d qy t P B8 wd ~ w L 7 D ~ DL>F W w L 7 DL#gF DH 1 G$Y - 7 ) >F W w L 7 DL#gF DH 1 sti j$8 q wd ) (, $ PBjjBbR P B8 N 88s ; Ys j$8 7-7 )( qyzr wd A {B8 R ~ wd w 7D > w7dd ~ w(d L - 7 L - 7d L L w7dd - d H wddd PB sjj ;, 7LdH 7$t{ ~ w(d ) ( Y t P B8 w;d j$8 qy$r {B8}j R Y } BBP j$8 X^? wd? W wd ^? qwd? Wq wd ~ ~ wd ) ( RB Ys )( ( G,tBb Rs BZ srk8}b${ RsA$j$k RZj qy B 8 1U qy R {Bt Bj RkR 8 wdd $R srk8}b${sjjk RsAj $P $ Rs$Rh R Y # }BR$$% T sj {BtI$$Bt wxd _ BBPU 7 jwd # ( B8 wddd $ $R R s$ypb bs I B {B8}Z - 7 ~ wd RZ} 7 d by - 7 )>F W w L D L #gf 7 DH 1 B8 w;d F W w L D )? 7 Wq D sti P B8 wnd gf D ) g? q DRBYs- 7 )>? Wq D #g? q DH 1 qy PB ~ wd RZ} >? Wq D #g? q DH 1 bwd D wd1d 7 qy $YTYstI R$I BP wd1d {st A ABZtI I sr $t >? Wq wd L #g? q wdh 1 > E E? q wd? Wq wd PB RB8 > k( sti PB sjj k( 7$t{ ~ wd $R s }BR$$% TI ht$ PZt{$Bt Y t Y j PTYstI R$I BP wd1d {st A ABZtI I A jbb Ak Y tb 8 BP >F x wd,f W wdh x < t{ Y -$RR s {BtRst > d RZ{Y Ys E EE F wd E F W wd E >? d RZ} q wd E? Wq wd E PB sjj k( qy PB P B8 wnd E? wd? W wd ;>(, D E w> d LdD RZ} M E ;>(, D? q wd? Wq wd 1 E E wdnd

10 7$t{ Y AsR Tj$t s RkR 8 w1d $R srk8}b${sjjk RsAj sti? q w(d )? w(d? Wq w(d )? W w(d, Y t wdnd $8}j$ R Ys wdd $R Nks}ZtB% RsAj qb {B8}j Y } BBP b t I B RYBb Ys Y Rs srk8}b${sjjk {Bt% R 7$t{ \ q $R RsAj Y t P B8 w1d qy PB P B8 N 88s x j$8 j$8 ^? qwd? Wq wd ^? wd? W wd RYBb$t Ys Y Rs R srk8}b${sjjk {Bt% qy$r } B% R Y Y B 8 ( G tbb RYBb Ys Y AsR Tj$t s RkR 8 {st }srr Bt $R srk8}b${ s{,$t } B} $ R B $R R {Bt Bj RkR 8 qy B 8 nu 7Z}}BR Y # }BR$$% T sj {BtI$$Bt wxd $R Rs$Rh I yp j$8 q wd )( Y t j$8 wd )( _ BBPU B8 N 88s x j$8 >g? wd g? q wdh )( ]BtR JZ tjk j$8 wd )( qy$r {B8}j R Y } BBP ( qy B 8 n $ti${s R Ys Y {jsrr${sj Xk} >" A Ys%$B BP s AsR Tj$t s RkR 8 $R $ty T $ I Ak $R R {Bt Bj RkR 8 7} {$h{sjjk $P wd sti QwD s }BjktB8$sjR R$tsjR BP I tb s Yst > $Pq7E zwd )(sti$puwxd {Bts$tR s j sr > $t sb R Y t Y R RkR 8 wdd YsR 9 B R siktrs s{,$t B } B%$I I $ Rs$Rh R Y # }BR$$% T sj {BtI$$Bt wxd )( )( x 7} I ]Bt Bj BP s j -$Aj {Yst${sj 7kR 8 yt Y$R R {$Bt b s}}jk R {Bt Bj I R$t B Y R} I {Bt Bj BP Y Bs$Btsj 4 -$Aj 8 {Yst${sj RkR 8 RYBbt $t $Z 1 qy$r RkR 8 {BtR$RR BP Y $t $sr {Btt { I %$s 4 -$Aj RYsPR V R %B 8BB I $% R $t $s O n sti Y R} I BP $t $s O d $R 8 srz I %$s s s{yb8 qy {Bt Bjj $R $8}j 8 t I ZR$t I7_V] BBjR >dh V 8B {B8}j I R{ $}$Bt BP Y$R -} $8 t {st A PBZtI $t >dmh R$I R $t BIZ{$t si R B RB8 BP Y I s$jr A Y$tI R {Bt Bj I R$t Bt BA` {$% BP Y$R R {$Bt $R B I 8BtR s Y s}}j${sa$j$k BP Y 8s$t Y B ${sj RZjR BP Y$R }s} ts8 jk qy B 8R dtn $ R b {BtR$I Nqy P IAs{, {Bt Bj

11 J J2 J1 Srvo motor Tachomtr flxibl shaft Amplifir u dspace Board y Filtr $Z 1U 7{Y 8s${ BP Y Bs$Btsj 4 -$Aj 8 {Yst${sj RkR 8 xd q si B&R $t Nqy P IAs{, {Bt Bj V AjB{, I$s s8 BP s j$t s P IAs{, {Bt Bj RkR 8 $R RYBbt $t $Z n by gwxd I tb R Y {Bt Bjj sti hwxd $R s strp PZt{$Bt 8BI j BP Y B} ttjbb} RkR 8 P B8 $t}z ` B BZ}Z r =R$t -} $8 tsj P JZ t{kt R}BtR Iss b $I t$h I Y }jst sr hwxd ) ;E(Mnx( wx Ldx1;DwX 1 LndX L1M1(DwX 1 LnE1X LM;ED G }BR Y PBjjBb$t R} {$h{s$btr Bt s RsA$j$9$t Nqy {Bt Bjj gwxd B $jjzr s Y j$8$s$btr sti si B&R $t Nqy I R$t d stib$iy {BtR s$tu qy Zt$kTs$t { BRRTB% P JZ t{k I ht I Ak /Uwi D/ )d 8ZR Rs$RPk k n$ 1 *$RZ Ast{ ` {$BtU NBbTP JZ t{k I$RZ Ast{ R s B A ` { I R} {$h{sjjk rwid QwiD (1, by t $ n 7 trb TtB$R RZ}} RR$BtU <$YTP JZ t{k R trb tb$r $R B A RZ}} RR I $ rwid zwid (n, by t d($ ; VRk8}B${ } PB 8st{ U B R siktrs s{,$t B B {BtRst P t{ sti I$RZ Ast{ Q R$tsjR x!% RYBBU!% RYBB $t BZ}Z r B s {BtRst P t{ RYBZjI A j RR Yst 1( d(

12 r _ C(s) P(s) y $Z nu jb{, I$s s8 BP Y j$t s P IAs{, RkR 8 yt 8R BP BI R} {$h{s$btr Y h R bb {BtR s$tr strjs $tb 8$t$8Z8Ts$t JZ$ 8 tr Bt Y B} ttjbb} s$t /UwiD/ s jbb P JZ t{$ R by$j Y Y$ I R} {$h{s$bt }js{ R st Z}} ABZtI Bt Y$R s$t s Y$Y P JZ t{$ R qy PBZ Y R} {$h{s$bt JZ$ R gwxd B {Bts$t st $t sb sti Y hpy R} {$h{s$bt JZ$ R s }YsR 8s $t BP s}} B-$8s jk ;x H srrz8$t R {BtITB I IB8$tst{ =R$t {jsrr${sj jbb}trys}$t {Yt$JZ R b b ZtsAj B 8 sjj BP Y sab% R} {$ht {s$btr qb $jjzr s Y si B&R {BtR$I bb {sti$is RsA$j$9$t Nqy {Bt Bjj RU g d wxd ) d1md;mwx L;;MnDwX1 LnnxX L1MxdDwX1 LxdxMX L d((e(d XwX 1 L1xdX L 11nn(DwX 1 L d1e1x L MMMDwX 1 L1nX L 1xE(D sti d(x;e(wx LDwX 1 LnEE1X L 1MDwX 1 Lx;dX L MED g 1 wxd ) XwX L 1(EDwX LnxMDwX 1 Ldn1MX L d1(x(dwx 1 LnxX L EEn(D $Z ; {B8}s R Y BI }jbr BP Y {B R}BtI$t jbb}r U d wid ) g d widh wid sti U 1 wid ) g 1 widh wid NBB} U d Ps$jR B Rs$RPk Y R trb TtB$R RZ}} RR$Bt R} {$h{s$bt s Magnitud (db) L 1 (j ω) L 2 (j ω) Phas (dgr) Frquncy (Hz) $Z ;U BI }jbr BP UdwiD sti U1wiD )d($ qy$r R} {$h{s$bt {st A 8 Ak IZ{$t Y s$t BP U d wid sr IBt b$y U 1 wid dd

13 qy$r $R % $h I Ak Y $8 R}BtR r B d( <9 R$tZRB$Isj tb$r z $t $Z x 7$t{ ABY I R$tR RsA$j$9 sti R$t{ ABY jbbtp JZ t{k s$tr s {BtR s$t I Ak Y h R bb R} {$ht {s$btr BI :R s$tt}ysr js$btry$} >dh I${s R Ys U 1 wid 8ZR Ys% {B R}BtI$tjk js }YsR js sr % $h I $t Y }YsR }jb BP $Z ; qy IZ{ I s$t $t U 1 wid {B8 R s Y -} tr BP s R8sjj }YsR 8s $t sti Y t{ js B% RYBB sr RYBbt $t Y R } R}BtR R $t $Z E - tr$% Zt$t BP Y R {Bt Bjj R Ps$j I B k$ ji s I R$t 8 $t sjj R} {$h{s$btr yt Y t - RZAR {$Bt b RktY R$9 s R {Bt Bjj by${y RZ{{ IR $t 8s,$t Y t { RRs k si B&R.8.6 LTI dsign 1 LTI dsign y t (sconds) $Z xu ]B8}s $RBt A b t Nqy I R$tR Ud sti U1 BP BZ}Z R}BtR r B R trb tb$r zwd ) R$twd($D x1 i R ]Bt Bj * R$t sti VtsjkR$R WBb b Z t B R {Bt Bj I R$t by b -}jb$ $R }B t$sj B Rs$RPk Y sab% R} {$h{s$btr qy I R$t } B{ IZ {BtR$RR BP bb R }R sr I % jb} I $t >nh >xh sti >EH $ R b I R$t s j$t s {Bt Bjj B 8 sjj Y R} {$h{s$btr T -{ } PB Y B% RYBB {BtR s$t B -s8}j g 1 wxd $R s RZ$sAj {YB${ qy R {BtI R } $R B R j { Y!i:R }Bj K B 8 Y B% RYBB R} {$h{s$bt yt Y$R R} { >$Z x 1H } B%$I R s Z$I j$t PB Y$R {YB${ =R$t Y$R BBj b R j { K ) d; qy RZj$t R {Bt Bj RkR 8 $R RYBbt $t $Z d1

14 LTI dsign 1 LTI dsign y t (sconds) $Z EU ]B8}s $RBt A b t Nqy I R$tR U d sti U 1 BP BZ}Z R}BtR r B {BtRst P t{ wd # d qb RsAj$RY RsA$j$k sti R siktrs } PB 8st{ b h R {Y {, Y # }BR$$% T sj {BtI$$Bt wxd 7$t{ g 1 wxd RsA$j$9 R Y t _wxd $t wxd $R srk8}b${sjjk RsAj V R$8}j R s {Y sti {B8}Zs$Bt RYBbR Ys i >_widh k ( PB sjj ( by t # ) (((M R $Z M yt%b,$t qy B 8R dtn b {Bt{jZI Ys Y$R R {Bt Bj RkR 8 $R y! sti srk8}b${sjjk RsAj sti 8 R Y srk8}b${ } PB 8st{ {BtR s$t $t R} {$h{s$bt ; $Z RYBbR st -} $8 tsj RZj % $Pk$t Y -} { I R siktrs } PB 8st{ x r _ FORE b=14 (s+14)c 2 (s) P(s) d y n $Z U i R {Bt Bj RkR 8 PB Y 4 -$Aj 8 {Yst$R8 $tsjjk b {B8}s Y } PB 8st{ BP Y Nqy wzr$t U d D sti R {Bt Bj RkR 8R $Z R d( sti dd RYBb Ys Y R {Bt Bj RkR 8 YsR A R trb TtB$R RZ}} RR$Bt B s x <9 R$tZRB$I sti B by$ TtB$R E <Bb % Ztj$, Y Nqy si B& -} $ t{ I Ak {Bt Bjj g 1 wxd Y R {Bt Bj RkR 8 YsR {B8}s saj str$ t R}BtR sr RYBbt $t $Z d1 x qy R siktrs BR{$jjs$BtR $t Y R } R}BtR BP $Z s IZ B s{yt t sb $}}j E qy s8}j$h{s$bt $t Y jbbtp JZ t{k R} { Z8 $t Y R {Bt Bj R}BtR {sttb A } R tjk -T }js$t I <Bb % BZ $t R $R } $8s $jk $t Y s tzs I Y$YTP JZ t{k R} { Z8 dn

15 R(h(jω)) Frquncy (rad/sc) $Z MU _jb RYBb$t i >_widh k (by t# )(((M y t (sconds) $Z U!Z}Z R}BtR r BP R {Bt Bj RkR 8 B wd # d QwD # (x, k n zwd ) (d d;

16 .7.65 rst control dsign LTI dsign y t (sconds) $Z d(u ]B8}s $RBt A b t R sti Nqy {Bt Bj wzr$t U d D BP R siktrs BZ}Z R}BtR r B P t{ wd # d sti R trb tb$r zwd ) R$twd($D powr (db) rst control dsign LTI dsign frquncy (Hz) $Z ddu ]B8}s $RBt A b t R sti Nqy {Bt Bj wzr$t U d D BP BZ}Z R} { s r by t z $R A BsIAstI by$ TtB$R dx

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18 E ]Bt{jZR$Bt qy$r }s} I % jb} I s RZ^{$ t {BtI$$Bt wy # }BR$$% T sj {BtI$$BtD PB y! RsA$j$k PB s {jsrr BP R {Bt Bj RkR 8R qy$r {BtI$$Bt sjrb j I B s R $ R BP RZjR $t{jzi$t srk8}b${ RsA$j$k sti R siktrs } PB 8st{ qy # }BR$$% T sj {BtI$$Bt bsr RYBbt B A Rs$Rh I $t st -} $8 tsj I 8BtR s$bt BP R {Bt Bj {Bth 8$t Y BAR % I } PB 8st{ sr b jj sr I 8BtR s$t $R s}}j${sa$j$k V{,tBbj I8 t qy szyb R bbzji j$, B Yst,! Yst, s _Y* {sti$is $t Y ] * }s 8 t =t$% R$k BP srrs{yzr R V8Y R PB 8stk P Z$PZj I$R{ZRR$BtR i P t{ R >dh y <B Bb$9 7ktY R$R BP IAs{, 7kR 8R V{sI 8${ _ RR W b OB, den >1H!, ]z <BjjB sti O ]Ys$ X_jst b$y yt sb U Vt -s8}j BP i R ]Bt Bj!% {B8$t N$8$s$BtR BP N$t s IAs{," ] * }s 8 t q {Yt${sj WB '](dn1((( =t$% R$k BP srrs{yzr R V8Y R sjrb RZA8$ I B y q strt s{$btr Bt VZB8s${ ]Bt Bj 1((( >nh y <B Bb$9 sti _ ibr tasz8 XWBtj$t s * R$t PB ]BR BP IAs{, i IZ{$Bt $t 7kR 8R b$y Ns _s s8 =t{ s$tk" yt ts$btsj FBZ tsj BP ]Bt Bj zbj 1; WB E }} Td((d dx >;H _ ibr tasz8 i IZ{$Bt BP Y ]BR BP IAs{, $t 7kR 8R b$y Ns _s s8 =t{ s$tk _Y* *$RR s$bt G $98stt ytr$z BP 7{$ t{ i YB%B yr s j d >xh O Y t qy B k sti _ s{${sj ]BtR$I s$btr $t i R ]Bt Bj * R$t _Y* *$RR T s$bt =t$% R$k BP srrs{yzr R V8Y R dm >EH O Y t O ]Ys$ ]z <BjjB 7 $taz{y sti WB X-} $8 tsj * 8BtT R s$bt BP i R ]Bt Bj * R$t" yv] FBZ tsj BP ]Bt Bj t$t $t _ s{${ zbj M WB 1 }} ddntd1( 1((( >H F] ]j XV WBtj$t s yt sb PB 7 %B8 {Yst$R8" Vy q strs{$btr _s yy V}}j${s$Bt sti ytizr k zbj }} ;dt;1 dxm >MH < <Z O Y t O ]Ys$ sti ]z <BjjB X!t Y BTyt}Z 7sA$j$k BP ]Bt Bj 7kR 8R <s%$t ]j yt sb R" _ B{ I$tR BP Y V8 ${st ]Bt Bj ]BtP t{ }} ;(MT;d( VjAZJZ JZ W d d

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