yt F VIs}$% ]Bt Bj sti 7$tsj _ B{ RR$t 7} {$sj yrrz Bt ]Bt Bj b$y ]BthI t{ 1((d wb s}} s D ]Bt Bjj zsj$is$bt f

Transcript

1 7ZA8$ I 1 7 } 1((( w % ( V} 1((dD yt F VIs}$% ]Bt Bj sti 7$tsj _ B{ RR$t 7} {$sj yrrz Bt ]Bt Bj b$y ]BthI t{ 1((d wb s}} s D ]Bt Bjj zsj$is$bt f q 3 i!ewe] G, q ] q7v!, sti p 7V3!W!z VAR s{ qy ZtPsjR$h I {Bt Bj {Bt{ } } B%$I R s Y B ${sj AsR$R PB I$ {jk %sj$is$t {jbr IT jbb} {Bt Bjj } PB 8st{ P B8 B} ttjbb} -} $8 tsj Iss B % t P B8 {jbr ITjBB} Iss s{jz$ I by$j stby {Bt Bjj bsr $t Y P IAs{, jbb} y sjjbbr Y$R B A s{{b8}j$ry I b$ybz 8s,$t stk } $B srrz8}$btr sabz Y }jst B tb$r qy$r s}} Bs{Y B -} $T 8 tsj {Bt Bjj %sj$is$bt s%b$ir Y {BtR %s$r8 $ty t $t $ti$ { bbtr } %sj$is$bt s}} Bs{Y R Ys JZ$ Bt B h R $I t$pk s }jst 8BI j sti Zt{ s$tktabztir P B8 -T } $8 tsj Iss A PB stsjk9$t {Bt Bj RkR 8 BAZRt RR ]Bt Bjj %sj$is$bt $R RYBbt B A Y P IAs{, t sj$9s$bt BP B} ttjbb} 8BI j %sj$is$bt {Bt{ }R Ys PB 8 Y AsR$R BP %s $BZR {Bt BjTB $ t I RkR 8 $I t$h{s$bt Y B $ R / k cc IRU ]Bt Bjj $I t$h{s$bt 8BI j %sj$is$bt BAZR {Bt Bj ZtPsjR$h I {Bt Bj d yt BIZ{$Bt yt sjj t$t $t I$R{$}j$t R -} $8 tsj Iss } B%$I R s 8BR $8}B st {Btt {$Bt A b t Y B k sti } s{${ 3B {Bt Bj t$t R Y R$Zs$Bt $R tb I$& t ]Bt Bj Y B k 8s, R tb {js$8r sabz Y } PB 8st{ B RsA$j$k BP }YkR${sj RkR 8R Btjk sabz Y $ 8BI jr qy t$t byb $R {Bt{ t I b$y {Bt Bjj$t }YkR${sj RkR 8R R,R RB8 srrz st{ Ys {jbr IT jbb} B} s$bt BP Y s{zsj RkR 8 {st s{y$ % I R$ I } PB 8st{ BA` {$% R qy PB Bt{ s {Bt Bj jsb YsR A t I 8$t I Ak bys % 8 YBI Y 8ZR A s bsk BP %sjzs$t $P Y s%s$jsaj -} $8 tsj Iss {B BAB s R Y B ${sj } I${$BtR BP } PB 8st{ ibazr {Bt Bj Y B k $% R }Bb PZj {Yt$JZ R PB RktY R$9$t {Bt Bj jsbr by${y Y B T ${sjjk } B%$I } PB 8st{ sti RsA$j$k Zs st R PB Y {jbr ITjBB} RkR 8 <Bb % sr $R b jj,tbbt Y R {Yt$JZ R JZ$ s }jst 8BI j sjbt b$y st Z}} ABZtI Bt Y srrb{$s I Zt{ s$tk w8bi j$t B D =RZsjjk s {BtR %s$% Z}} ABZtI $R Yk}BY R$9 I by${y 8sk RZj $t } PB 8st{ j$8$s$btr V 8B $B BZR s}} Bs{Y YsR { tjk A t RZ R I Ak R % sj R s {Y R >d 1 n ;H $t%bj%$t $I t$h{s$bt BP 8BI j$t B ZR$t -} $8 tsj Iss ]BtR$I s$bt BP Y$R } BAj 8 RBBt j I B Y {Bt{ } BP }jst 8BI j %sj$is$bt wztpsjr$h{s$btd >x E H by s 8BI j b$y s Yk}BY R$9 I Zt{ s$tk ABZtI $R %sj$is I ss$tr $t}ztbz}z Iss b$y Y YB} Ys BAZR {Bt Bjj R AsR I Bt Y 8BI j {st RZAR JZ tjk A s}}j$ I $P Y Zt{ s$tk ABZtI } B% R B A %sj$i w$ ZtPsjR$h I Ak Y Iss >MHD 7Z{Y {Bt Bjj R {st A qy$r R s {Y bsr RZ}}B I $t }s Ak V3!7i p str 3;E1(TxTdT((x sti 3;E1(TMTdT((1E G B $t 7s jj$ 7kR 8R ej 7 ZtIB ]V =7V _YBt dtnd(t;detx1; 3V dtnd(tne;teen e8s$j YB8sRPA B9 t {oab $t{b8 q ] qrsb bsr b$y ]Y$t R Ws%sj V{sI 8k * } BP ej { ${sj et$t $t sbyr$zt qs$bst Mdn i!] < $R tbb b$y B $t 7s jj$ 7kR 8R ej 7 ZtIB ]V =7V ej { ${sj et$t $tv7kr 8R * } =t$% R$k BP 7BZY t ]sj$pb t$s NBR Vt j R ]V ((MT1xEn =7V _YBt dt1dnt;(t;;xx 3V dt1dnt;(t;;; e8s$j 8RsPBtB%oZR{ IZ

2 1 #i$hwh_ q6v$ VW- 6V5$W$z I R{ $A I sr tb I 8BtR sajk Zt BAZR Ys $R Y s%s$jsaj -} $8 tsj Iss {sttb A ZR I B I 8BtR s Y $ $tsa$j$k B } B%$I Y I R$ I j % j BP {jbr ITjBB} RkR 8 } PB 8st{ yt {Bt Bj s}}j${s$btr Y Zj$8s Bsj BP 8BI j %sj$is$bt $R B ZR Y %sj$is I wztpsjr$t h ID }jst sti Zt{ s$tk 8BI jr sjbt b$y BAZR RktY R$R BBjR B I R$t {Bt Bj jsbr by${y b$jj RZAR JZ tjk A s}}j$ I B Y }jst 7B Ys Y k b$jj Btjk s jk A $t%sj$is I Y ZtT { s$tk 8BI jr ZR I s k}${sjjk {BtR %s$% jk {YBR t w b$y ZtR Z{Z I Zt{ s$tk B b$y 8BI j B ABZtIR Ys s js Yst t { RRs kd qyzr % t by t R$8s$t 8BI j T B P B8 Y Iss {BtR %s$r8 8sk ti B j$8$ Y } PB 8st{ ss$tsaj b$y Y RZjst BAZR {Bt Bjj R yt sii$$bt {YBBR$t Y b Bt Zt{ s$tk 8BI j R Z{Z 8sk sjrb RZj $t ZtIZ {BtR %s$r8 sr PB -s8}j by t s R Z{Z I Zt{ s$tk $R {Bs R jk } R t I ZR$t 8Zj$}j${s$% B sii$$% }jst Zt{ s$tk ABZtIR w{p 7,B RsI sti _BRj Ybs$ >HD VtI htsjjk sr b I 8BtR s $t Y$R }s} % t $P Y }jst sti Zt{ s$tk 8BI jr s $tt %sj$is I Y$R IB R tb b$y { s$tk I 8BtR s Y $tsa$j$k BP Y {Bt Bj jsb $t JZ R$Bt B 8 $R I R$ I } PB 8st{ qy ZtPsjR$h I {Bt Bj {Bt{ } BP 7sPBtB% sti qrsb >d( dd d1 dnh } R tr s R$t$h{st $8} B% 8 t isy Yst %sj$is$t }jst 8BI jr ss$tr } TI ht I B} ttjbb} B ABZtIR {Bt Bjj %sj$is$bt wztpsjr$h{s$btd I$ {jk %sjzs R Y sa$j$k BP {Bt Bj jsbr B 8 s $% t {jbr ITjBB} } PB 8st{ { $ $Bt qy 8R {Bt Bjj %sj$is$bt sti {Bt Bjj ZtPsjR$h{s$Bt s ZR I $t {Yst sajk Y BZYBZ Y }s} yt Y } R t }s} b -}sti Y$R Y B k Ak s RZIk BP Y {Btt {$BtR A b t 8BI j sti {Bt Bjj %sj$is$bt G RYBb Ys {Bt Bjj %sj$is$bt $R s P IAs{, t sj$9s$bt BP 8BI j %sj$is$bt sti Ys $ $R j RR {BtR %s$% B ZtPsjR$Pk w%sj$is D {Bt Bj jsbr I$ {jk sy Yst ZtPsjR$Pk w%sj$is D Y }jst 8BI jr P B8 by${y YBR {Bt Bj jsbr s {BtR Z{ I qy PB Y sa$j$k BP s {Bt Bjj B 8 s } PB 8st{ { $ $Bt {st A %sjzs I I$ {jk tb }s ${Zjs }jst R Z{Z B } B} k t I A srrz8 I qy }s} $R B st$9 I sr PBjjBbR yt 7 {$Bt 1 s A $ P RZ88s k BP Y {Bt Bjj %sj$is$bt Y B k >dnh $R } R t I V R} {$sj {sr $R ZR I B $jjzr s Y } $8s k $I sr yt 7 {$Bt n b RYBb Ys 8BI j %sj$is$bt $R s R} {$sj {sr BP {Bt Bjj %sj$is$bt by Y {Bt Bjj $R Y tb8$tsj }jst 8BI j sti Y } PB 8st{ { $ $Bt $R s 8BI j B { $ $Bt qy js$btry$} A b t ZtPsjR$h I {Bt Bjj R sti BAZR {Bt Bjj R $R -}jb I sti Y {BtR %s$r8 BP 8BI j %sj$is$bt s}} Bs{Y R $R RsAj$RY I 3$tsjjk Y {Bt{jZR$Bt RZ88s $9 R Y RZjR sti RZ RR PZZ R s {Y I$ {$BtR 1 ]Bt Bjj PsjR$h{s$Bt ]BtR$I Y P IAs{, {Bt Bj RkR 8 BP 3$ d qy Bsj BP s}}jk$t Y P IAs{, {Bt Bj jsb ]B88stI w0d ]Bt Bjj ]Bt Bj `w0d _jst _!Z}Z rw0d _ 3$Z du 3 IAs{, {Bt Bj RkR 8 B Y }jst _ $R B trz Ys Y {jbr ITjBB} RkR 8 R}BtR {sjj $ q Rs$Rh R s { s$t } PB 8st{ { $ $Bt yt t$t $t } s{${ Y }jst $R sjbskr Btjk }s $sjjk,tbbt sti

3 _$Wqi$NNhi zvny-vqy$w n Y PB Y RkR 8 R}BtR q b$jj A Zt{ s$t VR s RZj Y sa$j$k BP Y {Bt Bjj B trz s I R$ saj R}BtR $R sjrb Zt{ s$t ]Bt Bjj %sj$is$bt sr,r Y JZ R$Bt XGYs {st A I 8$t I P B8 Y Iss sjbt 2" Ak 8s,$t s {j s I$R$t{$Bt A b t {Bt{jZR$BtR I $% I ZR$t srrz8}$btr sabz Y }jst sti {Bt{jZR$BtR s $% I s ZR$t Btjk -} $8 tsj Iss 3B Y }Z }BR BP I$R{ZRR$t {Bt Bjj ZtPsjR$h{s$Bt Y $t}z\bz}z I R{ $}$Bt BP RkRT 8R IZ B s8 R >d;h $R Y j}pzj =R$t Y$R s}} Bs{Y b %$ b s Ikts8${sj RkR 8 sr s R BP $t}z\bz}z }s$ R w?, rd by${y s R$tsjR $t s}} B} $s PZt{$Bt R}s{ R ; < yt Y$R P s8 bb, RBjZ$BtR BP P IAs{, $t {Btt {$BtR BP bb RkR 8R A {B8 Y $t R {$Bt BP bb s}yr $t Y } BIZ{ R}s{ ;e< s8 R sti 7stIA B $$tsjjk ZR I Y$R s}} Bs{Y B jsk Y PBZtIs$Bt PB 8Z{Y BP $t}ztbz}z RsA$j$k Y B k >d; dx de dh 3B srk %$RZsj$9s$Bt b 8sk {BtR$I Y R} {$sj {sr by ; sti < s Y R}s{ BP sj tz8a R 5 3B {Bt Bj s}}j${s$btr YBb % $ $R BP t {Bt% t$ t B %$ b Y R$tsjR sr j 8 tr BP Y - ti I % {B R}s{ U 1 qy XA Ys%$B sj RkR 8" {Bt{ } BP G$jj 8R >MH {st A s I I sr st s}}j$t {s$bt BP Y R } $t{$}j R =R$t Y$R {Bt{ } b {st %$ b Y }jst sti Y {Bt Bjj sr R$tsj {BtR s$tr wr RD $t Y } BIZ{ R}s{ 5e <e 8 by 5 r <sti ` 8 qy }jst by${y $R Zt,tBbt $R } R t I Ak s R _ 5e<e8 wdd I ht I B A Y R BP $}j R w, r, `D 5e<e8RZ{Y Ys Y }s$ w`, rd Rs$Rh R Y Zt,tBbt }jst:r $t}ztbz}z js$bt V R$tj -} $8 t } R tr s }B$t w`(,r ( D $t Y 8e<T}jst Bt Y s}y BP Y Zt,tBbt }jst Vt tr 8Aj BP R % sj -} $8 tr {BZjI A } R t I Ak sii$$btsj }B$tR Bt Y s}y BP Y }jst qyzr -} $8 tsj Iss } R tr s wps$ jk R8sjjD RZAR BP Y s}y BP Y }jst sti {BtR JZ tjk BP 8e< y $R {Bt% t$ t B srrb{$s Y -} $8 tsj Iss w`(,r ( D b$y Y PBjjBb$t 8A II$t $t 5e <e 8 _ Iss ) Iw, r, `D 5e<e8M ` ) `(, r ) r ( J w1d by${y b b$jj P B sr Y }jst Iss R qy$r R _ Iss $R st $tt ABZtI Bt Y }jst js$bt $t Y R tr Ys _ Iss Zt{ k bsk BP {Bt sr BAZR {Bt Bj } BAj 8 PB 8Zjs$BtR A $t Ak srrz8$t st BZ ABZtI Bt Y }jst js$bt by${y ABZtIR }jst Zt{ s$tk $t Y R tr Ys Zt{ =tpb ZT ts jk RZ{Y st BZ ABZtI {sttb A {B8}j jk %sj$is I Ak stk ht$ s8bzt BP -} $8 tsj %$I t{ Ztj RR Bt R$8}jk srrz8 R Ys PZZ B R b$jj t % -{ I } %$BZRjk BAR % I T B R O YBZY s $% t B ABZtI _ Zt{ 8sk $t{jzi sjj } %$BZRjk BAR % I -} $8 tsj Iss Y {st A tb Zs st Ys PZZ }jst A Ys%$B b$jj A t{b8}srr I Ak Y$R ABZtI qy $R tb B}$8sj sti { s$tjk tb Zt$JZ s}} Bs{Y B I ht$t Y ABZtI _ Zt{ P B8 -} $T 8 tsj Iss e-} $8 ts$bt sjjbbr ZR B %$ b Btjk s RZAR _ Iss BP }BRR$Aj }jst A Ys%$B R by sr BAZR {Bt Bj JZ$ R Y RZ} R _ Zt{ N$, Y }jst s {Bt Bj jsb $R s {BtR s$t Bt Y R$tsjR r sti ` VR RZ{Y $ } R tr s RZ Ps{ ws R D $t Y R}s{ 5e <e 8 5e<e83 wnd N$, b$r s } PB 8st{ { $ $Bt q W $R R$8}jk stby {BtR s$t Bt Y R$tsjR r sti ` sti YZR } R tr s RZAR BP 5e <e 8 sr b jj q Iss 5e<e83 w;d

4 ; #i$hwh_ q6v$ VW- 6V5$W$z qy$r {Ys s{ $9s$Bt BP Y -} $8 tsj Iss {Bt Bj jsb sti } PB 8st{ { $ $Bt sr R }s s R$tsj {BtR s$tr } B%$I R s {Bt% t$ t P s8 bb, PB Y I R{ $}$Bt BP Y {Bt Bjj ZtPsjR$h{s$Bt } BAj 8 FZR sr Y $t}ztbz}z RsA$j$k BP $t {Btt {$BtR BP RZARkR 8R IZ{ R B {BtI$$BtR Bt $t R {$t {BtR s$tr RB Y {Bt Bjj ZtPsjR$h{s$Bt } BAj 8 sjrb IZ{ R B {BtI$$BtR Bt $t R {$t {BtR s$tr I ht I Ak Y Iss {Bt Bj jsb sti } PB T 8st{ { $ $Bt WB Ys PB }Z }BR R BP {js $k sti B s%b$i Ztt { RRs k I s$jr BZ I$R{ZRR$Bt PB{ZR R Bt Y R$8}j R {sr by {B8}j $tpb 8s$Bt $R s%s$jsaj w w`(, r ( D U 1>(, De U 1>(, DD sr B}}BR I B Y 8B t sj {sr {BtR$I I Ak 7sPBtB% sti qrsb >dnh by Btjk }s $sj $tpb 8s$Bt w Btjk }sr %sjz RD sabz w`(, r ( D $R % sj I Ak Y 8 srz 8 tr 3B BZ R$8}j$h I {sr Y ZtPsjR$h I {Bt Bj Y B k BP 7sPBtB% sti qrsb Rs R Ys s {Bt Bjj $R ZtPsjR$h I Ak -} $8 tsj Iss _ Iss $P sti Btjk $P w{p qy B 8 d BP >dnhd _ Iss? q Iss wxd ejt wxd RskR Ys s B}BjB${sj R }s s$bt 8ZR -$R A b t Y R _ Iss? sti Y {B8T }j 8 t q Iss BP Y R q W $ _ Iss?? q Iss ) 3 wed qy tb$bt BP B}BjB${sj R }s s$bt ZtI j$ R sjj BP RsA$j$k Y B k 7sPBtB% >dh RYBb I Ys ABY $t}ztbz}z sti Nks}ZtB% RsA$j$k { $ $s {st A $t } I $t Y$R {Bt - 7} {$h{sjjk Y RsA$j$k BP Y P IAs{, $t {Btt {$Bt BP bb RkR 8R $R srrz I $P Bt {st B}BjB${sjjk R }s s : Y PZt{$Bt R}s{ {Bts$t$t Y RkR 8:R $t}ztbz}z js$btr $tb bb $BtR Bt {Bts$t$t Y s}y BP Y P IPB bs I j 8 t sti Y BY {Bts$t$t Y $t% R s}y BP Y P IAs{, j 8 t 7$8$js jk {Bt Bjj %sj$is$bt JZ$ R s B}BjB${sj R }s s$bt 7 >d( dd d1 dnh PB s {B8}j I % jb}8 t BP Y {Bt Bjj %sj$is$bt Y B k V R} {$sj {sr b$y s R$8}j {Bt Bjj R Z{Z $jjzr s R Y AsR${ {Bt{ }R t${ jk N ZR {BtR$I j$t s $8 T$t%s $st wnqyd {Bt Bj jsbr BP Y PB 8 ) ) Iw, r, `D M ` ) f w c rd J wd by f I tb R {Bt%BjZ$Bt $R Y P t{ {B88stI $R Y $8}ZjR R}BtR BP Y {Bt Bjj sti gwxd I tb R Y Ns}js{ strpb 8 BP VjYBZY tb t { RRs k PB }Z }BR R BP R$8}j${$k b RYsjj srrz8 Ys $R RsAjk $t% $Aj qy PB gwxd $R } B} sti 8$t$8Z8 }YsR 7B8 -s8}j R BP {Bt Bjj k} R by${y Rs$RPk Y R srrz8}$btr s } B}B $BtsjT $t sjti $%s$% w_y*d sti j sitjs {B8} trsb R 7Z}}BR Ys 8 srz 8 tr BP $t}z `(w0d sti BZ}Z r ( w0d s s%s$jsaj qy$r Iss {st A $Y B} t B {jbr ITjBB} Iss =R$t Y$R Iss b bbzji j$, B %sjzs Y sa$j$k BP Y {Bt Bjj B 8 s $% t {jbr ITjBB} } PB 8st{ { $ $Bt x w, r, `D ( q R} { ) Iw, r, `D M x w, r, `, 0D (, 0 k( J wmd by x w, r, `, 0D ) Nj d f w c rdn 1 U 1 >(,0H L Nj 1 f `N 1 U 1 >(,0H cn N1 U 1 >(,0H, wd sti j d w0d sti j 1 w0d s Y $8}ZjR R}BtR R BP $% t RsAj 8$t$8Z8 }YsR b $Y$t strp PZt{$BtR P d wxd sti P 1 wxd R} {$% jk $R Y $t}z P t{ R$tsj r $R Y }jst BZ}Z R$tsj sti ` $R Y {Bt Bj R$tsj qy$r { $ $Bt RskR Ys Y B R$tsj c r sti Y {Bt Bj R$tsj ` RYBZjI A XR8sjj" {B8}s I B Y {B88stI R$tsj Y Ikts8${sj b $YR j d sti

5 _$Wqi$NNhi zvny-vqy$w x j 1 I 8$t bys $R R8sjj 3Z Y $P BZ Zt,tBbt }jst _ b B A srrz8 I j$t s $8 T $t%s $st wnqyd Y t JZ$ $t Ys wmduwd YBjIR PB sjj bbzji A JZ$%sj t B s b $Y I 8$- ITR tr$$%$k } PB 8st{ { $ $Bt E} E Pd C E E P 1 gc ]E E E E I d wd(d by C $R Y R tr$$%$k C )dbwd LtgD w{p 7,B RsI sti _BRj Ybs$ >HD qy srrz8}t $Bt BP st Nqy }jst bbzji sjrb } 8$ ZR B I IZ{ 8B P B8 Y Iss Ys sjj j$t s {B8A$ts$BtR BP $8 TI jsk I Iss sjrb 8ZR Rs$RPk Y }jst js$bt by${y $t Z t bbzji j si ZR B }js{ wmduwd b$y qb }j$9 8s $- {BtI$$BtR -s{jk sr YsR A t IBt PB Nqy 8BI j %sj$is$bt Ak _BBjjs sj >H Z R$t{ b 8s, tb srrz8}$btr bysrb % sabz Y }jst Y Nqy qb }j$9 Y B k IB R tb s}}jk qy Btjk Y$t b,tbb sabz Y }jst $R Ys $ t s I Y -} $8 tsj Iss w`(,r ( D b b$jj srrz8 tby$t jr qy PB Y }jst $t}ztbz}z A Ys%$B $R {BtR s$t I Ak Y Ps{ Ys 8 srz I Iss $R $t Y s}y _ BP Y }jst ]B8A$t$t Y$R $tpb 8s$Bt b$y Y {Bt Bjj js$bt ` ) f w c rd b Ys% Ys $P Y {sti$is {Bt Bjj b $t Y jbb} s $}j Rs$RPk$t Y {jbr ITjBB} RkR 8 JZs$BtR bbzji A w, r, `D ) wk,r (,`(D wddd by K ) f `( L r ( wd1d by I tb R Y $8}ZjR R}BtR BP Y $t% R RkR 8 $ Y R$tsj YsR Ns}js{ strt PB 8 dbgwxd qy }YkR${sj $t } s$bt $R sr PBjjBbRU qy P t{ {B88stI K ) f `( L r (, wdnd by t s}}j$ I B Y {jbr I jbb} RkR 8 b$y sr {Bt Bjj bbzji sjrb Ys% t s I Y 8 srz I Iss w`(,r ( D G P B Y$R R$tsj sr Y h{$$bzr P t{ R$tsj y tbb A {B8 R {j s Ys $P x wk,r (,`(D k ( b Ys% } BBP Ys Y {Bt Bjj {sttb 8 Y } PB 8st{ { $ $Bt 3B s P t{ {B88stI YsR A t PBZtI wts8 jk K D PB by${y Y {jbr ITjBB} } PB 8st{ R} {$h{s$bt bbzji A %$Bjs I b $t Y jbb} yp Y $t JZsj$k x wk,r (,`(D k ( $R Rs$Rh I b Rsk Ys Y {Bt Bjj $R $t%sj$is I B PsjR$h I yp tb Y {Bt Bjj 8s$tR ZtPsjR$h I B %sj$is I i 8s,RU sd qy stsjkr$r sab% JZ$ R tb srrz8}$btr bysrb % sabz Y }jst!tjk Y Iss w`(,r ( D $R ZR I B I sb {Bt{jZR$BtR sabz Y sa$j$k BP Y {Bt Bj jsb B 8 Y } PB 8st{ { $ $Bt q R} { AD qy Iss 8sk } B%$I tb $tpb 8s$Bt s sjj 7Z}}BR PB -s8}j Ys `(w0d ) r ( w0d ) (, 0 qy t b Ys% K ) ( sti tb {Bt Bjj {st A $t%sj$is I %$s Y stsjkr$r sab% w$ sjj {Bt Bjj R 8s$t ZtPsjR$h I Ak Y Iss $t Y$R {sr D qy PB tb RZ } $R$tjk Y s { s$t {BtI$$BtR by${y Y -} $8 tsj Iss 8Z{Y Rs$RPk $t B I B RZ}}jk $tpb 8s$Bt sabz Y }jst qy R {BtI$$BtR s s,$t B Y b jjt,tbbt } R$R t{ BP -{$s$bt {BtI$$BtR by${y s {B88Btjk PBZtI $t Y sis}$% {Bt Bj j$ sz w{p >dmhd

6 E #i$hwh_ q6v$ VW- 6V5$W$z {D i sj }jstr 8sk A RZA` { B I$RZ Ast{ R sti R trb tb$r!z {Bt Bjj %sj$is$bt Y B k %sjzs R } PB 8st{ s }BR $B $ b$y R} { B Y s{zsj Iss by Y tb$rk B tb qy & { BP tb$r b$jj k}${sjjk A Ys 8B {Bt Bjj R b$jj A PsjR$h I R$t{ tb$r IZ{ R s{y$ %saj {Bt Bj } {$R$Bt <Bb % $ bbzji A $t{b { B RZ}}BR Ys Y } R t{ BP }jst tb$r B BY Zt{ s$tk RYBZjI BY b$r {Yst B {B8}j${s Y {Bt Bjj %sj$is$bt Y B k B $R s}}j${s$bt ID _ $B A j$ PR sabz tb$r RZ{Y sr,tbbj I BP }jst tb$r } BAsA$j$$ R sti }jst tb$r 8BI jr s stby 8s s$r$t $RRZ R I$R$t{ P B8 YBR s$r I Ak Y }BR $B & {R BP sj }YkR${sj tb$r Bt Iss WB$R } BAsA$j$$ R 8sk b jj s& { Bt :R {YB${ R BP {sti$is {Bt Bjj R B % t Bt :R {YB${ BP Y Bsj q R} { Z }jst sti R trb tb$r Ys% tb I$ { $8}s{ Bt Y } B{ RR BP %sj$is$bt BP $% t {Bt Bjj R b$y R} { B $% t BsjR ]Bt Bjj 8BI jr s %sj$is I I$ {jk ss$tr BAR % I Iss by${y s }BR $B $ $R sjbskr I 8$t$R${ qy {Bt Bjj 8BI jr A $t %sj$is I s j$, b$r I 8$t$R${ VtI Zj$8s jk Y } PB 8st{ R} {$h{s$bt $R s }BR $B $ s I 8$t$R${ PZt{$Bt BP Y Iss v % t YBZY s h R R$Y $ 8sk R 8 B A BY b$r $t {sr R $t by${y b Ys% } PB 8st{ R} {$h I $ti$ {jk $t 8R BP s } BAsA$j$R${ {BtI$$Btsj -} {s$bt BP Zt8 srz I R$tsjR $t tsj B Y Zt,tBbt }jst {B8}Z I %$s } $B A j$ PR sabz RB{YsR${ 8BI j$t qyzr } Ys}R {Bt s k B s{si 8${ $tz$$bt RB{YsR${ tb$r sti } BAsA$j$k Y B k Ys% tb RR t$sj Bj B }jsk $t {Bt Bjj %sj$is$bt Y B k B $R s}}j${s$bt RB jbt sr %sj$is$bt { $ $s s PZt{$BtR BP Btjk 8 srz I Iss sr b Y$t, Y k RYBZjI A D yt$$sj {BtI$$BtR s }s BP Y R} {$h{s$bt BP s {Bt Bjj `ZR sr s BY }s s8 R RZ{Y sr s$tr GY Y B tb s {Bt Bjj $R $t%sj$is I I } tir $t t sj Bt sjj BP $R I ht$t }s s8 R $t{jzi$t $R $t$$sj {BtI$$Bt }s s8 $P tbt9 B $t$$sj {BtI$$BtR s sjjbb I yt BZ -s8}j $t%bj%$t Y {Bt%BjZ$Bt {Bt Bjj R wd Y $R tb $t$$sj {BtI$$Bt }s s8 A {szr Y $t$$sj Rs BP s {Bt%BjZ$Bt B} sb sr I ht I Ak wd $R Ak I ht$$bt 9 B n ]Btt {$BtR b$y 8BI j %sj$is$bt sti BAZR {Bt Bj qy $R s {Btt {$Bt A b t {Bt Bjj %sj$is$bt sti 8BI j %sj$is$bt by${y b$jj A {js $h I $t Y$R R {$Bt V k}${sj 8BI j %sj$is$bt R Z} $R $jjzr s I $t 3$ 1 by Y tbs$bt $R {YBR t B $jjzr s Y {Btt {$Bt A b t Y bb BI j %sj$is$bt sr,r Y JZ R$Bt X$R Y st j 8 t BP Y }jst 8BI j R RZ{Y Ys Y BAR % I $t}ztbz}z Iss w (,r ( D $R } BIZ{ I -s{jk2" qk}${sjjk s }jst 8BI j R $R R} {$h I Ak s tb8$tsj }jst 8BI j p ( 5e < sjbt b$y st srrb{$s I 8BI j B { $ $Bt e 5e(!t -s8}j BP st B { $ $Bt by${y 8sk A ZR I PB 8BI j %sj$is$bt $R $% t Ak e ) \ e w, D e NN c6n N U1 >(,0H U1, 0 k( wd;d >(,0H by ) r c p ( PB RB8 6 k( BI j %sj$is$bt {Bt{ tr by Y s 8BI j $R saj B I R{ $A s }YkR${sj RkR 8 w`zr sr {Bt Bjj %sj$is$bt {Bt{ tr by Y s {Bt Bj jsb $R saj B s{y$ % s R} {$h I j % j BP } PB 8st{ D * ht$$bt d w_jst BI j zsj$is$btd V }jst 8BI j p ( $R Rs$I B A $t%sj$is I wpsjr$t h ID $P }jst $t}ztbz}z Iss w (,r (D {st A ZR I B } B% Ys $ %$Bjs R 8BI j B { $ $Bt e yp Y Iss w (,r (D {sttb } B% RZ{Y s %$Bjs$Bt p ( $R Rs$I B A %sj$is I wztpsjr$h ID (

7 _$Wqi$NNhi zvny-vqy$w K r u 2 Plant Model G 0 Plant G u 1 y Σ + e P 3$Z 1U BI j %sj$is$bt sr s R} {$sj {sr BP {Bt Bjj %sj$is$bt qybzy $ 8}YsR$9 R Y {Btt {$Bt b$y {Bt Bjj %sj$is$bt Y PB B$t I ht$$bt $R {BtT R$R t b$y BY R $t Y j$ sz v{p w_bbjjs sj >H 78$Y sti *Bkj >x EHD qy 8BI j %sj$is$bt } BAj 8 8sk A }BR I PB 8sjjk $t Y PBjjBb$t bsk _ BAj 8 d wbi j zsj$is$btd p$% t sd srz 8 tr BP }jst $t}ztbz}z R$tsjR w (,r (D 5e < AD V tb8$tsj }jst 8BI j p ( 5e < {D V 8BI j B { $ $Bt e 5e ( * 8$t by Y B tb Y sa$j$k BP Y }jst 8BI j p ( B Rs$RPk Y 8BI j B { $ $Bt $R PsjR$h I Ak Y Iss G Y t R Ys {Bt Bjj %sj$is$bt A {B8 R 8BI j %sj$is$bt $t Y R} {$sj {sr $t by${y Y {BtR s$t R I ht I Ak Y Iss $R _ Iss ) F e w, r, `D e e ` ) w `d `1 W,`1 ) (,r ) r ( k (, wdxd Y {Bt Bjj $R ) F e w, r, `D e e ` ) w `d `1 W k, w, `dd p (,`1 ), wded sti Y } PB 8st{ { $ $Bt $R F q Iss ) e w, r, `D e e ` ) w `d `1 W, w, r c `dd e k 3 wdd ]B8}s JZs$BtR wdxd wded stiwdd b$y JZs$Bt wxd qy -} $8 tsj Iss w (,r (D I ht R s X}jst Iss R " _ Iss sti Y tb8$tsj }jst 8BI j p ( I ht R %$s wded s X{Bt Bjj " wby${y R$t{ $ IB R tb Z$j$9 Y s%s$jsaj R$tsj r } B%$I R tb P IAs{,D R 3$ 1 3Z Y 8B Y 8BI j B { $ $Bt e I ht R %$s wdd s X} PB 8st{ { $ $Bt" q Iss

8 M #i$hwh_ q6v$ VW- 6V5$W$z qy PB b {st Y$t, BP 8BI j %sj$is$bt sr s R} {$sj {sr BP {Bt Bjj %sj$is$bt BI j %sj$is$bt $t <T$tht$k RZ{Y sr {BtR$I I Ak w_bbjjs sj >HD {st sjrb A {BtR$I I s R} {$sj {sr $P Y }jst $R srrz8 I B A j$t s $8 T$t%s $st yt 3$Z 1 Y Rs8 R$tsj $R st $t}z B ABY Y s{zsj }jst sti Y tb8$tsj }jst 8BI j t s$t R$tsjR `d sti r yp Y I$& t{ A b t Y R bb $R R8sjj sr I ht I Ak Y 8BI j %sj$is$bt { $ $s Y 8BI j $R %sj$is I qy$r $R Bt R} {$h{ {sr BP Y 8B t sj {Bt Bjj %sj$is$bt R Z} by${y $R $jjzr s I Ak B% jsk$t Y {Bt Bjj sti }jst AjB{,R P B8 3$Z d Bt 3$Z 1 qy "{Bt Bjj " $t Y$R {sr $R Y tb8$tsj }jst 8BI j by${y t s R `d ws%s$jsaj AZ tb $t}z B Y }jst $t Y$R R} {$sj {sr D sti `1 Y s{zsj }jst $t}z VtI Y $R tb P IAs{, R$t{ Y "{Bt Bjj " IB R tb } B{ RR Y }jst BZ}Z VtI Y } PB 8st{ { $ $s $R `ZR {BtR s$tr Bt Y R$tsjR ` stir sr $t Y 8B t sj {sr BP 3$Z d ]Bt Bjj %sj$is$bt {B8}j 8 tr BAZR {Bt Bj ibazr {Bt Bjj R } R t Y A R Bt {st IB b$y Btjk s } $B $,tbbj I BI jr Zt{ s$tk R Z{Z sti Zt{ s$tk ABZtIR 8ABIk Y s%s$jsaj s } $B $ $tpb 8s$Bt ibazr {Bt Bj sjjbbr B}$8sj sti ^{$ t ZR BP sjj Y s%s$jsaj s } $B $ $tpb 8s$Bt B } BIZ{ st $t$$sj Z RR PB st ZtPsjR$h I {Bt Bjj 7B8 8 YBIR j$, I wrzadb}$8sj {Bt Bj $% sr st $t$$sj Z RR s bybj R BP {sti$is ZtPsjR$h I {Bt Bjj R w%$s Y b jjt,tbbt OBZjs }s s8 $9s$BtD ]Bt Bjj ZtPsjR$h{s$Bt sjjbbr ZR B %sjzs Y } PB 8st{ {s}sa$j$$ R BP Y R BAZR {Bt Bjj R I$ {jk ZR$t -} $8 tsj Iss b$ybz k$t Y 8 $t Y jbb} B $8}B stjk by t PZZ }jst Iss %$Bjs R {Bt` {Z I s } $B $ Zt{ s$tk ABZtIR Y {Bt Bjj ZtPsjR$h{s$Bt Y B k $% R s } {$R w$ tbt{btr %s$% D {Ys s{ $9s$Bt BP YBb Y R BP BAZR {Bt Bjj R RY $t,r ]Bt Bjj %sj$is$bt } B%$I R st sj ts$% B 8BI j %sj$is$bt PB R$t Y {BtR$R t{k BP Yk}BY R R b$y Iss BI j AsR I 8 YBIR $8}j${$jk - s}bjs Y -} $8 tsj Iss ZR$t Y 8BI j$t srrz8}$btr qy$r - s}bjs$bt } B%$I R $t & { t b Iss 8 srz 8 tr by${y s Y t ZR I B $t%sj$is s js R BP }jstr sti YZR {Bt Bjj R ]Bt Bjj %sj$is$bt 8s, R s {j s I$R$t{$Bt A b t {Bt Bjj R PsjR$h I Ak Y s{zsj Iss sti {Bt Bjj R PsjR$h I Ak srrz8}$btr qy tbtt{btr %s$% tsz BP Y {Bt Bjj %sj$is$bt s}} Bs{Y {st A JZ${,jk I 8BtT R s I VR sj sik I$R{ZRR I sab% $t 8BI j %sj$is$bt b Rs b$y s tb8$tsj }jst 8BI j sti st srrz8 I 8BI j Zt{ s$tk R V BAZR {Bt Bjj $R Bt by${y } B%$I R Y I R$ I j % j BP } PB 8st{ PB stk }jst 8BI j Rsk _ ELQq $t s RB8 bys js Zt{ s$tk R _ Zt{ $ _ Zt{? BAZR q R} { 3 BI j %sj$is$bt sr,r by Y B tb Y -} $8 tsj Iss _ Iss w 8A II I $t 5e <e 8D $R {BtR$R t b$y Y srrz8 I Zt{ s$tk R yp _ Iss _ Zt{ Y 8BI j $R %sj$is I $P tb Y 8BI j $R $t%sj$is I Ak Y Iss!A%$BZRjk 8BI j %sj$is$bt {st A ZR I B I 8BtR s Ys s {Bt Bjj $R tbti 8BtR sajk Zt BAZR y IB R RB ZR$t Y PBjjBb$t s Z8 tu wdmd $8}j$ R w_ Iss _ Zt{ D m w_ Zt{? BAZR q R} { D _ Iss? BAZR q R} { 3 wdd w1(d Z $ $R {j s wa {szr BP Y }BRR$Ajk R ${ $t{jzr$bt BP Y Iss R _ Iss b$y$t Y 8BI j R _ Zt{ D Ys JZs$Bt w1(d by${y $R Y {Bt Bjj %sj$is$bt {BtI$$Bt {st A Rs$Rh I % t $P wdd $R tb qyzr Y 8BI j %sj$is$bt s}} Bs{Y B BAZR {Bt Bjj I R$t JZ$ R ABY {BtI$$BtR BP wdd A Rs$Rh I B {Bt{jZI Ys s {Bt Bjj $R tbti 8BtR sajk Zt BAZR by$j

9 _$Wqi$NNhi zvny-vqy$w {Bt Bjj %sj$is$bt s}} Bs{Y JZ$ R Btjk Y b s, {BtI$$Bt $t w1(d ]BtR JZ tjk Y {Bt Bjj %sj$is$bt s}} Bs{Y B BAZR {Bt Bj I R$t $R R$8}j sti 8B I$ { y $R sjrb j RR {BtR %s$% ; e-s8}j 0.1 Open Loop Experimental Data From Unstable Plant: u 0 (t) = 0.1sin(3t) 0.05 u 0 (t) y 0 (t) time seconds 3$Z nu yt}ztbz}z Iss P B8 st B} ttjbb} ZtRsAj }jst V A $ P -s8}j $jjzr s R Y Rsj$ t }B$tR ]BtR$I ss$t Y R Z} BP 3$Z d 7Z}}BR Ys b Ys% B} ttjbb} $t}ztbz}z 8 srz 8 tr w`(,r ( D P B8 s }jst by${y YBZY $R } {$R {Ys s{ $R${R s Zt{ s$t $R,tBbt B A ZtRsAj 3B }Z }BR R BP $jjzr s$bt j Y Zt{ s$t }jst A Nqy sti $% t Ak h wxd ) xdx Lx( wx L d(((dwx c dd _jbr BP Y $t}ztbz}z Iss s RYBbt $t 3$Z n w,tbbt B } B%$I {jbr ITjBB} RsA$j$kD gwxd ) 3X L1n X L(3dE, w1dd 3Z Y RZ}}BR b Ys% {Bt Bjj sti b b$ry B ZR Y s%s$jsaj Iss B %sjzs $R sa$j$k B 8 Y } PB 8st{ R} {$h{s$bt $t wd b$y Y P JZ t{k b $Y$tR $% t sr P d wxd ) X1 L1f (3( f 1X L1 1 X 1 L1f (3Mx f (31X L(31 1,P 1wXD )(3 w1nd G Ys% srrz8 I Y R {BtI P JZ t{k b $Y$t $R 9 B B R$8}j$Pk Y -s8}j qy$r } T PB 8st{ R} {$h{s$bt JZ$ R Ys Y {Bt Bj B A R8sjj PB P JZ t{$ R A jbb sabz d w11d

10 d( #i$hwh_ q6v$ VW- 6V5$W$z si\r { 7} {$h{sjjk b I R$ MCwiDM MP d d widm, by C $R Y R tr$$%$k qy P T JZ t{k R}BtR BP P d $R RYBbt $t 3$Z ; 40 Frequency Response of Frequency Weighting W 1 30 magnitude db phase deg frequency rad/sec 3$Z ;U _ PB 8st{ R} {$h{s$bt P JZ t{k I } ti t b $Y$t qy s bb }BRR$Aj s}} Bs{Y R B %sj$is$t Y sa$j$k BP Y {Bt Bjj $t w11d B 8 Y $% t } PB 8st{ R} {$h{s$bt 3$ R b {BZjI ZR Y 8B si$$btsj 8BI j %sj$is$bt s}} Bs{Y RZ88s $9 I $t JZs$BtR wdd sti w1(d qb IB RB b srrz8 Ys Y Zt{ s$t }jst BP w1dd {st A 8BI j I ZR$t s tb8$tsj }jst 8BI j h ( sti srrb{$s I Zt{ s$tk R Z{Z w W (3dwX LdD d h wxd ) wd LP wxdwxdd h ( wxd v dl (3((dX Ld wxd X c d 3 w1;d qy Zt{ s$tk $R 8BI j I sr ZtR Z{Z I sti 8Zj$}j${s$% w1;d ZR$t Y s%s$jsaj -} $8 tsj Iss b {Y {, qb %sj$is Y 8BI j BP Nj d f wr ( c ( f `(D N 1 N U1 >(,0H ( f `(N 1 U1 >(,0H, 0 k( w1xd by j d sti ( I tb Y $8}ZjR R}BtR R BP P d wxd sti h (wxd R} {$% jk 3$Z x RYBbR Y RZjR BP Y 8BI j %sj$is$bt R RZ88s $9 I Ak w1xd qy Iss %sj$is R Y 8BI j sti srrb{$s I Zt{ s$tk R Z{Z Y$R RsAj$RY R Y h R {BtI$$Bt BP wdd V}}j${s$Bt BP Y } PB 8st{ BAZRt RR Y B 8 >dh RsAj$RY R YBb % Ys Y R {BtI {BtI$$Bt BP wdd $R tb Rs$Rh I qy$r $R sr$jk R t Ak $tr} {$t Y }jb BP Y R Z{Z I R$tZjs %sjz BP Y s}} B} $s jk sz8 t I RkR 8 RYBbt $t 3$Z E by Y 8s-$8Z8 %sjz $R t s jk bb w} PB 8st{ BAZRt RR bbzji JZ$ s } s, %sjz j RR Yst Zt$kD V Y$R }B$t Bt 8$Y 8$Rs, tjk {Bt{jZI Ys Y -} $8 tsj Iss YsR $t%sj$is I Y {Bt Bjj w11d qy$r $RtB Y {sr sr $R RYBbt Ak s I$ { R BP Y {Bt Bjj ZR$t Y Iss sjbt $ Y Bt TR } {Bt Bjj %sj$is$bt } B{ RR qy {Bt Bjj %sj$is$bt R PB Y$R -s8}j $R

11 _$Wqi$NNhi zvny-vqy$w dd Nj d f d f `(N 1 U 1 N d f >(,0H `( L r ( N 1 U 1, 0 k( w1ed >(,0H qy RZjR BP Y$R R s RYBbt $t 3$Z qy Iss IB R tb $t%sj$is Y$R {Bt Bjj yti I PB Y s{zsj }jst Y$R {Bt Bjj RZjR $t Y R tr$$%$k A $t PZjjk ABZtI I Ak P d wid R 3$Z M qy 8BI j %sj$is$bt s}} Bs{Y ` {R Y {Bt Bjj % t YBZY d $t Y$R -s8}j $ $R PZjjk {s}saj BP 8 $t Y I R$ I } PB 8st{ R} {$h{s$bt y IB R RB A {szr Y srrz8 I Zt{ s$tk R Z{Z BP w1;d YBZY tb $t%sj$is I Ak Y Iss wa {szr Y Z }jst PsjjR b$y$t Y R Z{Z sti ABZtIRD sjjbbr Y }B t$sj BP 8stk $t}ztbz}z Iss }s$ R Ys Y }jst $R jp {sttb } BIZ{ y $R Y R srrz8 I $t}zt BZ}Z }s$ R tb Y s{zsj Iss Ys $t Y$R -s8}j -{jzi Y {Bt Bjj by t ZR$t Y bbtr } 8BI j %sj$is$bt s}} Bs{Y 3B -s8}j b$y wxd ) wx c x((dbwx Lx(dD $t w1;d bybr 8st$ZI $R ABZtI I Ak Zt$k Y {Bt Bjj $t JZ R$Bt IB R tb 8 Y } PB 8st{ JZ$ 8 t qy$r -s8}j YBZY s A$ R$8}j$R${ sti {Bt $% I R % R B $jjzr s Y tbtt{btr %s$r8 BP Y {Bt Bjj %sj$is$bt s}} Bs{Y y sjrb RYBbR Ys {Bt Bjj %sj$is$bt sjjbbr Y {Bt Bj I R$t B ZtI RstI bys % I${ Y s%s$jsaj Iss sjbt sr B}}BR I B srrz8}$btr ti R sabz s }B t$sj {Bt Bj jsb sti $R sa$j$k B 8 I R$ I } PB 8st{ R} {$h{s$btr x ]Bt{jZR$BtR qy$r }s} -}stir Z}Bt Y ZtPsjR$h I {Bt Bj {Bt{ } Ak 8s,$t s RZIk BP Y {Btt {$BtR b$y 8BI j %sj$is$bt sti {Bt Bjj %sj$is$bt BI j %sj$is$bt $R R t sr s R} {$sj {sr BP {Bt Bjj %sj$is$bt ]Bt Bjj %sj$is$bt $R RYBbt B } B%$I s tbtt{btr %s$% s}} Bs{Y B R$t {Bt Bjj BAZRt RR Yk}BY R R ss$tr Iss y R} {$% BP by Y tb$r {BtR$I st $BtR 8sk Ys% }jsk I s } $B Bj $t PB 8$t Yk}BY R R B A %sj$is I Y %sj$is$bt } B{ RR $R jp 8s$tR t % Y j RR I 8$t$R${ R$t{ s }BR $B $ Y } PB 8st{ Bsj Y Iss sti Y {Bt Bjj s I 8$t$R${!t BP Y A BsI $8}j${s$BtR BP Y Y B k $R Ys -} $T 8 tsj %sj$is$bt BP {sti$is {Bt Bj jsbr $R }BRR$Aj b$ybz s }jst 8BI j sti b$ybz Y $R, B $t{bt% t$ t{ BP }YkR${sjjk {Btt {$t Y R {Bt Bjj R B Y }jst P t{ R d V < j8${,$ ] Fs{BARBt sti ] W ]Bt Bj B $ t I RkR 8 $I t$h{s$btu V bb RT {sr \I 8$t$R${ s}} Bs{Y $t I yeee q str VZB8 ]Bt Bj newd(duddenudde dd 1 in BRZ NsZ sti 7_ BkI 7 8 8A RY$} $I t$h{s$bt BP RkR 8R b$y }s s8 ${ sti tbt}s s8 ${ Zt{ s$tk yeee q str VZB8 ]Bt Bj nwdu1u;d d1 n p] pbbib$t p % R sti W$tt RR +Zst$Pk$t Y B $t R$8s I strp PZt{$BtR b$y s}}j${s$bt B 8BI j B I R j {$Bt yeee q str VZB8 ]Bt Bj nwdudnu 1M d1 ; i N BRZ =t{ s$tk 8BI j ZtPsjR$h{s$BtU V RkR 8 $I t$h{s$bt }s si$8 {B8}s$Aj b$y BAZR {Bt Bj I R$t yt _ B{ yeee ]BtP Bt * {$R$Bt sti ]Bt Bj %BjZ8 d}s R n;1un; W b! j str NV * { 8A dnudx dx yeee _ RR W b OB, x i 78$Y sti F *Bkj BI j %sj$is$bt u s {Btt {$Bt A b t BAZR {Bt Bj sti $I t$t h{s$bt yeee q str VZB8 ]Bt Bj nwdu;1ux1 d1

12 d1 #i$hwh_ q6v$ VW- 6V5$W$z E i 78$Y sti F *Bkj BI j %sj$is$bt sti }s s8 $I t$h{s$bt PB RkR 8R $t I sti q d yt_ B{ V8 ${st ]Bt Bj ]BtP }s R 1Mx1u1MxE d1 _BBjjs _ Ys Bt,s V q$,,z F szr sti Ws}sj V $8 TIB8s$t s}} Bs{Y B 8BI j %sj$is$bt yeee q str VZB8 ]Bt Bj nwxduxdux d; M F] G$jj 8R _s si$8r sti }Z99j R $t Y Y B k BP Ikts8${sj RkR 8R yeee q str VZB8 ]Bt Bj V]TnEwnDU1xu1; dd 7 7,B RsI sti y _BRj Ybs$ Zj$%s $saj 3 IAs{, ]Bt Bj G$j k W b OB, de d( p 7sPBtB% sti q] qrsb qy ZtPsjR$h I {Bt Bj {Bt{ }U V I$ { }sy P B8 -} $8 t B {Bt Bjj yt V 3 st{$r sti V qstt tasz8 I$B R 3 IAs{, ]Bt Bj WBtj$t s 7kR 8R sti ]B8}j -$k 7} $t Tz js W b OB, dx dd q] qrsb 7 qy B ${ VIs}B 7kR 8R _Y* Y R$R =t$% R$k!P 7BZY t ]sj$pb t$s NBR Vt j R ]V * { 8A dn d1 qyb8sr 3 B9 t { ]Bt Bjj yt%sj$is$bt yi t$h{s$bt sti N s t$t =t$% R$k!P 7BZY t ]sj$pb t$s NBR Vt j R ]V * { 8A de _Y* Y R$R dn p 7sPBtB% sti q] qrsb qy ZtPsjR$h I {Bt Bj {Bt{ } sti j s t$t yeee q str VZB8 ]Bt Bj V]T;1wEDUM;nuM; d yeee _ RR W b OB, d; p s8 R!t Y $t}zubz}z RsA$j$k BP $8 T%s k$t tbtj$t s P IAs{, RkR 8R v _s R y sti yy yeee q str VZB8 ]Bt Bj V]Tdxw1 sti ndu11mu1nm sti ;Exu;E V} $j sti FZjk dee dx yg 7stIA!t Y U 1 TABZtI It RR BP RBjZ$BtR BP tbtj$t s PZt{$Btsj JZs$BtR jj 7kR 8 q {Yt${sj FBZ tsj ;nw;dudxmdudx de; de yg 7stIA V P JZ t{k IB8s$t {BtI$$Bt PB Y RsA$j$k BP P IAs{, RkR 8R {Bts$tT $t s R$tj $8 T%s k$t tbtj$t s j 8 t jj 7kR 8 q {Yt${sj FBZ tsj;nw;dude(dude(m de; d p 7sPBtB% 7sA$j$k sti ibazrt RR BP Zj$%s $saj 3 IAs{, 7kR 8R yq _ RR ]s8a $I V dm( dm _V ybsttbz sti V *ss ibazr sis}$% {Bt BjU * R$t stsjkr$r sti BAZRt RR ABZtIR yt _z B,BB%${ I$B 3BZtIs$BtR BP VIs}$% ]Bt Bj }s R dudx1 7} $t T z js W b OB, dd d F ] *Bkj F Gsjj sti p 7 $t _ PB 8st{ sti BAZRt RR stsjkr$r PB R Z{Z I Zt{ s$tk yt _ B{ yeee ]BtP Bt * {$R$Bt sti ]Bt Bj }s R E1uEnE! jstib 3N * { 8A Mud( dm1 yeee _ RR W b OB,

13 _$Wqi$NNhi zvny-vqy$w dn 0 1 w p *( y 2 p0 *u 0 ) L2 [0,t] 2 p 0 *u 0 L2 < 0, t: Data Validates Model [0,t] 2 full scale x 10 3 blowup around origin time seconds 3$Z xu BI j %sj$is$bt RZjR PB -s8}j 2 Plot of Structured Singular Value Vs Frequency For Augmented Plant µ Q (jω) frequency rad/sec 3$Z EU 7 Z{Z I R$tZjs %sjz %R P JZ t{k PB } PB 8st{ BAZRt RR {Y {,

14 d; #i$hwh_ q6v$ VW- 6V5$W$z 0 w 1 *c 1 2 *u 0 L2 [0,t] c 1 2 *u 0 +y 0 L2 < 0, t: Data Validates Controller [0,t] 2 full scale x 10 3 blowup around origin time seconds 3$Z U ]Bt Bjj %sj$is$bt RZjR PB -s8}j 5 0 W 1 1 S 5 10 magnitude db frequency rad/sec 3$Z MU 7 tr$$%$k sti ABZtI PB -s8}j