~ to.) ~t. d~sttdbCUl\ca. eVt+~ ~ pro!Q..S.s Ilia.. itt. 1'\0\f)-MMipLtlcU~~ s+r{!QMI\ j thus fpy- {~w~ corrfro-L)Mea.SUV'~ etfw.r ~ A (JY 8. ,vaw, fi..lt ~lcnl)()ftuofov"UJaK"~ con+ral i~ -ro COMp~sa.tt far -tlt~ efff.a:-of oistu.v-bGtMaS ~ ~ pv-oca.$S i~ afff2c1t.o.ltle N'\t\.r\lpul.aJ.e.'~ sfre ~ i:::> SUqjiU" tv ~ 3 .se~()()el a:! t"t1U.5 for efftUive. FF CO'Y\trol) cli-sfut-.b~~ClSJr.e~Y)t""l; MI,.{~1- bl. obmiJ.'\ td wjfh e.n~~ fiwle..10 a.li0'lV ~ otlcLy~ N'aMipu.1o..te"d s+r(2~ +0 ~fV'S-~ a.M~j j ie. ~ dtShlY~ce. mu.sf- be.. ~~ett- lea.sf- 3 ..sees before. it Y\+e,vs tiA.e proca.ss. l-t~ce.~Q.sJ.)Jr t- a.r A .

(bY W re.~ aia3r~s 0Jrt, sht1\V~ ~lo'uJ i:~ Fl65t6.1~, b, C/ cl rt.spe.cnvtl y (Or (i) f~Q(orwCUr~ j (Ii) ~dlx

t) Fee"F()rv~rd.

ProcessStream

y516.1 (a)

I'r 0

PrUU!99

Stream

10>mI.n ,

y

l'nx..l) 99StreBm

yfeeDfoRwAJ> + f~e;PBAa-rcAScADECOwrR{)L..

1'1,.2.) [0..) Fr"om t'fJ (tfo.7) ~V"I iiA.e tlxt) ().pon jV)fyoaUc.ln,5~ e(e.M~.s of -HAt tr~fer f'tw,wcn MOdel 81Vlj\fOY" tlAe, ~lYMtr pt'Ote.5S, we obta.iv'1 ~ fo{(al.l)i-~e:tpv-ts.sion for itAt fUloforward on(y contrc?lJr;

~(,s):=. (11.05 +-1) ~d.-550'0

j~st-

Tht.. iMple.~~ bloU

Feedback alone ~v-Feedforward alone ~~-

Feedforward + Feedback 0 --

~ 20

-20o 80 100 120 140 160 180 200

time (Mi,,~)

As. lLLustrce/) ~ I de ~Ly fiea~wa.v-~ oloV\~ is CfU'~SU.s~\*ib\ +0 ~ fftck of NYJ~ evrar-~. ~ Cl,\m D/JN\tof off5eb" wi Ll aep0\~ on -ttA~ U{\OW\t of ~o.ae1.e..Yror".

FeedbGlLk .l1Uf\t wilL (eM. nD o~a (if iLter-t.is lll\t~raL a.ction) bu,t obstrve. itrat -tW. pr-oass upsetLa.st'ed fov- e.-lD,se +0 1DO rniV'lutes: tuoback controLi~ lJ.V\ CLbLe. +0 CQrre.d; fOy- upsets W\til 1M proLQ.$ ;oSo.ffe.crM.

w heY' -\'\At. faQfcwav-~ .5che me t 5 ~~V).Je~ w\~mcba,c.,K

J~ ~ +he Qflfiapatvr~ nafuv-t of fe2o-

fOt'"WClYd.. ct,Lctl~ ~owV\, 1t\e.. lV\~lW"ll.A..tM- 'UN'OW\.t ofae-Vla-e-COf\ ~ Set-pOLV\t j LV. also see.. ~ feeoback..el'IIY'\\i\Clt\~ f\.\e .offSRr. Th[S ~bUAll~ '1it~o W ~5t- l'lSf'Wi.

'/ -. TrCUf Ttw1pua1uv-L (T - r'f' )u. ~ ~flA)t FlM v-a.e-e ( R.- R*)c:l ~ fua flt;w V"ate ( F- - F l )

"The.. pro c.ebS MOoel. beC~5

(_IS5)j = _ 2..0 e- d.-t

305 + (

!':3J..

f!) ~ -tYa.uuft-v fi.u'\cti~ for~ff i!. 5lVeN\ by

-13"S/ )4 e. {65-1/(3D5 + l)

/ ) -I~S4 (65+ ( t3Ds + (

11\Cs is rt.aliUlb{e. be.ca.use tk CQ'\~V\.s 1\0 UN\stableeltvt\LlAts) ~l~ ()()(j,!' U- ca\taiv\ My pV'~oCdil/t. .fe.rWls.

~ ph'jSical. ~$I ~ ot1ay 4550CLal"U U/lilA-+IAeffevt of ~fL.tt flM r~ d\~~ Of\ +M. ~ ~p-e,rabu.rt. (2. "'&~~S ) is le.ss -\1AQ.&I'I ttA az1~ Q.SSOCl~~ ~ ~ of fte2l flow ra.t~ fUtc:tt.ttti~ Oh1f~ te.WlPVa.tur~. Thus Cl wt-LL desL(jV\ta M(Gv~Cffi"1'foLltr ~A.S ti:W'e fo COmp~ s~ for feeo flMmu ciishv~c.Q..S

T\.\e.. ~Licl /; ~ pV'~SSiGvv fav clrl D..V\B~ in U. as a..resuLt of opsevVO d.'\~$ itA d. i5 :

U(s) = 4-(lPsH)il3.54.[S) (lb.tt)30s + (

uCs) -= 9(f 2-5) -Ih:: tr{6S t ( e .

(.:os +() 5

8y pax-fl:a.l fo,cticv\ ~pQ,V\siOllJ fo{Uwe.o by La.pla~ il/\vtv-.siQ"Of" by ~calll~ tlAt V'~0V\:~e. of #\e l.Cli)/~ ~s+eW\~'lJt.lI\ tV\ e\l\a.p~ 5, obtClLV\

u.Lt) =-1 08-

~ re..>~ Ie;, pLotUd be-tow (,u\ t=:l(7 Sf~'4

6

l1...,J'II

u(t) "1~lbs/ht'

ei(t: )

fi-~--i-~--i-~--i-~--i-~--i-~--i-~--i-~--i_Z.l1--i--1-

60 801'inw (M'I\$)

Lt2. 222~+1

/5-OSHI

Lt. 02.5(05t/

FIG' 51'.5"

(b) ct,9ff',S'

DS"st l

+~+ G( .9c

1

Ll,2, 22 4- ~I 02.5- -2.s +/ tOs,t-/

FIG Sl'.~

w~t9ff

/5.:: -OS5 t I

22--2.5 + I

gff ::.- o.~gf8 (25 + I ') (/baS)

(O.S"~ + ( )

wV\eV\ -AA:.. proc.e~ ~V)~oe-L i ~ e.x-hremLly we.u. b1CWV1) itA--teeGforweoro ~Ql S~tgy is able. 10 pu{t1v-M Lf\ea.v- per{tcb'd,V5tubaMCi- V"~ecCiOYV ()Slt\j CuA ea.s; ly ,WlpltMQJII taMe lea/)/~eleW\et\C' ir.d~O UA _ &:t (I~5) about. Feob4ck l-nfroL tMtLcO(f"tcl; foy- AA~ ,-eSIOUaL et'V-VY dl.li. ro lmp~kd Moae-lin3'

Ov\ tiAt ~ ha.na i tlAe cctScac) S~e.Me. 'Ie.lU5 en.pux, fuabe m -HM (aa -t'tat"ell j~ MeCtS urabtt J of CIJUJrSi.

~ :::.

tjc.l :

9c =I

~=I

9c =2.

9" =,soL =cl( =9J =

I

LL=

s=

csrR.. tClt1pe.t"a-ture L controlled vaYLable.) jc'rR. +e.Mp~ ~- poi/l\/; jMo.Ste.r TtIt\pe..ra:tLtve covhvtlr)

De.sw-o .set-p,oiV\t" ftv -g..) kwlpuature of reaC:/wft0 e)(. - preheatev';S{ave. Ca'\troUq: mk\.atv- ~ mpel'a..tuYe.coYl'lv"oQe.r

)

Pre~ vaLvt trQN\S (e fi;.r\cJiCVI.)1f'C\)/\5fu" ftJ.~~ apV"e.>Ul-tt"~ pr-htaler ay~t(.~ jR~ad;cmt- ~era.tu.rt T~ Ldts.twb~'.)

Lt"CW\5'ft,r ~iliU\ rttatinj efftr;t- ofclrl~e~ U-\ T~ on 1j:) o.ctual (ta.d-tv ~ ~j?r~nlatv va.l.Ve. 0Plj\~'1jI(ClIr\s&v fV.~ {t;tr CST?.j r~tl~ If +-t> T,

(5)) Ccn So ltctak~ tni\U" lbOp first to obraiJA

u.. ::. 9z 9v 5c..L.~l

t &, Jd (lb''')'P~;-3,9v9

(1>.8)

~ ) wiiiA

Cd) u.,",~ 1t\e.se siN'lpLu ~~L~SJ iW. bJoe-K dLag"-Q.w1 isOS s\AOUJY\ below UA FIG- S({Q8

FIG Sib.8

Wtt\A Q., V'e.u,J dUIQ.c--tei5JU. e~a.ticxl:

pr~ lV\fovM a..nCAl'l J

5Kc,(t-2s)

('l.5-tt)2t.35 t I)

OY

( 2.s3 + Ibs'" +(7-IO~/) s + (1t S~/) = 0 (l&./()5hlb~l\~ (Fut- l41 '>O)

\'f\(Jl)J ~iv't.5: ,

(7 -IOK,D =9 kC1

A",o ~ by cCW'pa.v-W\j EcfJ' (lb. 13) UA'tk. "tt-\e llflt '(rU'W:~ LlA.(I ~. to) l.AJe O~e., WaC 11Al. sr-a.6i Lti2j ("av-ge fw q;m v-e(\+iOAOl fu.oba.ct

O.Ss' t ~.ts2.t' 0.2s + Kc. = 05to.bi.lL~ "'VW ~ct;uir~s

(i ) kc > 0) CWclOi) ct., tl2 > Qo 43.J ,'v\ +4tS case.

lkc: < D. '+4 I~) ~e- ~t-OJ con-tro lltv .sl1ouLd ht. ~&1.Uib +0 a.(ctft:p~s~UYt.. 1V\ta.sUN'~Mt..jI\t~ CU'l~ lYlaNllpuLatL-ti1i .st~ v~

OPlj\~ 1'1Ae. b(t>a~ oia:ram ;~ shDwn i,1/\ FiG- :S16. (0 ~IDW.

9"1

1 + 9 9*'3 h. = 0I I c.,

wittA '1* Gt5 ill\ d tatt-u t..V\ e-CJ-(f b. (b) abo IJ. "T't1 js ~'fU a.tio'r\.v-eC\X~i.S 1'0 ~Lve.

I -+ 9v kc (f + 9 s, h) = 02. I ILlf'1t" iV\+roaU~j #\t. ~LII-Vl. ~sfU- -ft.vlcliCY\s, w. obfrtl.v\

I +O~~5t1 + (~~, )~:~t,)K'(00Z:1

~) = 0IAhic1\ SLMpl~~ 11>

AtA.a noW s\ub~(L5 fe-quirest!\ kc.>'O

Ui) 11. I )(.2.2 ;.. 05..< 5kc:..

or f 1

II".i](c.l) 'Nt:#\. l StabLtL~ Mavjtv\ de.sf9~MtW:0, we MO-y plot- iV..e ~'3aLlI\ f'Iatr-a.l" ~ OlA9rct.W\fvr "1t\[s S'fSrt.w\s 01,..TF . ~ tv\~.s case

3. = 91 (~~J'1C(n3L = /0'5)1- ID ~)(5s t ( ~S~ + It .k.2SH9L, :: ~1 KCt

(5S-t I)L~~)S + I )(O.2s + I)111e. ecile. oiajra.m for -tV\LS S is SlrtoUfl1 WI AG- St').12." at0~ hue ~ otdLtCQ., ~ fo(l.aw~~:

ku = 311.7Pu. :: ...:Uc .:: ~n:-= O.58b

uJY.> (072

The. l -IV ('twrf\MU\(yjj) .sedi~ 'fliY ~ PIO uM1r~U.er GVe:K. ::: lB7.02 ) LZ:: 0.195 j Lp = 0.D732.5

AM 1PLITg 10-3E

RAT 10-6Io 10-2

PHAS 100E

AN-200GLE -300

10-2

FREQUENCY ( RADIANS/fIME)

FIG S 16.12..

(b) i1'\. r~on$. shOWn ~V\ FiG 510.13 1(1 acfua.1 {aa is +iAe,oveva.t1 S(hW\ ~MSe. -to Ov sl4"lu.!fcwle'\ts w\L+ ~tep ~lll\ a

lQ,v\J. Cl st::e.p cllCJJ11-- of rflD.jr\ifuo.. 5QOO j~ ~2.!-me.

OllevaM. ccvrtroL s"l~tn i~ SO eif(idi~ -fi.\a.t" cltsfuN'paN1cts ill\"~~u.ye (dJ,.') nO ltitl~ a.~ -tiAe pr-O(5So =eJiou.sr Fur~lltu.strC(,ti~ tit\is poiv\cl6 ~ "extra') ~OY\.S -shawn LII\FIG 51bo14 ~ +\Ai.5 [s ~t ol/uaLl ~W\ ~SPoYl~ 10 a. .U~;tstt'P c-lAaN1~ il/\ dl.' Nott. mat- ~e. -scale on j is x Ii:

klo~ t1N;tt wittwut W1trol) C( W\lr- c.J\~( ill\ d, uill ca.u.se G{,.(0 cJ,\t\N\~ '11\ 'jj U u.~~~c\Q.I.I\~t iV\ ct:l. MIl c.~ Ct o.{SO~ ii1.!j.

d : 1 ~ = 5Dou.I ) 2 J

XlO-5

0.4

30. ~)TIMe (AAlnl.{lK-.5

FIG- 510.13

30TIME lM,nut.!s)

fiG S~14

ll.3 2..~

gc. % D.02s+lV'dUtet~9

FIG-St~. (5 Block dCa3raM -(Of" P'1y~ PtZJ(.a.ss.

(b) fOr "flAtS prvCQSSI J. tp.L -- _

(0.025t 1)(3.5 t 1)(Ssf ()UMO t\A.e \' 3atV\ V\e.utm.L'1 eaot o~9ram (5 sh{lW~ 11'\ FIG Slb.lb~ wlAtYe. Wi- obtalll\ ffN. foUaw~Vj:

At

.b. oetuli\d. ""IS rflo..y be aO'ne. 5werctl aitY~v)t W{Ur~' tve.cl.\o()..$ --fz::> v-e.OlA~ [".r f1uw' 1. C I +-0 01. The. Lf'esul:ti~ d()~lCCf sys~fV/{\ ~~Ofl.st i5 5\t)OUM LV'I FIG 51b.t7 j -11; is s+iLL'tU-~te. o5uLlat()'(8 J bu.r now -LL- is slnhle.

AM 103pLIT 1UDE 10 -3RAi 10-6o 10-2

PHAS -100E

AN-200GLE -300

10-2

~I

0!:1

tJ ~i2tJ~iSC.-0.02

jl

-0.04

"'I

-0.06

(c) UN\W ~ ilAd~~ ca.sca..oe UK'rfr-c;l S(.L\VVllJfue. ~ oia..gn:trtl is

Mo~ifiaO a..$ shouJli\ iV\ FIG 516.16.d3

ell.

FlG S I~.\8 Clock: dl9j,(Cl.rIl 1r>V"PolYMer Pro(e&5lMoer CQsca ()e CoYl1roL.

If ()OUJ 9c ::: t:cz.. = - 40 uJe. Must lI\OW IJlO!;e +0* tl.\t"SL.oYl+rol~1 wi~ -l1;s ~a.tiVe. va./.ue.. ho.s maoe *'~;V1V1lV- lCtQjj)\v'\to (k sysre.vn with Cl POSlTlV~ j'tlVl. 1Vlis ;lIf\pli~ +lA.o..t-~con+tolltr il/\ tlAe Ou..te-r lDop L iJ..-1! onSMaL vIS WSrty UVltrOUrljjiI\\l)~T Now HAV A PDSrtlV6 6AIAJ:

~l)..S, M-HA I(c, ;. +l5 0 j LX" 01 Loeru:Ylla fr()m 1.01) ,fey ~ VC lSC\)J(\e a.s tV' pWr Lb) exapt ~ tVll. s[jt'1 cJt.~e!)-ti\e proass ~pOt'lse rt-o ~ ,stU'f\e Mputs ill\~+i,~a~ iV\ (p) 15Show~ be.low in. FiG- SIl~.~9.

Ob~Vt ~ not OY\ly is it\t. .NlOJXlMUM aeyLa.tt'cJh ~ _ "set- -.po~1I\t sll}~L-Rca.ntLy ~ebuctd (nofic.e.. -tVL ~t for ~ ,'s )( It) I)-tV.e ove.v-alL ~GWL(f(" is belttv': ~ osculatiCVl> ~ 3t:M.Thus t\..\e. GlOdltiM of +L\i-s ca.s~ Coop ha.s -St5tAificevnH.yIMpvovid. pvoce.ss ~.spO'l1se.

XlO-1

0.05

~ 0,i;\

.~-s~~ -0.05

1~& -0.10"2

....:::lj

-0.15

30 . 40I1ME" (Mm~res)

FIG 51(".20 BloC~ d'G1G1raM fe7y tb(y~"'przxeS$ UI\OerMLAltilaYlltU ca.sca CCY\'trt:'~.

\iov~ ;V\1\rl)OU!eO5~nais fYlNn ~,loops f.Jt\e at" CL~+-ctUrt:

c, ~O Cz. r.lSp~ctivdj fw ~ C-untreL-ru0 Be we. C01 Soll \late. ~ i"'~41

til!l"lt ,S" ~n~j wi/!. tt.L Ek" loop -tv

2.39c~0'02S+ ( C of

----- :4l + ~'3B,1.

o.02$-t I

U2. =- (0 ,.390.3 )c + [cH{O,D2S+I) ld (tb'~0.02.5 .J. i + 2..3~ 2.. 0.025 + t + 2.3..9C .3! 3 j' .'(U,.2i>b)t.\l.

ow d= 9 c" -to 3d ~.3 3

W~~ ~s coU\so!;oal"ioo, h bled<

+ r 0.5($5 H) ldlieostl)(5"H It a.s.9t~,~

(lb.2~

~:. l.fJ ':!d t U,J c! t i" tt'd d 2. 1- ~ d.3 (U,.Ub)~ L 3

l.Ui~ tiAt. t'rQAAskt" fUMdiN\S

~ 0

~I-0.02

pred5~ly 0.5 CKijiv"aJl.y Oe.Si:JlAtb iV\ ProbleM fb. 8 ... +!Ae rsp/.Ct:to ft..\e S)Jtl\t ol-sfiurbQ)l\~s C d2,. :. +3DC) d

3::- t"2. p.s:) ;5 ~OUN\

btllW 1", FtG- 5lb.24-. Tnt fa.s~ Fe. ~its it'Ie, ob~('O~ ~

Wi) ~ ~ rlsw.t 1tAl.tS prooL.(CQ.s a.s ~ ,se.I:--poZVlc fCY-H.1t.Altl.A1 i\l\u.M CO caXalyst f'{tJW rake

@) Des'i~lA ~II\ o.pp~y~a.t-~ filM) CIJY'rly-oLlr tD nCEilje #\1sSetpoiV\t UAAO MON\ipu1at-e. -ft1e. l/aWe on tIAe ClJcato.LyJt"liV\e .

1V)e pvvces~ O~YQAfI\ fbr ~u~ a. Sd1~W'/~ ;5 S't16t.tM be.1{)Wlll\ fIG Slb.2,5.

VanatiumRcUtD Catalyst~~ R.

ProductionRateController

ProductionRateEltimator

(P)(i;The. ai$~~ e-atiSlS T Lt1Ae mlX~ 5t.Y~ ~)*0 ~ ) TCf.J (?- profOitiev'al-CXlLy CtN\1roUu) l'esf~N)~ byCloSLVS 0 ff +V\i. by FUSS va.we. by tUI\ o.NIIOlMAt p~~+0 tW. obse.v-~ et"((J(' [\1\ T;Ui) The re1 coYYtr6l CtCh~ cau~ a ...ise LlI\ T uJ"'.icJ.,. Is~DS t- iv\s toN'I{;Q,v)01.L,$ j +tArs .s~. a. e.tio'Y\. is LO'rlItl UJ'~caJed+0 TC2.Qic') Tel t"l.sponOs by irlc.reasL'5 stt.QrM flow f7> tf,.,e, ~atX.cV\tvI\!1e..t') whic.h u;\ll ca.u.se. T to (rlCYutse. but" em a s(t1W'U"tiWlt. SCGt.Ie.

~Il) As -ri.\t Tel. actich.s bter", w -la.L ()(\ lCz. cU()nl is liMI1t)by ~ skv oy "amlc-s aSSDcillJi~ wHL, k if(ed- ofst-t.Q,A/V\ fWw n:U-t c~ o'n T.

~ c..offiyuL Syst.t.W\ V"seOYls' to a. -t()F Sk!f ~ L'JI\f~ +t2-M fll.ra.b.we, i~ s'v\OUM 6tlM M fiG 516.2..7.

TeMpe~TUKE.co~U>1.. 8YJAaGr c.ool-IIJ(T

,4 6 8 10 12 14 16 18 20

time (min.)

(b). U~ fut.. UVlOt.lASt' unit +0 aOti:w(l. ttMpua:twr evrrlnllWlpllLs ~ ilttt appYOpt"ia.k MOdti 1raN\sfe;r ~ i.s

-.1$92

= - O5e, 6b.2Jf)25 t (

cw\o ~ 2.- tJ rU!J'MMtV\?:ti}) -sttti~s a.r~ obt-~~ CiS

kc '::. 09 (2.) = -3b, 0-O.slj:"i

'r = 0.33.3

::\;\~.s cast I -iV\e. c1os~ (1)0}' .sys~ resp(7l)S{. to ~ ~~[6 F ste.p C~ i~ fei4 +ervy>uaJ:ur-e..) Llsf~ iVe O\JU~C(7toI~ for ~pe.ra..tuKe.~) is S~OUIf' ~t\ FIG 51628.

T~fflATl)ReC()1JTTll)~ SfO\lf:RlteADC()IJoe1J5efZ, ~u06

-0.020L--2'----4'------'e'-----'8----'10------l.12--.l.14--.l.1e---'-18---'20

time (min.)

(c) W~ ~ -ft,Uo contrDt~S QY~ ctNnbW\~ cw:o U~SCM',~.l;\t:u"toU.SLyI ~ Oveva.tL pV'"()a~~ blocJ

(\Jaw, ~ Bel as Cli\ POKC~) (e l~:: - 33.75 'Z".I. = a) I j I /

~ uA-t\A ~ as ~ pro~ pcvt ()f ~ CPJ'rtY"f)l!u-G2,.l'" pcwe- Q?)) i-e 9cl, -= l LIi\sta.biLit:1. ")

~YJ UJrtk Cj, Gb\) 92,. ClS c}l.1i~ L-IA (I~.Z~aW>Ll~.24) J m ~ Loop ~C!e.Yis1i,", ~ah~ {or-t\..e. Sl)~ Wl\OU ~ ~1r-oL LoS:

l -+ ~~ .::. 0I I

~s sta.b'lL r-odh L (vv J~ ~i~ CPnwL by IfsgE)..I ~~ Qc.2. ul~ t1lUl.rQ.M~ ~

t + ij CJ" ::. D~ J,

na.s sta.btt raob ({w- CP\'\.~ ~l~ by LtseJf) wit(; lV\ftU:b" nor 1f'k-assf)J;ly 8uQ"QMtu ~ L:'.25J will lAa.v'eno ~tt.blt. rWrJ' FIG Slh.&) ~.s -tL\a.t- ~arrtroLlty- par~ ~ fa.cJ:- make. tlAt.. sysk.M UJl\sf4.Ii..

X 10'08ii

6

4

2

a

-2

-4

-6

-8

-1010 11

VNt>~ e>1M.IJt.T,A-NeoV~.J PAIU\.lL,.& O~L. usoJ G-/NOIVIDV,4:WjDe-Si6N~U>~$.

1\1e. ClfPrvp(~ PyZi~U.V-t. r~ 17> cl".a:?.se he, 'tX ~ Kc2 ~.~6~.2.5) [Or by GWly ~Y' 1V\tQ.V\,S uJl.'\icl\ ~ '+t\~~~ ~Llla.tiVt- e~a of ~ -tvJo COV'lfy~llus 'in!?>coo5ld~).

A stvaf1't-fO,uJax-O wOj of oe.CU.~i~ iV.e. ~lers l.SsiMply -Tv cl.tt ~ aatli\6 bOCk. fu ~~~I by cLttti~-HAt Sct~~ iV\ LvUf) l~,:.-".875 ..i kc2, = - iB. 0')itAe. ()V~ cJ.osW toop s~rLW\ ~ be~ sfaJJle....ON'O w a.ct-uaL pe.vfOfMaAAa. LS s~own 111'"1 FIG 516.31. .

~ covr~"~Ol~~ ctKriToL ~ for u( [~J~cool~1A3 weuv-- ...a,t-l) ~ U2. (cIJr./J.JI\SU ctdWj u.'tltt2.rV'ate..') are. sV\oWt'\ i\l\ FtGS Sib' 32. ~ 5l6. 3:' ~~cf"-lVt\y. j\)o~ to.n fUlly -ttAa.t- u2,. ifu.rns +v ZJZ(O 1.1J\1;/t.llL ~s +0 a.. vaLc.te. of (/.O/~) ~ ratio of -lV..e..Saill\S a.SSOCLo.~ wi+4A. Set Q}J'I~ 3, .

"The ovtrcu.L respCV'6 CQN\ bt 5PU4~ ~ by l~c"'eaSi~ 1

0.091

0.08

0.07

0.06

0.05

>- 0.04

0.03

0.02

0.01

0

-0.010

U~DER. REVS-S16N&j)fAfAU"eL. CDtVlROL.

8 10 12time (min.)

8 10 12time (min.)

II 0.8C\l:l

0.6

0.4II

0.2

0

.' -0.2 0 2 4 6 8 10 12 14 16 18 20" lime (min.)FtG Slb.33