58
)l htht 6W - €. tt-ttuuC 3ol'u&'orrr fu, bs, brct Af frer,R rffq! Drw^t ,-tru et u*,rfi{ T-+ Xt L*v, be, bb = 14r &,* + 8,4 *K1 u1-x) #Bo_ o{a,-nr) df -M ./ .\r r,-r '-*/ , -r}_ _tr_ b*-n i** UNrr - 1.. o a4y"fu ffr*d"e tu ,r*uha,,ia.l F-v q f -c ob-Wul a.,oobff'^ \ wvf f+7 ^*ee.e,. *,r,rl ,.*J, ary.afr6u. J+'- kl ?u" Kp-, ttr) #-) = 6*, r be, +$ r., *bu,- o= b,q, + b*_ + ,,u_ ul*n * hu,_ = M, % r-rn* *Bt* r-Kr (x,-x,) t q2 *. (wr* rtr) ,4 $Lt Lr ", bs.. -, trr *r bev-1 k7la,-fq t2 d" x d_v # = .-oN* ) 7c0 * M, Mpbcp,*n,fr. V ve-torry , dx ff=v , L=Jvdt- # -LB, v, #kr J tu, -vr) M f) ^. + \^

Control System MLM

Embed Size (px)

DESCRIPTION

control

Citation preview

Page 1: Control System MLM

)l htht

6W- €.

tt-ttuuC

3ol'u&'orrr

fu,bs,brct

Af frer,R

rffq!

Drw^t ,-tru

et u*,rfi{

T-+ XtL*v,

be,

bb = 14r &,* + 8,4 *K1 u1-x) #Bo_ o{a,-nr)df -M ./ .\r r,-r '-*/ , -r}_ _tr_

b*-ni**

UNrr - 1.. oa4y"fu ffr*d"e tu ,r*uha,,ia.l

F-v q f -c ob-Wul a.,oobff'^

\ wvf f+7 ^*ee.e,. *,r,rl ,.*J, ary.afr6u.

J+'-kl ?u" Kp-,

ttr)

#-) = 6*, r be, +$ r., *bu,-

o= b,q, + b*_ + ,,u_ ul*n * hu,_

= M, % r-rn* *Bt* r-Kr (x,-x,)

t q2 *. (wr* rtr)

,4 $Lt

Lr ",

bs.. -,trr *rbev-1

k7la,-fqt2

d" x d_v

# = .-oN* )

7c0 * M,

Mpbcp,*n,fr. V ve-torry ,

dxff=v , L=Jvdt-

# -LB, v, #kr J tu, -vr) Mf) ^.

+

\^

Page 2: Control System MLM

E B

o= t'4> M* + xrJrr& f B^ y- q \k,Jftt- v) ,!t +- Br- Lvr-v,) --+@

furcr

"ht

Vo>rahr A+rar-o &ovE Cl<v;

*) = Lu)V) -- rr, Mrr,l-r 5,=RtV, = {2- f4, = L> g>= R2-

8,, = Pr7Lt Rt L-s.-

{<t = '/",kz = ,1r_

Rp-

cz

Ok) = t d.i,w t"f,,;D= L cl"f,,-

k

L(r =lL1

ko-,tL2.

+ (, f,* *i)dt *d; cf,-i) *@

" +; J i>at

Iu"*i,)k+3> tz- ,+)-cl

* e." (ie_- () [email protected] - Cu<enorr,.

#(+> = i u>

V, '+ Vr Mf -olV2- ** uy lnlo , C.

A-l:)t-

- Fl

B-(I

R2_

Br>= -\ -Rrs_

Page 3: Control System MLM

,>

1-.

i ct)

O=

M

% duuw

+ J_v.&I

'= b*' *[u,

o*- y1t &,+d*

Jv,-v*) *Cvo-V,)

+ )_ cv,_v) +I\2 Ll

++fvoW+.ruz_,t Rv

i

+ f J (v, v,) dr

+ #-',

Sotn .Hon,

b*,fi*,bxtba

bs

*{*, + bu, nbu=

g\ d\, f kr,(r*dt

d-Ur * n, ) + Ba 4(x,* x"1&2

&t dt"

Page 4: Control System MLM

tf-.1

flI

i

r-| 9(r-4n,

bn, *-LDK>g

be.-.

Enp

b*"

be"s

Br'3

bes

O, t4, dV,7t

O z t-rl, dU,_M

o> baz * baz0= Ye d'^u

dt_, t B4

t Kzz Cxr- n) +

Pt2-

o= b*, +ba, *Luo tbu-o= Mt d\-

W {kzt lq;e(=) +

+ b*r, F b*,

dtry-x,d,t

+ Bru 9V2-- u) + B.t (V.-u)

l-A

83

o ? l'4s dvsw B*g Cva-v-) .r *ru JUn_rDM +_

EsCvs*\) 4@

*"=* x=Jvok

d_drf

(t, - x,\

+ E,'vt + r, lv,&t t BrLv,-v2) *Becv,*V)>@

+'R,eJe,-u)a*-

Page 5: Control System MLM

Forcz * vo kaye-

bD' 2tt)v,Cl) = r'lVrtD= t"r

ue &) = fs

r A.trL-r -* +

t, af,", +_M

1'{i,JM

Bt= Ri

Be--= ?z_

83 =R3B-E ':> R>3.

Syatrwt:

k,*-1cl

Krg= I

cr7

C=

o=

Oz

Fn* Lttnq.er*f,

u2 ct) __ \r()us(D . V(t)

**$=*t)dt * RrgC,", - t)

hual Pu d.ty,(w+ :

fv1, _ n, / -)A1rrI lq Aa' La/--

M"3 =- Ca

v. Ilr1 - ---:--L1

kr2-3 --

-Lve'

frna* g*nt

M,=L,

frr--- L=

y1e=b

R' 'f' - +;J f a* * R, cd, -r,) + R. ( r', .-i*)

R2 C ia- P,) -tf c,;-,e) df + ?rz]i, - e).

4- Rg Cis -i,) n_

tu )," R2s

Page 6: Control System MLM

\

.,#; + (v,-vr) -o.+ v'; "i J v & "t (v,*u) +JF3

'" *"cW

q clusV

dt

)-o(vr* v,) + *,frn -yO ott + l- ( vn- B) --o

Rzz

i cvs-v) - ;.,rJ,r_

_r,)& +.1.?*3

Cvs - v) -*o

T)L>

0=

o> Ml

6r' +I

d.N t*M, +

L r, +blt

g , d- (r(,-xr) + k CN,* x)-t w* ' -/ t

Mr-

Fr

T2(1 M1

<- ts\

&lwtioyr,"2t1

Page 7: Control System MLM

h*,b,.r -,b,b,

bu,

M"v

6r'

brD - M2

& -)'vdt'- ffi )

0= lk1, db'ffi-

6ft) = t4>

cl'^, Iw* cl, twr- r'Jft

cD

$tD= bpr+[o, rls, nlu , *bo,

K>ct> *ur+ + B1a

*&, co1*-tr),

dt*ro=u ,=JvM'

* Er Cv,--uz) + f' _Lu ,*vo)&t ---+ G)

*e + rr{u, "* +BJ z- + Bt ( v*-y)

rkrlar_v)*__*Foru Vo llage I

0=

ek) =

',* i-R, ci,- t") +{ J,, ,- |,) *

" +; ! ,rff) di- +

* Fz c tz *ir)

Lzd4,oW

Ryl'y

')bt &;-'

Page 8: Control System MLM

0

hrcn c'u'rvp*f t

0= &t

2bt aiu

,t{efrocvvk,

* &, -vr)Fr

+

ri(V, - v,)'-+

Kr

Av,

-&c2

J ru,-v,)b

J-lt-, J

fu"

dv,M

tvat <5", y^ cfrk|'x f, [ut 0.8, e-]n,rol

+ Jr""

v, d*

-v) At

+VL, tRz

P2-

+ 1v\G)

tftp \Cx-rrt'cxble- e k) =

et7 ya*rfabb vr-ct)

Yted = E[s)

v2_(s)

f lf v a'txaXe

7

Treve,ff?\ fi"t^o-kow =-

Page 9: Control System MLM

&ur,rtc,

v1

*ua"r,.4l,rwtaffie.v,,

Fc_ Vs

v,.-v2*

f- 9t

1

v&)

JAI vwc/.z V r,,

et*)Rl

vl---- -{-

Rr

Vs--v t

R2-

)r^*xgr.!-,(

yr o5)+

B1

vt-c) -vrcs)

B"

v>cs>

+ c, *p ---+od*?2_

Af vr.o&.

o

L*plo*

PFt

Y0q)R2

Vr os)

Ec9-6=

P2

t cz_s uz_co ---+6

vs-t

4- c, Av,' .zW_+@

t* eq@

v,(9 - urcs) + Cr s r/r cs) __+@

?z

= Rrf

L

V cs)

+ e:S

vrcs)R.,

v,c)R-

v>(s)

c-s ILLOI -fi_l

V&R2_

Rr .l-Cr.9Vrfd)

Page 10: Control System MLM

P2 I-L

SgV.rr]V" Cg)?/J

?yt

8

- H,'r."€-"[ ry.Rrf uzcr:s-:z

Lsvzcs) zd

-]

*

ve-

tcSV2 I\/>(S

P2-r

a

l%,U<)

37-

P.

9C,

R2_

cs) I_l

\ + orsr,_

vz(9

P,

+ ',n[ P2 krcs) + 2>

,rlru

trP + [.o u,ts) +

[+ vz cD + r--,sa2 v>

,P;c)s.s.q= we

Ecs)

€1+scz v2(0 Bi+ * ,rcs) + 6s C_wtg+-cre yl<g<= + c, ,zc?_urc) Rz_

)lv,H

b cs> +S q vz-cs) pz * ?>v(, +ors(2yz.cs) _ \tgP2tci sva es) f e, S2c, y.rc,s),

vzc 9)

P2r

Page 11: Control System MLM

.4-,/1I

I

i*,!

rR, I R, ur.O * 6c-_urcs) R_i

= - Vz Ls) +CrJ \,;c:.p,

+ r/ u*cQ +pr, S*rt@,

trO{R\ + g* urrEB r * pr2sg vrcoR,#cr 3 vrcs) R,e, #<\ s?_ v_cg B, k..

*c, gcr\G> E"J

&"

Ect =

R, Prlrcs) *! o,

- %_cs) e,

a

ES) :

% cs)

=EG)

RrRz +Sc, f++e & €,,-

Rr { piers- c, Sre,

{o-Rr *Rfut.el

*el%-R'

R2_

f nr(z * Bc-I , RiRr

| #c, st?,, R,

+ PiR.' + Bis.r*, _^;l;c, s'.,. R=&\ l

Page 12: Control System MLM

.9re ADy .974TE r'RRoR

{--l.ghttic qf-'

o

tt)

.9rr+Ttc ERRon

W ayttu ff*:S+ottc 'Q-xter 1gY''stantt

pxttional eeL>h cnalunt

VetodQ cntol ccYrrhr't-)

nlo"% Plas

kp, kn , t(a

9'sS

A **U fiaedhack A.ftanr\

t^ tt"v = .g-> o

&o- = .rT"

01ss A cq

satururyrfuu qi) rffi q *Ao "tr^ rii)Att

acCahrotob aLq.c4 cce"ztan;t

Ald tiii) E1-xtto &t^ &"tf.$trttteh

Cr tg f| Cs) E

at oxY

q Cs) H Cs2

s" c'r tO # cs)

=: +o Cs't--:)

s(s+r) t-v+)@qeft C^D - "ffi^cnt:,.fi

B*A[ l+sr) Bno*

i lp ur"rtln

+o Cs+z)

s (St) ( s*+)C6x6rda, Fl-C s) . I

S ( tf s) t+;(t +o'q5s) s (r+s{r-a"r5g

t ii) Euo,r

v

% plu at o*W

cn $$rcfuL

ei) No"

kP

S+c

Lt

S+o

s (sr) (s++)

40 s( ttzLs)

Irnagu/tack + ,

U

& C9 Hc-e) =4o (z) [r+ o ,q g) Lo [l+o'as)

tt gc c srz)

S (s .r-r) /.e+^ t

Page 13: Control System MLM

ry. rg +o (t+ %,

Ls+,) Cs++)

etryLr_t C+)

kY : ,ll,

ky

=oD

4o (v)[) t+)

=tt-Jto

+a CS+Y),

tso, arl-+)S 4o CS+ r;s (-s+D Cs++)

kL Lt,S+ c

gz +c &+z)

s ( sH) Cs++)t:ls"Pts+r)tsr+;

}rLt= S+c

k^=oLlir; ^\ -

&tror , *@l x+#e ea.Loff

A C rnaSnttudq =4€sj : Vru

+2c

€ss .: g.L

€ss Cs+.p i lr)

f.,, Ar-e irfltt

Wfr x"*,p 7lr

u"tfl, ntctgt t*tutt=Iiffir

=lkq

6)-s.g (p"xatn0-t. i tp)

Page 14: Control System MLM

,(&

rr,a #";H';-r /n ri'd{ftq zta.,d"{ ^+oftL

AApl 'ts l&-ss tR4'h o "l

Soh^.fiPr,

- C,i*, i lf h C9 ' tr6t

shr r-ytac. Trollsp un- % xCtS tr'o tr RC9

RB): LLrlrt =L[r tafl

R t9 = ,,rn L ls'

zALcL 6 3*d,'rndn uC) f's f* W

gCs) E Rfu)

t t&r t!) HCI)

fls't {ls"

o&HA+alr1 hr Tt'ltqu ff*'fu W

a

LDRorl thL ; lP t k) = tt-dt Td..a";^t't

(-- k, ( zs+-,2 --l

L-t " srss*)twoi

[y, n rtt) sfss+,] t t9"

sCrys+r) t ru)? kr (rst9

Qc e^h bQ- **aiwd F"*

S+"

4n'@&Cs)=

[email protected]

epp$ackV

k, (rs+r)

p-ts) =

,dtqt- t-&,tDA

Vot.u'.2 tft.e-Otaom

e$ [tf -;^

6t'^t

Page 15: Control System MLM

(s, = ^ [t-

JJO ^1 , + 6 fstasrrerx:l.') / s f s(as*) C tt-r)k' [vsr.)) s" Lsdssu)(tt)7L L- +x't>s+tl

s (rs rt tt+s) L

s &r.pft.rsh rto+r$ &f"-f -r,-re br-)

_tt.9+ o

€ss = 9+ Vk,

eil€fi -lfiaf e.$ < o'l

o-l = -L

TRz voL* 5 k,."ffr-o /Kv-o-U ,3't1te

;Ao)ild h 'le$

€Jr-'x '\e/'3 ff.at'

fRCI,. &.

O, I

f't

k, = ^/u.,

Page 16: Control System MLM

narnfr- uegr

Errvor StLL(A'.

e{r) = rft) co a rr[b) c I + ""(L) cz +rP ca +-zt 31

r(L) ' rnpu! stn^ol '

co ) Lt>Lz ' r tz;.;.u{ c'e{-6't'cia'^}+ '

cn = lk dq FB).E)o@

F-r"ror cor&tnz'1L :

O ^-o/Q.F(s) :

r+a{s) I-lLs)

s c{rttln^lt-For a clos-[ ]ocp zsist<Nl' 6{9 =.l=. and \i (s) =

Xrr$^o,ttsrd e^Lo{' coe}fdenls o'nd gnd Qr\/Lo{ t*-'Les

F(s) = I

t+ c($tts)

t+_S Suo \StS

i

^i-? )ie/i

II

I

I

I

I

I

I

I

i

II

I

t

I

t

eYrov c oofiy'et urK(9 = lx

S)O l+ J-.S tS

-l

Page 17: Control System MLM

c1 = Jh d- IsrI )s,o #L:#r/ L'-' t-Lsi^fl+ ry= )L (S+roT r )- [s+ s)c r) o+uw^;"t;'c'riovr )r-)oG

= l* S,S)o (s+roJ2

Cq : S = O.O5Ioo

c>-- w &l#)s->D asz I s+to,

cz : )J a_ t:_1ry s-)o Af Es6"-J

S)o L6+,rr,c2 = -l- =-o.ol

loo

Ca = il6 a3 fsrs-lv--l_1s_)o ds3 fs+ro_.1

= t* d /--rD -1S+o ffiLm-lg]

S-> o ks.rr!5ffi

Page 18: Control System MLM

L+)

@

ek) = r[L) !r* ;(L)(o'os) - ry to'or) ';;f,)qo'o*?.,

e[n, o.sY[L )+o'osv(tl €c)'oDsr'b) +o''oo 5. "V

+

A*ae.lEtvot.c"*b&

t

Erffor AAie"

'. Ct = O'OS

C2 = -O'ol

o.s ttL) + o'Ds ;@-o' oos;ft ) +o "';l fO

1r,{)

Ac*.vo|^ww1,tc?+mw}oc,t.3[rudbod<-,.sA\aou}ru

-va tha' Vf u)nalr's +t'tz' *aAP@)'!- t{Uf @ r1^g- J^Z'a

bwP? lp, Cjrtn 44o& cu = o .} oJ-s'o c^!,,)ae +1/.-l^1 ic-,-

+i rnr , '7o^y-r1' rn-a'rrnarinr-u-rru {2aa}'CI\d'Lsh OY A #^B

i:vtw

(s) =

l2tg)t6

SZ+O,VA

1L tb,^K&t\.s'+o.V*tb

.,5 ( 6+ Put

O -

, t, z , I

Page 19: Control System MLM

ct9T, -)? DIL

42+o.82+lbt4+ l6

corvtpttnq*U abov< zqsrch'@ cDiY<'

& con c{ etrdrl Syrcrn zal't'eti on tu"d'j^dan^f; )

uJnLL

6z+2bu+1*0n

,uC r-r'= I b

r"3n = Q <ad /Le c

z&an = 6, B+\6tc

z*Ltb = o .*+t6K

fE = o's+l5kgIo'S = 6't+lbLc

(.-{ -o.g --l6K9.2 /_ V

)b

vf,1So Sulc vt --o.2 t rZ aAl.,.aJ''ot C

UDQ * S-9 = r?e!8)-az+qb+l b

R(L )-- )/' ,tS

&=ffit6

---'1

1r162/qt+le)

A 4 B*+cA 6,zatafrlb

Areat),.trr\L{Eg+Da

Page 20: Control System MLM

ct9T, t6

42+o,tZ+lbL<A+ l6 -Dc o/ytpLun q W a-bov:Q zq*ah'vL c') i +w

& con c{ ordr* Syrcrn eal*p;,i on Ct-v-rd'r'td"'"P*l )

ooLo

Szt2bu+jltln u

,r r'r2= I b

r,3n = Qrad/z'eC

Z&6n = 6-B+\bt{-z*uq = o 's+l6K

fA =e't+lbttgxD'S = 6'k+l6Lc

t-l-O,g--lbr-3.2 -- v

)b

V#1SO SuJo vL -- o.2 t 'Z Qe/'.lJ;o ,.' O

ta e(g)1---

az+-VA+l b

Uceq* cG) =\J --

R(s)-- k&=ffi

tbffi*e = A +ts*+cA 6za-,aflb

A I rzr.rrr r r r-a\+{B8+ O A

Page 21: Control System MLM

Pr* At otb=154.tr;t

e--11r+H1

0=

I1 -'tr'

S

I

3

I

-L.E

II

S

S--S2l,t4/S+ 16

s+2

Ix+ZF+ t/i"*

{?vcot.G r

-- LlJ

*++*+ lu

t L -tJ .fi21s+eF+t/izP

-'fiI, [a+zf +6DL

tg d-?bsJ.,t..tr? t).- t) raVsa(,nO

oa$$'uo'\'ts 4 *'

Qqp.a-h-r' nV eo eff'cr 0^}5 a* S

t{A+c--D

"ffiCN) -6--

cls)

ra-Ll-(#r b-Lt 1n. 'z

-ffi-*'W

Mu,fr

Page 22: Control System MLM

R f S-t tirnz = .I1-g

6d

0 = uan-,f .'fl\E )

= +oo-,c, .r?zo)e = l.oqr

w4 = wnQz= ,, nr[G.rf

? Qro,f6LtO4 = 3,t{6q yd/,"q

z fl -f"OV'l3.\L Ll

I}ss ti,"^a z Q. buc

P{-aJ( U'mo q

-^

w6r r-q-

TIq{Ahz

--f3.q6 q

kp =O,9/\.LL

;Qn/q" ^roo

d-toon/^fffi_

{ffi)

-l

o,r ,/

'/. vP =

x loO

Page 23: Control System MLM

'/ 'v p=

,/,HP

-1.*129L x loo

= )6 /

lrs = j1*Qan

=qfiq1bE = le,uc

Page 24: Control System MLM

QV Apu, Joiy r.F '+ uot+y {rnCba&- ef NLrn t* @t*^lGr rr: ,- v-- M^]"* 3 ol"a T oro,0-

u c,rtstanlt '

Do$a-'t *,*'Pff * bvt ,dilfu" ftaj,'-'' Pt,J\'''r td ae-

{uxrr+i ?v[}r; +}?fl} @v #€rrl [o*pa-,a ;;' -fu*

ffi^Ytl'--lls,l,) .

&,Lrd{eor.

oWpAWr"F = r1c9 F[cs)'Il+& cs;l ttcf

k/,0

tt +rrst'*- K

s(t+rs,s(r+T9+(

C*.pe? ru-tft

sxda d"s"d !"tr

'Ifi.q v a.bn D6

2$rD6

q

,k (k 1r)osrry [email protected] &^^ % Sac€rd

,&Ll,slat,- u)^ou D*+, $D,ft o^1

'b-r-Y xo*- s,

NoLD #A 1s ,1 %

lQnt r,*

nzOn' = kl, u\ . J-+rl

"T: -_l = l{F

zr t}n zfJn-i

=li z_m

f"rr ( rnax-iynuvn p-k eL,o gh"rt Vcckn)

,-- ^*rtgffi" _rz*.

Page 25: Control System MLM

@

ry: 1ry/ s lt[0o

1ry = too €*$ $|fi:A'

o'1t = t'l E lJG6L

{-akir\q h 614 l'dtff '&AwJ

/^ Co'1s) = -rr 6 l-[ t*"o.2BJ6 r lt$

oh wt) ffr"

?

€" = B" 3to3rX to*3

€*T4,f_il T, "

btft a :C.za

=. *n6,1JG,"TI ,< Yt-

My

ahd Sa np 2_6 ,/.

@=) o.25- =

t"k^? Lj., sh

{h C t,rE)

l' gk6s

(o'oBv1D(r-€):n'+' .'.Tsj.rfB. as -{ to-3 C r -6) = €r'

q = o"otil

t -f,'.&ru.a-Lth? oor lrcttfr

Page 26: Control System MLM

,A"^\3

C ta) l^* 0( vwat W

2p nn^ +-t tl-. ' /

o. AeEtryr;+ :

sa h+R ,si{u

c r - €,")a4Lt:

Yr

= TT' E,'

o.lAeq

7s/ t" 2s /" a,

tb o.+o37 *$,

-+@

t/ s-f\r

l, 9zt8

9'+o3'l

t t Cha^ffl,V firor""

r",,xf bL ,*Y f" o' oq t/

f-"^A Aa% g

@1o

4: D.oqtl

g,ogil 6

% O ar'd@

p'QP5-6ff+ -:

hlou-, E. I LTu Waau')2Jkr

p.4a\t =*!- +o

t';FVr-R,

g'05Pq 2 = -ErR.

h",il*VL?r4 \ D.osofatW

k1-R-

- . h r.A6 ,fl ^L

Page 27: Control System MLM

/^ll

B clr PLoT

rYw oWfi woP tra,ra'tor1 +uhcti on

+wdbau s Ys 4axn is hc s t :

sTop " I

^yz\--^--',1

0* &; _\

S(S+r) (s'+zs+E)

s cg+t) Cs"+>s+S)

fscS+r) F (4 *

I

s c 9+)) ( o''tsz + }'Jrs+' )

tnc)ur)

I

wu+a

UM Wdo Plo*U to +tytd lnun pha-ya mMqin Lwrc)fi/d w|c.(i,',1 How slrr,o uLd bz +ylo Awfi adlw+ 'th

ro d {iri) Bou swu}c w w hun adaw so *ha+

w Lqc : 1 .z -vq[l ) wc Gv; hot't'r shl uA be ihe 0 tun

qdJLtB+ so ;rha* phqw YYqAqin ln 4sde

Cn cs) :

102--> -L

-

\5 r)

Cr\r g)

)w c )tr + r2 ( o' zw2 +0.4 tut +t)

Page 28: Control System MLM

w

ste? I g€-.-Z't_-/

\+{ rd TYM

It-

r+ju/

._0.2 w> +0,&jctu+ I

l-l4,

I

2 ,23

[.u n'

tUn

ltln

=6; \f5'

r Q-A?

_l__j tt,

I

4acb"{ wYYrM +vq

t+jru

t

slowloWr

8D

&,93 - )1 o

* o.ttti +aq)w+ I

I h z'zg

4a,titc t w) \ 4w-l

r'qgl \'Z

lCrtiur) = -1a

Page 29: Control System MLM

tc\ \ Cr.dooF"(poI(so,. l"-;

e=

-a'(SC\

,\]

IN

t(-

^\ \l

)\

'c)"bP

oa\

0u

I

^*\l

('.-'s_oru

o-s&GOc)pCI-fp6Rec)o$'}\',,

Page 30: Control System MLM

Ad

-Detgc.ni"tCpt &Cs) =

.t?La open ,bopdoo ( s +ro)s (s+sXsrpo)nnaxgin .

t*c,anefrH

Co.\ctUa+efru-rnlrov^r

&in o.qy,il

eod '^A Is-*,"ILto J$h+']

c-lrt I .e

"_\ *

r.-9_+t\o

3Es4I

.\o : &o L",t s *[sIc'Q s+ U F'uss+f

Sxe-qponu1,Step E \' T'c, S\\cd Cpsr^vralt

Fac*or

__]-J\^)

I

o-\tU+t

o- t3w* 1

I

&s

O'\g+\ r -f-- =\D : t.,trCIo.&g+l j o t

-5 : Ll)C1'o.& J

O'O5S+l r -1 s&O:r_roC1,o'D5

9orFn s\op Pxeq"rcr'uy

-&D

-&o - )-tCI

o to 5.

5 to \s

"-&o ;' rDlp JC\o

-3s -ho ) 5 r"r.

Page 31: Control System MLM

\-t

C

t

-x-

.,

t^_L { s ( C i l;!"'- - :: :" "t.

{-*r : ",-" .::.'" .. --;.r- : .'... ..--.i.- ..:.-.::i I r: r.:.-:j. , i.,:r-.::::...,, r,ir.:i::.:-.:.t :

1,":,'::t;,!::ll,',t. t. ,i,'i.,iiiiali,;t',i ',r:';;;:i:;,,1: i''i;;: ..a,,',.,f'a .i i:i1il,:'ii'ii:+.tu,.i,,,;,ili];,:,:,i,;,'i:il,'',,l'i' i,,'" .,;. ,rll.l.1;,,,,1 l::;i 4t:i..,. ,-:i-":::::-.!,-l;i:'a:::::i.::.j.,.,...:r:.3;1,,.,,r.,,,, .. .-,' I

,::i::lr,i .:._ a.., 1,.t, rr -r:_.!rrrr-;i.::: i,,.:a :

u!.-..:. 1.:.:.,.1I t i.,..; ,

.... rl trr:.

.i-.i...; . , g

,i1j:rffi-ffi. _ ..... .t i ... _;:_i.. _ . l. _,.,,_ ..,, .. .rlr ;, i: li

,,.t'.. a- | '): ; :r::::ar1:i : i-:i:ji:n;:;ia:r::1.:;::.i:r'i r: I . irir,l:r+

li:"t cc;*r.i!.f.y: ;t , i I I I I :':'i..i--r-l i 1':':''i-i'; l

.ft.i}lft}i",,1:i:,';;t-,,i;''';;11',.i,l';,+

' t' "

,.'' ': r - I

' ' r F,*-u' ". "'. rt .., r t

'" ',,-

:.- ,,.'r'." " ':'t. .-'-,...tl::'--- , I '

' ,.-' .- : ' '',, '"

-" . i t -

'.",...'. ".t-: -,r, .r: .. ! "'

,:::::, rr;::$l:r:r:::riirri: I I :;l;r:i:::::,:i

'-::::-l;: I :.:::-:: i :':li::l-::ir:';l:r ::,1*:l:ir-:i :,:,.i::;;t:ttt:!.:-i i i:i+

,t.1: ' - | .t.., r.,r.r. ].., :. ; l. --._ . ..:-:,r,".i"-i i ' .....-r--.+..... :

. .i ........1.;. ..i..., ;

4,: -.;,,';:l;lii=r,i,{;# :#, ii:i:,;,, -tXffi.

.*.",i_ '..ii=tii r.i:j-'j:j.ijii=,*ril5;ii#'lr.: /, ,' nl , i

'i l, .,.;i.l.,1l''i_;{il .'':.:tlri'."'i ;".i,,t:,t-':,',,,'.}:;":i :: y':il:,,,-

,-iE,i# , .l - i"l:,.1" ];rjffil'- rffi ,ii. i =:;*ffi

i"t::;tq1'"1,.1, ;'.'.i .t'i';,i, .-.i"i-'_ji,r'il', i; .,:i.,,,il,:',,'lli--lil';,, rl. : ffil' .

.,.,,,',:" y". i i-11f,,; l;i'...l.., .'..1 ., i, $'::,:;rr.

.,,f'j'r,..i:..:.,,

':), ",,,',,,,.: :.' l.;;.ji''*i:irffii',i'',,''j.'-.i:, .i.1:tii*t-*"-ft'*-ffiffi' -:;i;',

;,,;:, j -, ffi['tj-i';:,';;,1,........,...'

-=. - ', ,,{, i'/*ffilr l:: rri,::: . I :I lr::i:::i : i i,

i,,,1ii$",,,1lt..,:ri,,rri 1{,|:.###In'" : :-1 .

. , : I . -""'. i Irlti::r:':i' : i - - ,:'.:r:: ,r..i 1,,,,:..,.r:r:rr,.. .,..J.1,.r1..=,.r,. -.:-J..*t-.;'l..

fllllii'i ,', / * ,,; tI/ , ""/.t,f I ' 'l\, .

/ .: .r,,, / 1 ',#r': \ .,i

;:' jllF iif.iffi ll$f:ti{.}iffi

-il,r ;l'1;r.r,gl*,tffi ffi *, i

.:[,.i'.-'::', ,,ii'-1--1"'--;+-',"f i;l -:;-1,"]- ' .

-l

Page 32: Control System MLM

hu,"me{ot aun8ty FB W*&t$=- la-

s(t+o 2qt t+D.os)

d,*exni-ne vairJl- ob1<-, so *bct &/^D:

Pn = 6c .

A^) GrtT*) = K

Jo Cr{ ".&j*D (r+ o . osi'c)

lcntPrrlJ = h= \

(^r fc,-r o' a *) V;;;"=)r= )

Laci"D = -to- tq_",rfo.&uD _ta;,( o,osrr.,)L^) o.I

Cn tj* q' qI9tj*D -et,^(

o'st'qB--9.1 , I

t

o.c1

*|D4. I

b

o,[3-l{g.rr

l,o

g'04

-180

1F,

lSdB g-

b

o'LDL

-lb t,B

Io-ol-, 6s

PotJAR PLoj

M&g a-

Starh

Page 33: Control System MLM

,,. :. '.ii'.'-'.,1,1t'.

"'i1'rt t,;-..,".'.'i,", "...,,.t,,

('{

.*l

tl

r-\\J!

:HL-JJ

r:: .ii;,'.:a,.1

i.l''.. :r. r,'l

.. r.."' .. t.

;, -:' '

' ' ..'r..t '-i

Page 34: Control System MLM

a/ Tt* o?tn

$ivtn ty

bor

(xtn) =

CaS lcrncA

"k Sarn

ur";q *lA

/-rt" Po h'

b4attin

s/,n a

P/o/ +

-|rax* 4esz 4r*,

1

-sCc+s)C r+ as)

?\o>e- 1r,1ary[irrtD"bminp- -l+.-

C, cs>

ICrci*rl ] =

t-s C r-rs) ( t+ zs)

I

jr( r+j w)1 t+ &iw)

I

w{@,firtaJS"

'l^;' Lw)- +J tca'^';-Qo/ht,ia) =

(^) O' l

f ati,-,tll n '1s

lhtiw) - toJ

s.3s

2-L

-lqtr

o- h

l-s

* tso"4

o.Lt s

t. S

-ts4,q

o.S| "e-

-ILL

o.-1 I t-b

o 'bL o'3

*(8o -119

o.L

o^l

-tT I

r-l--- sa 0. tJn

K3

ry)n de :&o

" Q.1

I = t8o "f-Q 3.z l8o* lbg

t r)O

bg tr'\)

Page 35: Control System MLM

35(Pto

;i

24tr12G

ffi uoo< r-ocx ,'i!

Page 36: Control System MLM

3-q

3

5q?

*.>

LS

3\3

>

\

L+

1

tz-)

Cr*w;l

e; + €&+-zs tL-\ =o

? --7

eLF

2-\

Bt

1

D11

-{Dt;o

el\ 1 2fP-g<e

J:B

L---L

A'V .'7q

2_3+-l

=25

A=

-nnC)' S

A\\

P9,

+€2-

a\\

d.-I-e-

1

-\ea-

4'1D

-:aC)uD ,: | --rrtz"O-:zr:k+_s <-*Q: Q.YOe \--

= --tsL---rr-'o- ^9<s--

*-w%-t

\

I

D

9t^- tS^o-

^zaoc-D

T},-rfq' - zx-r<eaq-3 ?-e, Q..,^\

o-a "v^r-?

. €L&L->

3+ \ :D

= =-\

"l.e-e-

Page 37: Control System MLM

@ { + E$=t.r- q3E +-sqi qi+ z-oj- +4es f B(-c-.-

-:7=iaLr3L

.s6E3>o3c

55 1"2 o zzL

c-r a, O 3'GS"

sDoS

Ae,q =,k _O

La

-\ 4l* O

-='! A,\\ "-re-.Q- -xc,o\g

\J-L,.* A= =S'

dn =- 3b<a{g

'Z- @

S* '.rc'Lc\ \5 <1 \ \ Z-^aq:rr

2-

=l--Sl =:69

3 =-oA\\ ---ra.Q *roatg

eA". r roq&cJs

Page 38: Control System MLM

f

-2.> -\(,oc-,-.

A€,, lr=B

Arr

,4./\

dqJ--b

\\

I3"S

=, Y. zgt=s3 3L

* rD I

=t 'z-rl

3- 'zr t

A * ,-,*J-4o'-- - z-la 1c1=

S '-t<grt:D

2r.b3 zO

€, lC>

:6oo{-J

<>\-\ \ 'Z-A9.\_D -'rr-\S utr\

3.t-\ro rO

G<s-L-l_-..

e .- a-- I \ ZoPt-o -<c .-0\>'2_

- --e\

2_3>:s

'<e-rS*-

o\->

=-\

Al 1 "fqa-

:[W\

L:-- €a

/1I'D6tre"=qr

o1-3

o.9.-q- *v0.-.-.-\\ '1€.q

t-E-.-

-<oo t8

p--.O .-..;,or=t-*

>-\ LS

r 2- t.!

CD-

=;+F<-

% s -Ftqy\q

Page 39: Control System MLM

eD Ju- =4' nzr-^e +zq$o=.rJ

oou

.5t1

t..r>n-=Gfrq's--

bou-:a9cl+

- * Bkx-rzrq-'--\

- S.-tB -1<

-. AY 15-\a'a '

-a^>Qt

[email protected] ag<9- -. ve- e!.ov,"€infcS f'..'.-

=r-*\G' * a{-<Y-q '' fu Sqs{e'rn 'tS

_b5

St-t

B3z-

3I

So

5

i

zt"z3

15

2-t^

>-J-<

>1.7'>

\4"21

'2-L-l

2-1-<

ll"B3

l5

yz<a* I >-3s+ lS -=-o

2-3

r'E

x,c,otg or9g

-f^oS$ "-b-!t,-*Fd

+s'\-e.-

\e..-r--

Gc_--1-

t<,-_e_

tQ-e--iL

---E: L<\ V\}.-\)

Page 40: Control System MLM

!

i

- E L{ ^Z } -4a\ -rD=c

,=-Ca\G

, =t

.-D '-\ .-r'o

r -3 €.6s -tu-S3, n'L _L?"Lj --l c>

j-

I

r 1 -\b,=Ib;=:

I a -yCI

, 33-rn-cs- f-C's>:>^-g- <,'9'c-<-- *-\je- e-Lo-v^'^o--lz'-L< Tr'r

. 4i- za +e-4- P--"-^ffl a'9^-9'a-3'i-a :fg>Lr} "b !

It*o- , ^ ^ 'r,9, L^-"'g6-LlQa- A"- {-&\9-

Page 41: Control System MLM

or

..S+^lt U{fr^"t(t <1'J";1'frl C''k^ion' ^ *..i(F

T+ -tt'u^ C"cC n O co'*o*- * *o G tJ) tt c-r) 7\a^a-

ce.rrex po. tS +. N,J 1 ^'e+ bn{t* h^ +1^' : P t^^u

an^c'wul'u +Ltp- p ov'r b - l\i0 wt -Y^a w^+^c"!"'l's^/tse*

"ke&,"n a^ *^Ku'*-*#k:;:f ,Y( pW^z Y'obs t+ 6cl)lf cJ) t t "-

S yx *<-*.,-t n g^La' o , t e,4wt1 w Lnota o-L.If--

u ' L4 Jr

t | \qx|

;:ffi#i,*'uisr l':::T"l*"y + kt'" 4Ls

,,r+qf 'YCtl S+oLlrCo-"

Sr<p I

soki Q,v'#'a x i3t^|

, -io ;" :rvYt*-st-,?:: -;{ + sP \a'^"P-

s+I Jc*'^ I

tto ni

- -.\wlS -J' . \

Gt \C\\(r w,'

Gt$ r+cs) P\a-,

g.es)c

E p\ a.'nl-

CI g1"' lda- J-.r

;.t *,'lP;-"-t^o; f,,

t- 1 31e"'{-t alfuci;DH(i0' T,d""':'1;'- * *@ , ^- J^ - q0

atttL,U=O

u,t/ = M

or- PoW

S Pl an-"a'----L-----x..^l

W': O

Page 42: Control System MLM

To $*& \^^ooh t P1- "Jr"r@l qxis

O. CSK

j. + o . o.i3* 3+ q.6 j2-Lw

0.0s)(Gqto*(lQ.l* C l+ o r.irt +o.bde

o. osx--- -L . / l-o-nt,1FD- O'bd *,1W u I - t-,t' vs' t r---

,

p..*t-

$w

:oCt

| *- o'Q,-l-d=+ o. oS

)-s u,)

-2

u"lp,*d q vc*o, Ca'. \FPO

La *) S<^.^i c-,*"1"- i"n s P la"a

GsD s---r"^ .$Y,\

\A) - [rtortv

\^^ , "ol ,

-----s p ta,','t

i.SC\es-

o,

-otor,r$e0,: 4, ttl a r*l sq' -

- o. os-)a

o.b C4. q r){O. oo 4tr K

w',"}d" R-

R nJ*

.>/\2.

'.' R +,GqHc} z

to-\D 3 sTb-ost( X

-gC\+t-ttClto't$lt| R.nds

R->no

R-:9->

I

l

c"'€'S\(-<1* (tnxOS \)y

:\O J q [a^ I

No ^ - l^nno

=\o '; 6,,)HCo'ffr* nlq*,

er l:.5% ,

C1

o oJ,,n't n

p\^at- %{-\

JL e-ss)(o'ts)

Page 43: Control System MLM

-nY':,T/r

-'".--vJ;{€,."$yg argL "* 6re)r+a) P fu""t-

Ca" &l^i r\ {t r \ L'l

--:\

-)1

-I8o

6i1s;HtD -qp|z{irror

q

----'.--/

Seor{-,on C1

t't *f ptit Cr Ctr ( ->

n' [l-sr> r' t '

- j9' fl.->oKO r\ w IPlo*"n-'

Page 44: Control System MLM

}t+ q^^6-L:

<+..-\.1- "* - .*qolop n -Fva a""fu -,.s Pta^4- %r$*c\)

L-:vr-__h. -:) f

j[ - Tr.-1-

C/" uh witz

p b"a'

q or^ d. ._l 1_do ' -ilngo-

r^ro poto^ @ xrgrl'[^

-' . .-11^q- .J \4 l'^,' ;

Cur a*c-'"c-{"---l}' or--j' U

\ lA/r \

610r.+&)- Pis4

rL L A\g t

-

Ps;+ V>&*ez^,\i ' l Voxe A{. e

fo -. O L-S.

\c )&tr o

-Tw., T n 'A-)

d^"u.*.n.

=or[*'on k->o to'Jr"Jc+

\Aa o.,. i{ *

t-a,^,tyZ r V _'l >&4O,J o,ao 4t1lL=-f l ?- 6'oo\l I/

fil.C- C or,h\^ r t'^rs SSq'L *e'J- ^ktr "l> a-

t"*4\r1ro SrrnCriv CJLh,,F

6l -e P Lq^^^{

Page 45: Control System MLM

bf i'l"c)*u) -{trablLI

fonr'tr.^ot

to[{?q.a oF"-lhe- Nrdl rial-

l*F Mnrtn'k (l+<)1-

sE- ' +{;d

H,o+ fot o.' ./t rc+"h"

+hs. Ro^!.

.Ooyn--r{t/5 t*o$ k ts'

6rls)u+l)= k(r+s)-*@-l€* J'd-

cnt'-) *fuo ) =

M?elcr d*)

phanc *fi

"r"l :

KCr+6.-)'q-)3- -*rt

k ( r+,o')--tr: +O: :-b,it(..o) -:-to'

o.^d* o.E *-ZQ

t

Su^b

- Tlo

a"dtu}2urlo rn O

t&t*r$rd^D)(= I(D_ .>

C r Sa c ,f,.srr io Cn(c) or*3 h\o*

dt

(Farrf& "^f c0: o(l

r^e=Do io Olof"r$-)l=

' . C1 secahhn in 6nl9) $tr)

9ub hgro io @

= z+a;' (o) - 2-t o' lgub Uc ro0 ir @

--x---o[ ro>o in

b(s) r r^[S)

> z+*J @) - 21ot

Aoa^rn^-f-t5\ r-^' ^ r ,

*fro'

2-(qo' ) 'z1o'

l ro -17o :

t(fik D "V-)

U"FF,y l*11c,-,ffiIo$ G"fth" c1,C1 SlarnB a.F q .^, = o

l+to* V(tucl

k(r.tx)

-Qo'

Page 46: Control System MLM

C'roarirp ftqb +" "f

&t-^, ) $Vto) =

a*otgcrx

mn*.h\ 7lk ( tt uc)a

: k (^ r-.ot)

a4 teol anig .

k ( t-t($.o)'-"?',")

-d'o'uDg

= r<L-,,i* A^-^,]

LbtD--d

-(\,-L< (r-"rl) Ktzr-T- uF:* *i l<(r-u:z)r,cE ( @-

4v^h\-f Ee-'.l PtY F.*+C*fr Po'r* :- Q

' F<. [t- q')

u)3A€-^t Dor{-' r --28,

t,>t

-.)-lo---.--

t)'

:o

=(@

_2L

-

lL

=) k(r-*')=ol-tDt = o

-tJD : -'LD3 I val )we

-2hL> corl*if h\- .

G lg utrl j\a"*

(-

Page 47: Control System MLM

Ilaplirp o{ 3,p n4tiro (z

Rri"2(t^b

8+

fumi 0"-0s in ffb* orrhlo

!, l''- Pe t

?+d,

h ,-je---oL

-i9= O'9 \l

t^,t _ B: _Tf_ ,-_1

A19r'rfg) = o.;J"/:-

in 'J*lo- ton''., J R.jo

R+ l-.,".0,rs

0 + fr.o .. o*h,(r+<r)x rq-

= {< sz 6 K--- --g3 a

L '''b*& fl) rns) =

P) o<)

k(r+sf--- gt

?)-- =

l,; (t {eAear - 'z '

c\ t t) ld-r!)

11>l^c" g=f,"c^lt) t-;ls) : .- j ql-

Tt^a Puo*-" [l o TU a (*arr{-tt1 @ l&'rpaFtU a.*Pt{

: -flr-fll- = {(^^tki9* dlt+ anL. '^ -ve. (SSk*"9t d$f a*tt,'o +ua I cl.ac-,'or, :

"0*. t ^)

k^t;" qs,ofrM"Sr*p

)

Page 48: Control System MLM

M"&'tt(ub

4 ga;,lc't c'ty .

<, I rin Per'la('n

2K

LF

€-+o@e{o)s

fi= -{Tl- ) &r>rw{l)*,

$: $lo- , &\u) rls) :o.Tk

o.{

0( --

dD,{t

ol\L^dh*,^ b

rOto^ 9= /ro..nt

e *d,* o i-

V r hl. a.rpk

& +o lt, -9Pla'e

[ +s'i Fs I

-R- fi Cin)'gto

S- 1"-^"!ll

q u\-ao{

d eai3slz--is{h-

e-u

or*PU

6nl, z @ zr--.

.'. clp,ckr/D (,<4 &*"r*

{*---

Page 49: Control System MLM

C,.tg tttO do*9e,e3 eaVSe-e t Aeav

dtaUit\ CInal6'ir

tt rsi^^l \t^U,,." 4 [ '

-rf = -lKrtlz: o'5

Cgtz',1 y o,Dg"t E= o"2 - )-Qo.y) =

=-o.f-iz{^?

.l

rh c*t$turptar< ,'

d)v2 ,z

- "Lt > -o.q

-o.h

Page 50: Control System MLM

lle-,rc, +t." P\- *l kA on -tt^" G.{$ Jrdt o((.vorairp pb

He-r- cq .tilpr* t 5 & c0ouo ro rr-e er..d,.r,0.grr^on!

% k7D"5g% k-l

- XV{ flt-A tr): -i[, zD

; ar6t % amr.^.d - + eo€- Lt*o\^r- dnet cotla. ar'd o/v\z 4x dtcLge *

'a€-

Q-lroi r.0.q-*o ^

L

-t-if ,,o'tt0 Co.',*[ o,^-l gogh stE**[l.e-^q '+t^" ilro rb gtqHg ,,>Lao V.i o,5

Page 51: Control System MLM

s "C tfrxtrrs)&fforqd*) :

'* r,fo

I G,w,) rttdb;, :*'ffi;t

tt'lo )

ue \)p.*r-\@b+a)Fb-) : -Jc"^-r (+,o; _{anr ,*)

-nh' j pla,*lor

--+qJ'(**) - tB.,

&, c^lr)tHr) : t+lts

Lg

2-b

l{a{fuit *t &4 h"D c I

ott u)>ola.6.l*Y-)lh h") t+t+"e) *l gp'

a-t- uc > ,o

{tt*,trt.-) | z ohtdr)krt/*e) = -2To,

= (+r*ro

-z oL

=

q'

t\ao-lr\r'

qb *--;d (Tor,'i P\b'F)

ul{.")*tf4 = J}tr)10

-Qo'

(O*,)'C 116*) ( r+:6.o)t+ c+da.o

d'*'( r+3e -r*y

Page 52: Control System MLM

&*o

G*q- -")-a4-*3

ttrl+ +6'o

- ,^)o -a6-3+r*]

f"# |b Tr-Yo

(a*L *)* d*3C "zuo9 -,^>t) * rd.--

r

O-"d""X( { oe- ^o) *-rd^o3)

ClD'f - *')-- C3*=)-Ltoe- *to =d-3 r +6io (a,.t-,^*): 12 uott

CI -*- t.oo) --.(A *3)-2pY- ut 9o5 .oB- at,,'$ aza*

(?*L",j)2{g"t)=4*k'r lrrro

sF"*.t tb Ze-xt

t t rs t3.',>3- *'os z o&tlS -ro9= o

f trr5 = tD3

u) ^= {/ fLl

Lt.> ' o.tzSwz \ffi z os53,

g..^b uD ,- o €53"tn To **\ P"r+.\

2,D$-v*-12-tf - rouoY-,o L

1|ot-rDo)' *43*>1tqr.*!' *

7 -ln.L'J

*.r-,"">'*S3)-cO -Zc>?'r- c^.hro \,aQ a-h^.

Page 53: Control System MLM

Maft,i'1 4 Aodtso qs ( M\.c"rcnr iroa'6'a- "f q)

M"[t,nt od 6".'|.in (2.

(,^lgfill): 2

("b Sr [}PaNIt-sT

As

i&Aes

C, rf,

h3---4zs9

=2--<g'r-i zo

D. e u.r-- l-

=-ffi =t t- Res-P-ail i :.i

a> \^n*,s fco"rn la{- 'b -Tl -- -j B.irl-*d,n 9,6)- t^ls) Hr) : 0' i.ot,

&r.ijJ> Ltt)u[) : o' Q- -

S+onrhr1 S'{(a = -?rT1,-

t^&*f S^de = {')-Cr"^^tl *Tt -Bfl-- 3(r1 L= -3'lT

s z (s) Crt)

.- rn&c-,-f^ E^ dr"t'or * L'o' dr-tb7^

Page 54: Control System MLM

I-taftirp '6t= tF

RoI +g,T Es

&\s1 kils) :

Src-e Lq ,

e*joI

I 2 d u- -ju'

3a Cr) ( r)

: -ri]2- at!) rts) : d Jdt=r4z- aloffti)= d dtrr

htg :nh6b, {

a. ,.p [a : 'ii - ( -'ii)\ =ff

41litlit--L'-<

-Qo' 6 rO \+ CS) plol'C''

I(}

S+.*+T2.4,

"1

0-r^r*"9

Qo' ctoxr,r";

LT" REiD&ao

crl $nmr -fl1, t" iTt*- 1"^J 'V*r"aw\.-o n

A'tt-

Page 55: Control System MLM

@Jn,*- s

D*rz 6*unU lil,/ o^l-0

&"'$oLIoA, i,l.d : ,+ .!ri^tn*

aLwvaAtl,+#.

s6<+{^n4 ,/ 4*;L b L8-

-++NNe qr<it{" a/,.1 ilP v'Jn'

+-0\L lyV*,t #.,- 6;+'*L

dr.rr"oA i+--/:r x t &p) r^ N

b olp <qn

:l c -f I ,1 "C{

U Co,vf bbh

+ 41rs- o fes

',^^-]<NvJ b"1A4f

{-l...& x (t-)

A ,lnwo* );rrvta ,*, ^t

q,-1.r' aA--b sfl*P'w) ; C'!"^-"'l*;"t

,f +1^s-3'f*-.6 vanri ^lJs' WAt-('1" b'^'*'*b on

t4r@- Gnlro/Jal;l;:1 a-e Ob*nua'l"l'l'd * +<;*'fh

t ii]= [: '] L:1" I I w'lsd^''l-eqn

MPW Cor*- tbJ.r-a- E'()

trrl f\ wh^y,(^ *o,^tl.^s+".h :tr-tQ ft +-@

;[^t'1*- brwta- '

o bse-'rJ;1.fu:A .0 N-* s'6s14'"-l

ObSe^rabta- a+ +1^e- h'**.LoJf

Y o,^d. i fns oVerr a- #"ik-

"^$* 'f o A"/-c' *'iv'z- **d

ytD: [t lL;]A=L: I "-f

G**'stls|i/,fi |'4ri*" 21 &c

pB z f-t I l,:= L:-l*l

Page 56: Control System MLM

la.\ :Y",-l-

f [],['. 'n

o -'- "\d^*6l- in.q*d x

&" L z-.

Uo"rf.'d- Xtl--

A-L No + s{a

-Tf^e^ Siven "fl{-t"-.'

Obs*.r11/^ &z Ata'*.' n W,"

().: f .ilL-

-'-J

<- Va"'' ille- '

; 'r^6? c*v\tfd'h to}-'(ekt'

il

I*l : l-+ |il : -e-- ruo* "1"o1

+o o

-o 'Tt * Y*^^L+ fu= h =2

-'. *t-.a *tt^-- *Y* ; u"^74 0l'su'n^1"t"'

Cl^"& l{^q- con*'ot/'A'/'t c:1- +1'@ l"tltw';"y c-l*b sPqa.-

s6t+-"-r " \ .. *, - =-:

" * xz- -5*J ++tr "ltt

ir= k-fir- io=Lz xt! *C

ovJs- 6+ *ff*--:

CA : L' .IEt- u

3

Itl{i il0

Page 57: Control System MLM

@i

2-Aa'. AaJ

1l ^=[l ]rta*.,'rc a"-.[n ;

Ot*zJ

.- a.[D t

lo oL-t - 2-

Gn*-o Uo,U;l;tr

I,lI

I o , o) c o

L u'-l f L;

I? IL-. -f

:.1 ]*lLl. e o D ILs ;';f

= f : o 'lco-L o

-; iJl-i:- e ' ,_lI'L;f

olooro o 1 I -3

t I -3-3 1

rlg :

A'

.h,-

Pa

Page 58: Control System MLM

L*6x1

Acs

IVA/,re. vualn' a

YVo,, rr* -(l,^.A Iq

:ao o, tl-

o, -3 ;J

b

:

{mcc- SyS+vrn,

"' ,lt 8:- f 'l't -r-l LoJ-_J

n=L

71^e- dr* sd€+t,"" ; lor#o UsA LL '

ob+o- -H^e- l'^*'k* +"*'nAon Y'l"Jtul

q"k

Ia,fl=p^*-Loy Acs

fcr)

SIL -F

-, + te

5.

c=ft { P:C"l

: cC(L-")tB+D'

].ru"[{

s+"s

= .[:f -[-". I'- e E -t=l

ttr -,)-r : \ I -;1 -, rl

s clr.O | 6 \* -b ")rcr):.i,*r[r ;[I= it:

: =\ [e +s D[',1€ $*.*t \ " I

n t fnrs]-ffi:

Jn' it,t- ltb*'Y