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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$$%$k qy P T JZ t{k R}BtR BP P d $R RYBbt $t 3$Z ; 40 Frequency Response of Frequency Weighting W 1 30 magnitude db 20 10 0 10 10 2 10 1 10 0 10 1 10 2 phase deg 0 20 40 60 80 100 120 140 10 2 10 1 10 0 10 1 10 2 frequency rad/sec 3$Z ;U _ PB 8st{ R} {$h{s$bt P JZ t{k I } ti t b $Y$t qy s bb }BRR$Aj s}} Bs{Y R B %sj$is$t Y sa$j$k BP Y {Bt Bjj $t w11d B 8 Y $% t } PB 8st{ R} {$h{s$bt 3$ R b {BZjI ZR Y 8B si$$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

_$Wqi$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

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,

_$Wqi$NNhi zvny-vqy$w dn 0 1 w p *( y 2 p0 *u 0 ) L2 [0,t] 2 p 0 *u 0 L2 < 0, t: Data Validates Model [0,t] 2 full scale 4 6 8 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 x 10 3 blowup around origin 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 time seconds 3$Z xu BI j %sj$is$bt RZjR PB -s8}j 2 Plot of Structured Singular Value Vs Frequency For Augmented Plant 1.8 1.6 1.4 µ Q (jω) 1.2 1 0.8 0.6 0.4 0.2 10 2 10 1 10 0 10 1 10 2 frequency rad/sec 3$Z EU 7 Z{Z I R$tZjs %sjz %R P JZ t{k PB } PB 8st{ BAZRt RR {Y {,

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 4 6 8 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 x 10 3 blowup around origin 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 time seconds 3$Z U ]Bt Bjj %sj$is$bt RZjR PB -s8}j 5 0 W 1 1 S 5 10 magnitude db 15 20 25 30 35 40 45 10 2 10 1 10 0 10 1 10 2 frequency rad/sec 3$Z MU 7 tr$$%$k sti ABZtI PB -s8}j