Biological control systems - System Concepts-Mathankumar.S, VMKVEC

Preview:

Citation preview

IvMU/VMKVEC/ELECTRONTC SCTENCES/BME/EVEN SEM/FOURTH SEM/2OL5-2OL6 ICBCS-R2012- FU LL Tt M EI

V IN AY AI<A MI S SIO},TS U}.IIYER SITY

Vinayaka Mission's Kirupananda Variy* Engineering College

SALEM - 635 308

Programme B.E. BIOMEDICAL ENGINEERING Semester I 4

Subject Code & Name 34712401 - BIOLOGICAL CONTROL SYSTEMS

Name of the Tutor Mr.Mathankumar.S

Assignment. No. L

Date of Announcement 15-02-2416 Date of Submission I zz - 02 - 201.6

Dercriptive Type Qqertionr (Eroy Type)

1. Using block diagram reduction technique find closed loop transfer of the system.

2. Discuss in detail about the types of control system with neat diagram.3. Convert the given block diagram to signal flow graph and determine the transfer function using

Mason's gain formula.

Elaborate the various rules of block diagram reduction technique.Write detailed notes on the following:

i. Rules for Signal flow graph. (B Marks)ii. Properties of Signal flow graph. (8 Marks)

4.

5.

d N"&r^@ 4 r-/^r4*,{wtrt""ture of the Tutor $i{nature of the Coordintrtor

IvMU/VMKVEC/ELECTRONTC SCTENCES/BME/EVEN SEM/FOURTH SEM/2OL$-2OL6 I CBCS-R2012- FU LL T! M EJ

6. The signal flow graph for a feedback control system is shown in figure. Determine the Closedloop transfer function C(S)1R(S) using Manson's formula.

7. Convert the block diagrammason's gain formula.

to signal flow graph

H=

and determine the transfer function using

8. Discuss Signal flow graph with example. Mention its effectiveness.9. The block diagram of a closed loop system is shown in the figure. Using the block reduction

technique determine the closed loop transfer function C(S)/R(S).

L0. Obtain the closed loop transfer function C(S)/R(S) of theshown in figure. Use Block diagram reduction techniquewith signal flow graph technique.

system whose block diagram isand verify the transfer function

C(S)

R($

d' Hr*4*n'/**"*:'Fd-finbtuidof the Tutor rigncis,H"Kt ,l tu

uNbn l2tDeJ<, *yo-rn 1c,t1ctio" vtec*'niqy*- *i4-d cJ^es&L

*ro:t*yt+ j fr'@

.9lep L -- Mevt4,? fi,,L bvonc*t PU, \fr'tL blocte-'

Rrs;

s+3 L:* Re 'fr*b

Rcs)

St€"D 3.*-t

CnMn1, frle*

__+

RCS)

bvc.rrd.u ..poetrf '

{/ -/\

20

B+e-p 1,'* H;N,,;t o*re Fee&bot"c&,c PaJJ,L

R. Cs)

Csrn-br.n-Lvr-e. #tL b,tse*x i- aea e e L0

&s&+

" rr"fr, f,+

Srlap B --l-'

Q'e-&e, &+l+Fls hA &ta

$wu{r u

cs)

.S+e,o L.I

fire- Feeot*b ge:l,-, foLfi,,a ''-

I

-l

ccs)RCS)

l+ Fl r 6hg &q

rrI or/a+) (€ &y&s h+

&r Gz c{} Cn+

G.rg- elg h+

lrr!t''---

/+t-fl &y &aa:L_!p-1} uGasl*rL-.}rGtg &

€ & n*Gts &,a

J t-F* 1 &A& 4+ F*s&*&S

cCs)

l

T*ep T ;* CD rlrl.x; I

, '*f" J '* L'u IYL**\

R- t>)

)-r#-r-ig5 (,9+ Loacnda- btaalq'

l,+ ttr & Z&1 t H282&3

.tI ,./1

ff er &3&",A,* lle-&.s*&Sj1{

t-a

:

i

:1

i

;

:

:a

i

II

i,ii

T

!

tu-**.-

&r &g h+

-n

S'h*f : B ftfr-dl,u"*T N1!a"is-ve- fq3d"bmak"

*lt

ccs)

s/1

c cs)

Sfe+ g \*,

C CS)Q tetu&a&+

RC5) l-t*H1hs &+ + t+zQoGr3

i+bbL tr9+9.?" Il' G B1Qser++++"&rAil

gSe r&CS)

= e( rG(,t&s &+

t t Ht &ze<q + H:-&rQg

l+ t+r& *Q+ "L He &v&,3*-r

r-+gft1 Cx zEA&+

I + F{ 1 Gig Cxa + Ft a G""u et3

& r Gt:- &3 &q-f

I * At&dU+ + Fts &*&E+ F*a&,&z&a k+

2_, Siscurxa -i- cLe-h.t,t. aJootrb

o.{J.-}i+t^- 'n'Pnk' *"-1"lrG;ryl :'

3?% Y#;*'#u.H::

Tl r Rqfexsr:a*

' -Tt4'a- olP

ct,r-14- i[D

u^A W

,,Cern- t/lar-(

t'

d-4

of*^ "I,esf W Jd^'Q*

.-et @ olP

b-d

rOdt-)t

Vffi ,jtt/r- b"u.b

o/r

-,rth-e- *p(>s t Cr,n-b-rel Bpbern

W* *t Wr) {gpan- -{'ep

g) c],es=* J**f Y

ue-cl,@n'tve

Con*volled

vc*sjahie olr

v(*) I :l:]*,^,*.&\ [ ct+)

+ *r_4 w ffeg ry daes ,tab arrbm^l<eg

,<*e+><p-p-b& ,-pasubfubn "?t ;'t4 'lr 'r1 eat'lsa'

>T.t;-'rovrtlsLW'w'^3'-at'>e&c*w'BA2''*4*9t,r"""1/h.aA ',-nD W

*I* 'fr'11- 'ry V-""bzad r\

UJfu* *r* JDSP tro ,*r-ob Y*aclQ'

Jtb #Q-

9V"fu vv\AtAAa a olP rA

S I f "t'- vcat'\'vlLcl=cDn '

#r,4,5151sl .,*c,Jtrsrn

errlar2c*e- JE^L

'=/ P

*d cJ"-tr1?e-,

+ WV'eyL 'fr'"l-L

jh "}s rn'ab

.*^t: @

*-oo

6>$,et=/doo*r1e-g r

ExW"- -tgdrtlYw<-t^rry M,r

+ EL ss}*:nle St":i+ela-

9 A 'Taorgvssl '

"lrtr#,,e,

ryrPa d;-li-

w"e %

+xo -{""f Y, tu:3* -1- ")P aAz

@-\ffioaAi-ryAdva-nba-ne:':-

+ 'TI4.L bT tr* otl-e' ry +1 e-c-o'lnr*icot '

--\ T + tZ eqA:""- '*D Can*tvucb '

7 &w ' ' ' ' ' ra ^^ a2r'L .sLdtol2' '

+ be:t:>t% ,fiAe- Y J-T

o -^^,^'n#^ 4,D",LaAv-,r*af :-

va-?,*- ,s*r-a.9 Tt4-L Y J€Y vo'21'Q' -t^'t-a-eu*+otu 4

@

) 7t'1-Q- ;'- uou'E?)-b a'A* e)-@tu^aL

al11'ul^Ugv'u' ottg' 'tn-ab rs'4uut*j- @'

+'Tt4-a v@rJrrolte& *P** dJ+P'"AA ry

fln'

(frn+Y*f f #l

clpsE D LecP JXS-rFM n-

Rgf€,r4 €;-i @- evvoY' Dc**p**erv

-[npu-b

ar {*}

C{,s"se""L

*& WLQ- cjs.Ee€L -Ar)

fO O o*n --l-asea -0.bLrs^fz .^f a n?g-*UPn '-'.; n*arx:*aouo t"

* *fhe *f* J*f -*uY#e:vu {Grv

y ^tr y,rflrt?,1 a-

fu "&,a- "c,nf,rct

,s}lrv ffi"e- c'O

ba- \*u.g,ct"t-Fie.cL e-L c'{-,Bde&d

fg.g.rj-;tr,q-c)<' e

*a?w#r1S- fure(Jte-eed- J*"f

ucfin*rrol YgA Tex-o:taL

b).oou dub.nryo+..,- 3 o..r1* o.ulpnn-o.l=,e-

"r-ov.*rrot &-l- .qrY1- 'b/ ;'-' :*' crtove- *tt*-0

.--\:f b *'@'nx-&'U7€rrr_ €3,pts*r @V / O" (-srtbYsttQH

)

Con*yelLl ad*lpoPe.ffi."

',f,*f ey*

-xorrt-rpl uybe-rn -.^in

t

+ c,Lcse- L &"r)ex asL W*, rl"n-o,^8nba-tn fu

tr

trE-q.c-back

f8 e-naoY)

*fe>n fi^-u S/f

#qrarTa .

rtfts* */ p

-?rl Sry-d-efi

M

tu

V o.,t/-(€-.

g*rnvfa"wn*lLLd:bar*.'o\rrbY14-o*r4qll-.((r-oYretr*

_fr"- o/ p obr&

W *e r;J,ln

d,i4 br-7},61/^.€e- , H€rne-q g

M a-t**Pd

ft**- C y J-g? 'ffi 4n

+ *l.,t\e. 'x.e-ff?21eY1r'e' CS/e W) @-*b d,g3!rre-d* olF c

* 11^-a- tr€-e_al-b c-]d e

orr,A- rl,ruve-x*a i* dto

s..5 M % ryce'J* *aL rt" *lf

il,,e* @ d'L'Veu@v '

)

Tryy ryovbybJwrt

g*Wv M &'*-- *[f'\

% rka'nn-o-' 4f

*'Tt,e trzd,baok' YW .+r uLt 'i Y t-

-\ -fnve-,7€Pelt-CI." W

JA

Wvt

+.. oax' W fr,Le- e,t-* i

-.! n,&. ,,wnbol*>t *woalt.us.l-l a*,ffif"€^ .fr^-Q- eg:+*+ i'

) ,rw befu>t **u o-c,"f^ort,. j

I

o - ' 'Ls {*} Jto ;iU-\e- I

'/ ^^l't^o befu>t v@rt'ru-t'e" i

%-_ffi:; v.r'boru^elII

+e $D Y* itu ulr I

I

I

ElNtl;rrt De&cby i'

? -iFb rcryTrezl- *'*rolf '',o'"+t"- 3'*n I

W* x*o.b a-w'- exs<-sut W t

I

brt*ollert:- a , I

?:tr+6 ott&" 'YY' '^on' oel>l-ol,- W .*'1

v)n-nb ee{ 8?x t'q-.r"' t sPa-rr JPOP x@0

->:f+7(-e^n*:rctle>rx +-1

Yrrr,a fr/Q- q*;1]oo bryl*A .-c>n

\ (r,n,b'r-o[,

%qI Ag*ro.te-cL

Feed_b ock_ o,-

o

? .Irb ux,

4fr *t"lr ,

P(.g

Ll-n

-/1tr acJ<,o

vtd)

!

W.TtV#nv

Mry/ dslarea-qe*

{t

* *f14L

Waxv "f^

+ alnz-/

Mfu

=\ Tl4e7

y* ,n".to*r,--.rit-V &,vice 'wr^fuL'w

c*i^be-cts'1r)

ffias*, *% tu *ler'tfrrol a-*-donj^&

cCI

x@ *r^A * nar '

so

ee-r:lP@ .{ sl.;rya*ctr-on

crc-tey "t Ud Jn &n-Frrot

M41 €ch

o

.Aft

N\ Nena-*r)vs '|u^td.},uc;< "i f'uf&a*M

%ubun 1

} -TT'1& *\/Q-

MLed i- q *i orrlu-t a&Url"s'nee-(i

ufvaLoA{d}.-e-L olF & tr J""tp ,@'V'fo 2- (e>-<-zt-ov-

* Tt4i-

fr:-Q- olf *&

Yexl- *-* WMeA ',r''' 'Lo*^t,*e;'--[

s

? alns- frcel-t;ve_

o-l-so ftYa*

Henre- \/L

no -PG'-P1'G-lr!1*trt\/-- I i

Y ev** ac-.r-tlt€tfu- *.-A

ffitt %o\- Y ba- d

.**o&lL ,

deeenL J-"f *f**

d&*eA '-l**f

M

M@

Y1-p|(si€- .

#^-L

D/,&a^dv a-nt*flu' ,'*

ry? *TvlA lJ-sgeA W

o.>rJ- *errwytax s*44

** 84.itl'sro

j^n

rycj-ose-cl

g}1.8{"-. -

X 62J-r\,

? Hun-*tu* q f o-,..

OPQ;rL JsoP C**p

t' Xry ;r' "ff,Sr1-aJ^ ,-yl-D #

\-on #"a-*^fu^b

aldatB

1' Ott*?"r.t @wb;to

*t-ob @q& $*-ryn

3. Fer,r;]-votcje., @o

J.,A,

J**p

,ilt-a- Ov€>ral^

? *fie' Wsc-k'

% .flr& tr"*-\ efa-a'i'-t'Lt=X -i^ q'- -*-ofrt- 1>

eiVtnrvt -i- c-lpoe-t-

z-(, ,*oln1.;vJto&tP aAWIYL +1 urY(ote- ,<-c*z-i'u \/t-5 ,vr

* ,-e A,bdDl-L ,'.*,v"fro' ffi

Exat,r'Pln' :'

+ Ta't\f+ '4r''-

)$teJ_ -^-on*-nDt *td"*

c1-ose&

j"

FesdJeoucJ<, @ -{-A

4, evyoy @r *fA

.ory' 'Ect- JA .-tYr'etc-CJ${cufu- -*1

t

fretljigfv€' '#

cffisLurdoe.Jr@ c

abs*-,bl *.M ,tw*trS. ftd1'f"Iu6 @e'hz- ah

,

6 de-;t*d-t" kilr"(*bo-nc-g- '

-1 . t-e)>'L S^er1a;eltre'-

e$Lti v-o

*o #'a*

uW.T. ,ffi dve ctt>

''@*ffi,ruu> gj(-\ll\re)

q.Sry "# cD#@^e ry'

rr l-Iw Isrn-en & gA

tsru^€Lt-rsicl-tj4- "r& La-:.^oq-{

b ;tD%

orx^-d- W ?

!0. (S+abilfEad

-&ru"fldorlcr*ro')

rr. ffi **

LJ4Pfl F MCg* 'i

i^ tJ34,4- ry-

\./1

fr blocle &*a?Ya-\ ;assbta-d;'4

Ae*tk-a;W)

-4.-L^ kh"(u .,Pet c-'aA ce-te.

bl-sc-,e;a ct'rcbT

,f qd-ltL r'-

Aqt+ A qs.

A (A, *As)

A ( *t s* (ou)

4 Vsx:nuu\

1?*e - I

,Pu-LLe-&

%[oetcat

a

o*#)

oJ-n)

C

? NvL-u'L ':b-t-:o

--<atbvbrqck uLD

?a*tg - 5 ."-14o\d-,:"1

UDd4) ot14- i" 'pa-*t'd)-aL a-td-- -Y1

N-rra*-t "4.A;-fl

trY

Ar

R .J r-fr*

c

q L\Ll^.u'L ;Ltso

Codn,) il*L

&t;o r3'rn;vidrrc .L

tRr*,te, E9-:- W

tO]r)

bl-od<A -Bet

v

fLccJea .

#Ar- byq.rr c*\ #^A_ bls€k

Q.u,te I :* f.a ov'fi ,il,\t- B'}tanc'h- ?.fnt J*fr"* itl^4- bl'oe]e- '

$lt.r,te- E :*

bt,oc*,.

+A+-Q-

a

g

9 nu*rplrr^y ,#.,e- €t onc*. *oltt -^+t,tla- #'@ bn'bn'b

hl^ocje,

Movfr ,t&t*_ M\ W fr^A-

b

f&rte, -"L*- T,n+Qetchasra* d& ".reerL,,t i--t -f{>iln"f ,-ffi A*rntn

Aq \L-r A& * E&

+ NlAe4 un^ovirj ,fr,4e' ry fo'rc Y: ,*.,fuv& .ri alonl o- or-i"racdoo .at "t**' ' M(,Lt{ar'Ld #/e-

+A: A*C

Sffi Su"nr,tx-^? %[nb

I

*A

C R* cF{) 6-,

RGt * c-HGr

fze,,ic/*^o<kr l*'

,A

=Rq

rRe,

(P*cAr)G{

{=

*E

A.g- & - <_

{Q.r-r-[e, tm n %

Bs cF{

'GJ ,

o

r)

N,s4--h.

P;;Ja;

*eniteA* .vwte-s &rL fr4'a' joUorrl-cnn :-

trY$*YY@ ffi^-e- 'fury f-c-*tonb

5 o*Yffi

% tu *'/fr'LoL

bq,osld^- '

?swy,,YYY

*b

#4-a-

oouL.-(fest *V tr€*JJ-C,b

* Jned-a- fr/o<-off 1

,fr're

be- Wc-e-€L cfo=

bYaY.eJ-vo

,LA

o

a-Y LAUA

#xt a,'X3-

rPuJe- 2:--\ bA&7

,-rr1-Od@ -tn

x1

xq lr

,&ryffu%

&

X3 = O.-1 Kt + o(g Xg

A

L)T a-rrcir.a-t Ca-w b-L ,glrn-b)neA' -f-

bvc,.nd,,- JAr+^-ggQ- '*nanap"&*oaca- ;a ryA

-i-rrAri>'l?d,t.ual- lvo.rrcl"u',*t@'

oS

+ o#xr xgnn o-

xt *2 xg

Q;Je 5 :-Pg*todf d b*ra.-n &t-tA

tA

9b,SL'.l,.c-,.- JlIt4"OS{- *ta-rta.r*L13os-ae- J\ '-*to'

*t -}''div; a*r-at berart ctw 'itSr LL '

ra-#xs

xa

xl Xo.*.A

?*r-Le i 4:*

? A .n4.ixe/- '*,od,*- z-an* be- ry*qJ:e€L k

WZ ,fr.le- -f,to.n*w&fu.nee- *t -*t'tt",^? b^rane'w

1,f,.r^orn- JV'\,- *-ixa' "u.,d-u)*n fr"a- *m

oJL ;rarx'*t3 brcl't'tc'btts *) #"4'a-- ''noot-e- '

a-A

*+

x:l

Yt

=? t-

?

-/1

alrrr\ ,t-Lor-ba r^fe-/A, "7U.ze

y be"

s/ p qh ulr

*p#-y\-c,da- A-."uA--

#/,e- ''YL'e"

tX-L*

301 ? fr" *1,

3*^ "} bYo'rtelt

& bll-be^-Xt X&- ' X3

U

a-bl+ &c.

=?,- +X3 I

Q,ga;ope*="e/3 % --tn-c-L #*u) X**Pl,-:-

*Lfrebric- &JPdc-tA* z.a%-e- JM'd 'fr*

W #"r, tr*f* M bL ;tu fr^e

o

tr*t w + ethLck @We

g 3"* ; offll..xl*;-,l- ao -li''-es>+ tr* o'''-bd

* A uY1frd'a- ;L'4) w yr*AJ/L :r<CPtSrqq

q A -h-o&- *ol-ol*

b*l@ -h ,b4& {YJ"-r'r1- Jbr alL

**e- PoAi'N A'\n-e bo*a- ;r"fefi +

d*txga-

r/1,OdL',,-r, - o{ F brosr'e,'u %

au*uX

**axl*x*i*anL% a

g a?fi-Q* bxa'nd've;-r,Lc&.

; ,pt'La- ''Yru d^2' Y o

+tu W;bravel- oA,i *:T:3;

#4& 'rwnsul-d' ai-'-fu't 4^ uot"'e-n- JL '-ta

.a1 o .,e&- 'Lfo'q-w'i/;*.onc-z Soefu, *.arrl*+U bd frL n*t{ v

,fr^-Q- bt'enc'w

ary W tbu) w:"t ew Y;r{rth.e-ffi@

gA

ZO

W %f- *t tr* f* TY verl*be-

Cor..vesa-b .#1-L f* ';.-.,..l,<' %'w tr rff:^T^f^ ry:

fr/e' '*-tartsTc:x tt'-noaDn -'-*-n

f# ;-JT, *ffi ,,:1;*yjfug^ :,.fj Qmn, -

+ -r14-e- .rn-ootrx vouwae YY** ,-.- -: a_vestt

ot u,e:+Ld *YZ -?oln# ' *

bP4a.J"tc-I4-.fo"un-b

CS)

S+ef J- :-

o*-y1,.

e-m)&ry1,bggL -*1-L

S+€D L i*I

+ s&La&a ffi':-b ryoac.fdau/r,s €*-ax

Cr}acl^e*

CCS)

M M clrel%

*1c)rd-ost- t /2r 3 Srbc*' ,)

,s346bftesl " f*)

L L 4t qa I

in ) n,rfu* fr'a- ?*

fr.1e- eggv ,-r't*,dl- t3'''- JA^2- *'*^L'" ffd

vcortya-c.v 4J-L ,fr72- aw"-f*dr-'"? -8-\ c*';rtL

J47\b 4' v.rYl-oJt'l<J b d*ttee-rl- JE'12- nodo4 '

,./a

\.u@tw

.l-:o yd- -firy€Lxd 'lto1C'L '

g.r if*o;r1'c{, f o&t'

.: PL -h Pg- '|

Pt F G{( o &2,

S+ep 5I-I

b,eb$y

t&u +

9 D'gto{-r-t: tra'L

Vqr4.flo e;e *n-DobA *

F*ram ffie-

I I 2 r 3&14 Qzq t Lo >O > O > O*.;L ,O. >.O

5t 6.

6(,) f,.-,e--o

*-#g

be&llegvuy* $*'oee faffi--

@ .frl-e-

aoLg,-tr*cuj- fatu1*

t

P,(r)

S+ef J_:-

W A-Y19-

trCt() s e

&(1)

, I 3* 13

Arcs)

?L = * Qa

qp.s gg

6tr)

S{-e,p 9- :- 'T-sI

@ g$-e-

A = l*

*= l*

,-frt-(.- ffiict -P.t- .,[.oop &a^i,,t .I

*fr,ab ar.LoLiv i cl.;-t-.3.1-."O y4A-

bb

-Ln,d;)vid"r-t-'%L

Prt 'fr*

.gt-ef Z :- To

""t**p"'WJ€€?4 I ,

t9*ep+ 't'CaJ-M

^ s t '|-

t- Su-rn- fr

t&t Pr=

-H

# 7e trdrA*;^ dw,D u, --,'-tb)g'"4..*itt'

A- eh A. k 'c

rn-c{-Lvla-l.rot-

dr*c-b

J*y, Valr-t,e- +

.5 cLlr "*

#Lfv1-

a"ou4v*t .t

& *14rl,4* cffiry J'*fbn

',o,.jre Vq

(

L",,1

C- q,H)

l+ &r Ho

J.-'5

-rfuj-o- ,,oJ-e- r/1-o fe % ar*P'we

-t r:tn;*d.T A-O/t -

,)@4 o'rt-oL

Step 5 :-I

fa"+q ry F,laxon b Gl-ou*n Ilorn"1.uta

r=*4IC

AK PK

fu f(.s ltz | ^t

T5 * LAt?t+aso{

E-lt+E, h-{ Lu' ( & t&9-) + C,)k ctsl

f"dbaeJe'Try f" a- &'

cj.^ose-J-

*.tg

-bre-, PekN,*AA

J.^ec>f dhry f*etlso

Rrs)

&|.\fru:o4

Monxonl 's f*rnd

cO-{*,

c cs) / r+cs)

Gra

Dtil

e,;^PtE

S+"p I :

" fluxx-

-*,*-b

*tro P .-fi**o.,,r{?"* ?^i,, I

o.*ie- u*=,uo ffry *Poeu r(bc)

tr& 1,oofr,v ?& t>^u Pt q PL

rr.345Lo>clo >o>-olo

G{ | Gr &3 &a &s fis)

'3 f"nl;o;-ad YowuCx t &sGg &a 6rs

_ro

Prt>)

&a;*

D,fu

-/IJ}LSteo 2;*I

Cst I

[+g

b"p A,/1

oL ?*

hs1 e- sf'\.s LG-+--O#L cu > c

&, &t 'C*1 G (r)

*fi. fffi'Lc GIC*y

W A,-vu-

Ge, &g

$p-

toop8

,--r- @

O r(D

"fn crU--. tct r-,-al- J.Gef '

,b,t-)o q.n*on totrctni.lt ,f;

LW-*V* 'V'Rl

loop O

fu"p t"-i- *tPr, = Ca g.l-l

1

Ps-r = Gg Ftg

PBI = Caa Flg

041 = &5 [+g FFg .

S+*f 3:* To

J**P-

w "fA *\

.lp t*aJntauq J,eeP,a *(

Hg

*

Ffrsg. ,--&"tb-ino*ion *t

fu-b &\-a* nar: ?",-ot*rc-bfu- Prz

.dl

t^-d-.,rb f+

-E",divia*r-o.f .lr*P d @[

3 'vu r

ten,-, '@rvt'-ffia *f 'fu;;o ''rl'Dn -

&t+

dg,13e* Angfi* pfpu.c*! G' Js€76T*?

bof @.

'gt chr:o u/u.,n cE- soercl,.-&*q J€6fg

&drv

rb*tjruir,,q(

stef 4 :-

.p*a- $tusb *t W \,.*,Yl-binc uitr,n

\ z+ Cqs- Hr) (a+ r4B) = &*Qr

A + .A,tg.

L[<- Vo.-l"t-tox

"*- rrDn s

HrHg.

-To *trf*,d-

c,r,=L# A+

A=r-Frrerr+%,tP4I 42.

- tq* Hr + &yHr * &a t'+s * Qe F+e qr]

I '-- QzL+, &.yt-|z - &+ I-lJ - Q ;Ue_FI3

El + qs-& r [+r l*+B .

+ &z&+ F.l--; *2As

TO rl;\4^*0

, fVl,olt&

rb*

frE

AK.()

4a *1'O

..,(4) ? **n-

L CA1

& d,e ,)r1AF1 -far.Lt * TY

troel& ?*,q a*).

ou. A'l - AL = I ''^

St*f, 5:-

r'T't-

cforro.nxvefi,A'€- fl e*i"on =-r

ro

I

A

I-

b--...-a,

e!

#J1l{

4,k- ?*

A*-- PK,

L^rP'

I *- 6tz H r F CilA F+z F &a Hg - Glb l'lg- Fl-5

&, &*&g &a Qr + G'rr qs-h46ia

l '.: &-u &t1 br fu l*tr 'F C=t+ l"fg b Gf 6 Fte Hg

= .1.^

"r a5_ P{

/

So L^r-AAn:-

*rhlr ,*l*od*eA)d-pA va,x!- W "aea -"3"k

' *

"u% ry*\ "4

b"N1ct1-

o*€)

ffi

R (s)t

t

A W fto tr 'fia*- o-bsve- ?aia4-

ryYo.-rn-,I

R(3)

R,cs>

'-r I ,/

EtT [:- 'To +"-& $-oru)o'-*rd* fcdJ+- ?o*

f-ura.lt-d- ?* I

FLI"I) r= y, Pr +- ?2i

r r L I 3 Grr + I 5 G{9. 6 e13 't , I I Io ) o |'o ) o ) o ) c\ > C>-> o > oR CS) /\

FoYLuq:ud- PoWv r-r

'

Pr '; Glt ., EL'&gi

tq

'#

Rprrutrr-rd" ?a*+w -9-

PsE4,o&14,

,fr^tu

(Dtd-t

C C s) (tl'r1

C cs)

SLep L:- *Tee

I

LaoD I:-I

e- I g Qt 4 r s"

Pru = r# Glt C-to &g !

bop 9- :-

PLr s*Gt! Qz $4 I

Lcop b '-I S Qy & 6'19 .'t r 8

Pp.! 'E d &e- Qg l-$g .

I-ocp 4:-

*"e*p

,r/\

/

&t- & &s T

Qt 4'-LS &v,&

-Hz.

P4 I *16rlrxa

L-oop U :-l

Po, = - &raHz.

ant-o*<-o-()J ,r-$it'.idr'taLlp*r'*.e-v-[ntt'L'lid.ra4l

?ou-f,ru b2- P,, , Pr, , Pa' , Po'' Prt

'

11 r'-n l-mP'

Bte-p v i- Cnrr-in .1>t+ofuu ,ef, n-on - br-Lcl^t

I

2.-rW),--/-).x-a.\.Y't.otrblu-,crlrnbLxpddao%dbJJo

)* -To C-etlc-,tr'Lo'tz' A AK:-

l- [ S*"n *+ Jcvt* 'r^^d';vi etu"crf

L n ' ' 'aJ J$rlo olL

X c.L-"v fxadrrr}- ..ed- J

LM-on - ,bu* rmgal

IFl- +Plt+ PBI -t P+, t P{

t-'A

El.- Grr Qs- Fle &P- 8s lte '-f q t&+ * & + #g '

= t+ qr&e-&gt& r&e-F+>+&z& gllz*Qr &'++&4llz- '

Suh.:e- , M fM *t trY J: |l''-r,n _ .lotl-chir".1

4

sLaf 4

A.-F+ {L.&rfi %

W

L*,'

[c* r & L&,3)-

* l{.2

d-orcr:a.,t4 *t O +1 @ Ao, At = Az =l '

.S*% 5;- -i-*I

-1,,t*& Txrcmxf** f**cJn#n ;*

ff at<- PK

fult_J*- c&'*

*-t- I| -

<-----d

A [arn t Ae Pill*..

l+qr q1-q B t Qr& r H I + &'L &- 3 FtE- a 8t&1 tG'+ He!

Lfi,&&a{grt

8.

P ;T,*

f { Qr&rqs tq,&q

l+6r,Q- 6g+ Gt y&, F+g * 6tr- Lngt+ 2t & r Q+ + e'lbrL

-/\

O",l.u^a Y tb* T** a'oia'- exannfir

.,tta Wv€-n-!J"& I

Nleyr*fen

jtb

T9 A" W $*uu

&voYw -f" a- -r*?rqe*rn 'fr'eefu *t-qe-br?c-(

wn98nryry*-*:y:o-.n*lo\rm/,nvl.,t-&-r*e

d-orno,ir<, @na/,-#'t" fo"e>t-,"i*3 "& coftt:.ol

eal-r-d--" i^ g - oL^ornai-n '

drrcr3 dever-sper",U /*d I'r ' f'rtaAcn;- -u*rd'-

**-,"u* i"b

-*..',,;-.*.-:i,.-.i;'',l].'"'i'i$,-'.'::n";,4!']*i.is:!';M"n*']"E-*

I n_g* c.;cA)c*3e* *trurxJ- trtou.) &tof>Ja-

Wot-

jU/1*8*

Obtn.-r]ruzA- '

9 A Y f* av'sfr^- -cn'a;A*

dh @ ',r1-,c>t:>l..i-8

bta'.-rlclv 'l

Cor\-yv*ctre-e0-

%\

*jo-nru*La-

&* @oY{C

otiYa-c@j- %

+ E*dn.- .''rLodg--

Aee- loro'nil,uhluJ€*o,-,.-

VM ar4-aL-

',4raO '-fied-LA otck

* Eorc'u bvcrr'u.*t- Ja-x ? ?*

wwts- du}xe:r,&" '}

OJ{L-

oJr'\

y\- lJ:y:orr*r"^fWs'c&- '

j.b ri ;^

\1/1L et,}lu-od^or, 5- X'*t- 'iA Mb'd

ae*t-oto "sYv 'frlte- " u1;^^'n o'^ * #il- noln

eJAry Lfr^L brrs-n&1' '

TurLrnA W *** &rc..ia.lor-

Nodg,'.*

gA dNd-Q-

oJ*r)

41so;

sr{- *ffIBx'a-nch

"-)A

,A

?" J^,V 1 ,u Va-ar-abl

-o

BvancJa- .& di-re-obe-d* J;^4- 'L SrYLe-ftV

f4

% ,fr.,e

dg-,SO ,-l'1&&A - 'T'4-L Mw vM'

' .o -.'-, - o LaL "h,fr.lb d"Aos)JPo '% ry

bvart*1* ;A ;btwitfa-ncL 'i

,fr,,u bVo-nc!+

,-U.'*- G'fr*

--b,r:O nOd-PA 'T*t ofirr r^r1fltfa-n La :*

*vcw*rwL*eno&o ':fg&a)-,n ry

t.rT ,.On-A- vr1'Od'L

,*v c* i

* z-h ;" frl'e- 1v,GJl- bL', Jt CtO.\lQ-

au>r, J\)ekfiZ'o{1'

-DJ|- i'CJf}

fuo*te)I l4-8-

LA**

CSotr-Ytee):- o

=b A'* J-g 6t-7

-v\,.rldL Jd'Lo* r{MJ ortl*4

a- u4-O d,-a-

C,o vnJl-g*cf']ael bvc-nc.4--,:,

IdA

bv@ (A'L")d rr\'ot*-) rrb

oJA

bfrcx-fr ct*- o-}{}t-,otlJ , altt-L 'Pcffi'\;t

ct}(-}r-.O ta) r

(},,fJ12

oF*

J^.AA 'nvt'tt rh@ry+*t_/

brra-nclL '

Cr- r-n.od-Q-jerpb A^na bo*ta- *;' 'Corn*A

?eY,- **

n^od-t- :-

-"\. It-

J;nf t1'od-a*

o%r*Vtub

F4 *xe-L

g A ?o'#L rA

JUr,a* oU}'{ e-cti'on

?*o:-g AY "t'o#L @

v&n$,++4-tlu vYl&d4-.

G- utrave,/- %

.&lT

,g.}6ujd- *yag,l

a-b

u4A4

C,,t4ls€d -pa#& *-

.r -Ode

Fov u)ollcL ?a*tt '**

o

* -T"b dA

*" o*rT D/ p JA-od-Q-

uY\-C.d'Q- vlrl'D-TL W

* CJfis€d uPolH4- M -h aA^& o& "4ournL

trrtr'- ,.ert- =!f ,44-r,dL

qt-ob C-\roSS

Ou "PoefuI

.ffia-b o\Pe-x

&nL.

l**f :-

* Jr,t ?d^L J-oepa

-fndividlaf Joop:- '/1

a-.m-ode-W'pa:*;''*nfuvbqbLvc-u4butl'

fe 3 c'o\- tr d;*Ut *' '\e*Yr-e--

,nad*'

"urt*<n* ay*+&frn @{ '-nJ)ol'o- vrn-ae<-a- Jbl/\-orl oyw'

tffi? ea;,'1

+

Cnoi")

Non -

. -**-r 'o , I r-b vc+L byAncltu gbran'aroi

I* "& \fr'La- 'fttDotrl*-* - T

'#2- "l-o" P '

,-U&

otSQA Jfi-at M av

xa.i.o\- fu b4* rLon *'

wcfir.n-rru,crrv J-ootr fr4-aJv

.,.tpq J-DT*'

-fou-c.}4r*?

ee 4O-r'Yt* \-.n-D+*

Arv Afr,* On-e^ *O:l-ergu o{1&de-

Llrfl+e,oLr.-b *t

q) 'n4-t- btpcX,

,rTAADtr)Yt- itt

Lcs> / ecs)

ot;-a-jro.r' .,etr a- c-L"e{ed- .toop Y . u-n

fu1-L ffiu-^t- Us;t'1 'fl^-c- b{^oc}- '*<t-dueEtar>

,*uex*.;rrr- fr.te- c)-,+spn* w? ttarufst tr^'^"r*t

Stelo l:- sjr-ltu.\ ry ^* f o'u*;-

c5) I

Hr fs)

c cs)'

St€-p A- :- EI

ffil,r* Fee6,tl61.cj<. 'l>ofr"L

rlI

_t

I

II

I

I

H; Cs1

QzCs)

t+@ ccs)

S+*f 5 .'-' Movin-g Sur-

Rf;)

Y ,fr,^L 6{-^t:cj(

C CS)

?o.",-=.? '_/

c3tap 1:- lr1^ba)ic*Llt

(}

blr,&k t $'

P++-4*T:tr #1r-

bJ"@^c,' 'i

l+ rtcs) e$s)

R(s)

Bbef 6 ;- Etilr^-8^atu3"n Feelaark' fail.L- + FePt Foruuzct

{_*r_i rI

I

?-$) rtr-.I

+,

Grz Cs)

i+urCOar&)

l-1

-{ G'Gtl

, q)- CE)

l+.qz{s)Qz(s)

6'tC9,14ttS)

r+urlG) &7

6t:s), Ht CA)

Q"3I ; He- Cs) &rc$Crtr Cs) 6 r-C$) H r ts)

sef L :-

Rfs)

f-

I

I

1_

II

I

c cs)

JJ/

tr(b--^

TyG.-n'sJz-€+4 Funcl=tbnSb"1" 1 .-

c,

Futrrc-Lt-on € _9C*)R Cs)

9!1),e(s)

SzCr)

L+-Hy(s) q 9-Cs)

I+- HsCs) 6,r Cr) t 8, Cs) * Ht Cs)

, t nr,6 hvcs)

L&, cs)+f Cq'c, f

)e,&eCs)t-f'Hs

f.SL& t Ce) plr cs)t*"^;

/

&z Cs)

it-t+rcs) &s- $)+er,, ir:fGtfs)+ t

(erCs)tr ) QvCs)

t+r+zfs) &1 Lcs) t A t ds) Otzcs)

t t-4y{s)

t+r+z1s) &>-ts) + &LLCs) QrvCs)H-r CS)

10.o

Obba-rYr #.\-a- v4fue44d- J-eY' uUr*$r* 1-turo-tion C cs> /*C+

v% eq- tr* -r'gt<s*'e- U-oc-x' Y::

,;urffi f*ib".-t^ri-U'^- W #"ul TY

ldn-V aed-

*t "&,truouPn ;^

c^r A Vo,+ry1 fr"s-

!

Ste* I ;-I

fuq-a*nc)'v ?o 8*a

C cs)

c cs)ftcs;

Shcp L,nI

EL,r-rYufl-cr*-*cil

F€-e.*clb a"*,€1

PaJJ4-

-f"* wry

cca

SLeD 3 :-I

*? rfl.L We PoZ^t Y '#'La- btoeto

C Cs)+Frt&r

S+of 4 :- brvt"b\ni,-? d@e*)r

r-I

I

S+epT.'- EJrryar'*ej dnr- FeeAba;}y PqJJ'r-

I

c c€)

i+ t+ tQzHrGrQS*

t

St"p 6:- Combirrin? S^-0- btDetr^ .in ca-*eDde ar^^d-

e,Lfn4i,uajrt;,rt fr^-e' Fe'e-clba'ol,ru l-

{ +Fl r Q-u* l.l:fr

cs)Rcs;

_t r GngQ:_

l+F+t 4e-+Hz&p-& g

l+HrQaf Hr&r4sr",fl:

S*y a l- ?ols.tqjtuI HoclrA c^-a._L bn \bu* 1ru

G t&2-GL3

I f fttQ2 *{- H g_qr&g* ttf61 t &r_5._:

RCS)

CCs) s

I+ U, Q z+ H2 Az&S+ H1 6t tQzQg

8s &z&s + &a

t 1-- I+- H 1Qe-+F*1 &z&s++l, Gr 18y&3

A t&z-88+ Qq

l+ l-r 1 btz+ Hp-4->W tq tqz&3

HHr & z Hy+ Qzotz + t\4 t h,-Qs + h tSvQZt et +

{ * H tc-t2+ &*:- 9&*+ H t&{ G? z-Q3

&1qs-&s +&+I + +t t &>+ +rz &zers? Fl r &t &te g -t q tqzie r&+

q tq,eGts + qq

I +Hl Qa-f l"l.2QeQ3t [-r14 r&t&3Rcs;

S+e-p 8 ;- Ffi.r"oL *Tv*

'Tr*try

ccqR#)

&t&E-88+ &'a

F*nc-U.on E'

,rnFu-rn c-Abn

C Cs)

R CS)

a Cs)

Recommended