Biological control systems - System Concepts-Mathankumar.S, VMKVEC
Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC
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Transcript of Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC
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IVM U/VMKVEC/ETECTRONIC SCIENCES/BME{EVEN SEM(EOURTH SE$I\'20L5-201 6 I CBCS-Rz0 L2- FULL TIM E]
1. what is the pupose of Laplace transform is used in control iystem?2. Define step signal.
3. List the steps involved in obtaining the transfer function.4. Name the properties of transfer functions.5. Define time response.
6. Define differential equations.7. Whatis the purpose of standard test signals?8. Define ramp signal.9. Whatis an impulse signal?10. State various time domain specifications.1.1. Define critical damping.12. what is meant by type number of the system? Give its significance.L3. Define damping ratio.14. Define Damping.15. \{hat is the difference between type and order of a system ?16. Detine resPonse. Mention the test signals used to determine time response.17. r//hatis transient and steady state response?18. Define-rise time and settling time.19. How the system is classified on the value of damping?20. Define steady state error.
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V II{ AYAKA MI S SIO}.IS UI{ IV ER S/TY
Vinayaka Mission/s Kirupananda Variy* Engineering College
SALEM - 636 3OS
Programme B.E. BIOMEDICAL ENGINEERINGlSeme
ster |
4
Subject Code & Name
L0 - 03 - ZAL6 l Oate rf B
3471240I. - BIOLOGICAL CONTROL SVSTUNAS
Mr.Mathankumar.SName of the Tutor
Assignment. Irdo.
Date of AnnouncementI
$hort Anrwer / Two (or) Three liner Fxpgcxnstlon
$k{rk ,,{*rr#m
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4.
lvMU/VMKVEC/ELECTRONTC SCTENCES/BME/eVerU SEM/FOURTH SEM/20L5-20L6 I CBCS-R2012- F U LL Tt M EI
L' Derive the response of first order system for unit step/ :r.i \ rr rur.*,:.rl$ e-
2. Obtain ttre response of unity feedback system whose open loop transfer,function isG(r) = a/s(s+s) and when the input is unit step.
Develop an exPression for unit step response of undamped second order system/ o,restla-,n.r.c A,
Wrile- the expression for time domain specifications of rise time and peak time with
.Derive the expression fgltime response of a second. order system subjected. to a unit
impulse input for (<L and (>1,, where ( is a damping ratio.
6. A unity feedback system has an open loop transfer function, G(s)=10/s(s+2). Find the risetime, percentage overshoo! peak time and settling time for a step inpui of iZ units.
7. Develop an expression for unit step response of underd.amped. second order system.
8. The unity feedback system is characterized by Eu:r open loop transfer f,unctionG(s)=Kis(s+10). Determine the gain K so that the system will have a damping ratio of0.5 for this value of K. Determine settling time, peak overshoot and time. at peakovershoot for a unit step lnput
9. Derive the expression for critically damped of a second order system subjected. to a unitstep input f.or fL, where ( is a damping ratio.
10. A impulse input is applied to a uniry feedback system with G(s)=12/s(s+T). Find theresponse of the system.
5.
Descriptive Type Questionr (Erroy Type)
$"M{ffi, {rw#*/4;trlture sf the Coordiln6tor
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t
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t,tlr',+ B=*jt-..r6 eLE
eCS) € wnn s-A+s Ee+tr)nz---@
CCS) =.S _zLA+wn
s-Ta*c o
7 . v-,JJufia
,l:t;lQ9lA4 @ -*o.rtrfrCI\rrn )
vt*) CLt)
L
I
o:EYrfi
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ulr ryorv\e- 5 ova,1 **s*rud'
,^*i"t..\
The"+ A..'ru.,L*+d- A rd*4R/- fufi*
F t*nL,-z a c.u)^B +r.JnLs + L€r ilJn{
tv
.,a v ut't a.c.tt.,yz*' %*e-xL
#r,e clLl;r-r.rv';M
-":RPL -h J*w '
.dannrv;W be-
: - \wo L L^,6 ffr
f"t "fl-n '-co':n'- ba UYL'U
l f*'cI*^oo
o
Yeh*a %ccs)RGS)
grrta @
f*c*j"cn i^6J\-a'
t4 t1"'L?
-f,,* $tPo-
,4 Sz
sr ? 82
Lek
.e;3 *T"rury
jfhe-{
jr"
'o Sa- = E t,n F t'Lln ,{-fi
35 = qLu6 + L$n
M
ctepr-rn-
ces) =
Sa.- ,,&ruJ\- S t2_
f* 2Et ins+t*1'",'
v e-Lqt^,p Jr *pJFl
Fsl *o*-d- S6 = aSc-
UJnL
RCs) G+s") (s"l-sb)-e
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CCS) = t.t:nt R-Cs)
(s+sa) G+sb)
Ccs) =uJr,*
sCs +sa) G-*sb)
?B*i ? *fir-ra.cLt^on
CCS) ? tfrnL
,tt
otr
-J- B
S*se-
n
C
s+sb
e
B
7Ls
rrrn* = A[o+S,a-) {DtB)+Bd5) [o*oCb))+ cco) ( o+o-)
= A(o+sa-) [o+sb)
(ilnL = ASa-Sb
+ Bto) + ccD)
s[s+s*) (s{r-.sb)
tiln* E za (s+sa) Cs+u) *e[=) C** D*"O (""")
scs +s */s*sb) a Cs-hs { Cs-rs)
t...nl = A(s+sa-) Cs+b)-r ecs) cst sE r-c cs) c*+a;
3r;s= o,
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fr
= tUnu
( quu6)- .*rn W X 1*n t t,n W )f,,
= gx)n-
qu*no- *f &\l
wnz
EW-#,:**n'
= -WfiL = I
uJn-
?*s= -*Sc-)
ce* = e ( u*;{s*1 Gso- +s a) + e (-so) Gs*+sa')
+ c G s*f3o.-+84*)t
fb}sa, Gsq-+s b)
g 5= u.Jnu
Gsq- *sa-{€h)
x= (x)6
,NnZ =
;tt-.,n{fl,
Gs*) eydffir
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&.so-rffi,
B= -.:ry-o ., -f -
&q-l 8a-
F dWn
?urS=
u.Jn
-sb.2 = AGsb+s*) f"/.g+ e&sb) e./*r)*c$sr)
c-sb+s u)
wu'F c 1fsb)f gb+S*)
C s fuJr,2
CC
(-sq (-sb+ sa)
wnL
Gsb) CE/- rdln W + E/"- t^ro rfftr)
(' - +' tJ., n-
\-e
Gb) (zt*rn w')C = t^lr'rf _1 _
EbAUfiIfl,
e = !{osttsnW, ab
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23
Sub A, E) c vo-larx ;n eay'aVb" O
ecs)= * *^, L* | * tr'jn I '1
P r/qr-, ** S+sq' AtF ab S-rs bI
)-rn@ ota1:onr:- *t -dr** otoryrein Lc+) iA
( ,r- (>, = a : sa, S+sq, arF ab s-rsb'* ilgo_,
W r; rl1:ont?- *t f;'** oto'Yrein LC+) i^trtr)6 l,
r'| l.o,j = r'f* C, tk-.,'4,a;Cc+)= I - hin -t ;t*t-* .trrn + C
sbb
<r t_
a Gr-' uo e 'l;E ' db
, * u1 *r
lcc+>: r- t^lo f--s-u fl\ I
I I'E.r L s* su]l
.rr+)il Ctt)t'-'ttI I g=r.orl__I i -/--Tt -
I
I
III
Irr.ol.,! + &l7otL!2-, t
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+.
i;
W'S+j.b
*t 8";^
ryil,a- e-,vlxt:,.gio" 1,* 't;""- ''d-erwa'm
ft3"w ar,n *;'* ' "7*,./,e-*be
'*;*'L 't'eiwL Mba'btn- '^d-otivoleion '
W%o\rffib)
.-+,T
'iBa d-o*-l-nclrrvte-
aJUJv&- *
+ Tf4-a,. Med"
-Tln-a- ,*'eJ1a:.luQ-"*
n
a -!- ts a. r^ ^ a ."-&P ru'f YLX-J^) Jv*t-r^\ t furvtz
- cJ, uc.s u ct-cwPufa Ut-'c'
*e
W& ;t*Yb
nt
*gp+tvt-l
.:pf,4"q, -#,** ttv) "*+ :.* 'b "t;r"* Wa& P
&5 eLlach. d'"-rr''P-taa'/' {*- 8\
ZYN **"u ct-:-
*? "*f* -efi 'g,etord-
Js'}r-ol-!-'-L
,Y CgL
,rJ*rfu
J^*q L,Jnb
L[+) = l- g €-^ f *.lu +s) o
"dt b= .b.rr ) LL+)= (C+rt) =t.
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*qL$p*rrr-g+o
7h-e- *e>t-wt-
uYhxn # =
=5 S.-[^ce ) D/
S*b (uroLLT + @) :a
i
T, 2T,,*3tr . _ L F
rnot ?G+sib€- ryyq ) Ld"L b1 1bflr
L5
c ctv ) = I - ;q*":t /,,&, ,Lrroltr +p)t^{ r-q-
I
-gtcrntxI
JOt--\-, /\r3-, [.^r"ttrr +e) = I - t
'ITJ"*Etr>6tve
-dL L= *v1Ll
€;vlfarutn-b e ,Lc;n;--v>L bQ- O
oEC
o,r9-,;\
€4 (tr:Jtr * o) :B
e
oo
o,?
tJt-\
euag*
tr:
€ Tf'- C
Tr* ptnd,
?Urt- v&n**;"'*cd-*?
r-q qh { r -G,o d-\-ts
I
**ff?ek
ry ";*oflet**
1* q"
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rfurlp F -l ,l_
l+ eJxrt- ,t
g = +c.rr'fi?+
q,
tdrnw
*TF* bq-frr f,r-f,2 , s .,-t Jtf""a- ;^ Aec. I
t'}ntrf
Xtuo;1l-sl bL @t^Yt g&
t€Lv Lr.inry )
*o.nP= A"U-e-
Adiace.rn".b ^;Ae
G^ci-1a-ortton rudL Ecryw%o*o Arj* tt'h^e- Ct-)
9 vgh,L *o*', t
,gtM,
WZ bnfrt:.) dd4-c'- t
(Y o*.r-}.-,
/ I-- P-ryh { t-E
q/"rye) UU-;L * G
q
Ci__ € [-t)dl rY
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So , ,b',^ s Tf-t,G.JQ-t w&f-f
L^: g}L
?eox 'T,irng:*
,-+ -f * '^-?fr.;,.e- -furm*
Vg-lg-Q-OVc-fu./t1-,rJob
t,p :-
d-e LdL
,J+
_*_dt
* $c,:nbee,
r', 6!,r -ELuo Y I+ b e- /,Fq-
C+p) o*L C C+)
&oi
o ,e.ivel..-*3{
G quJn b
CCa) = | * e, .d)d xb, {tr:ct-b -h e} '
r*,l !*E-
c c+)
LC+) =o (- Qu^)si" (u':ctb + 0 )
c^p", (uuolr + u) ur{
* -To
t* tl4'- ^ {*" P
IJ;(.JYLAq-
ur*Lu- W uto t +e-ry'c't
LC+) I * o14 = bP
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rr Q t^:n U
g ( $t*n) sints 6,^-rn b
C,^r'Uttq) € g t
FV r-€.2
I
Ces(**u +d
Iq"* twnv
I€ e , Iq*, xl",(**Y +o)-cosC-"rtllvl-'
\ r_q"
?ul tr.t = Lun .lt-q'
+B)*g
{ryE ^fnC*"rb
+e) ?G*- CG,& (*a-t -jl|jinrr .eorratru- *n -^^f "bLe'4X'tL\+1 ,J 'f,q-i'l*" Y,
in $ rl.:n b
wr\ g
{flq*
' t' Je". Il{ptf-ruoLrA ''--!Lc
Ce&&= = 3 * q+{ d"PotensuA 4idr- I
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t-un ;q.*nbt,-s,-
I
,,,
.,,
6
Lun e, Qwnb
"$-^[tr:oLLt e) - q
f Cps e /';^ ( u-rd-E. +e)L
*1
!- S,:o g C€6 t lalt a e)lJ
h co& ( trrcLb -{
r-{,_q*
'i- Qwn g:t{."} n e-
7\i r- \u
-q wn?taJpl g '
fi?* €'wov
wnEre{ L_1_
t= LP ) *t'dY
g )^ :?w^b Pt-rp g
#\ar
\) t-E-
* e,' cg-rruncb
(vooLb +s) @,e d- (-s4 (t^:olu + g1 -rL 1f.uL*^
fo
L*
1,o'-1L /;t (ur.-:"t-t)l
C *r* +g>,4
dt C+) ;o
L ^i, [*+ upil
le eqP-o"L 'i']" otj
=A
? 6wnbpgfr*D.
ctex_rn- /r-?,- (*"L €p) -=o
o)"Trrffi)+iF'
an\-L
9=
M
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or--o,*}:.ce t X-e>to '-rt-s
, wd**P = TfI
+p = T/orL
JIq"
,xwv 1xs*a,Lb.[-e-'
.^s{c-CUt-
c>L_
&Y
= txJn
o+r
cC&) =
= - '..[f
r,un ,lT-n, " ?
F Q utnbtrun e-
{"r p srn C*au.+9-Jft-css (**st{
-ful+rr,i^ ,-co-n-ruoE bQ- qfld Jto 7e2LD
c&E
€t
q
-',i- (urror-t +*) - ,/fq'co* (*dL -t s) =o
{ft' = s[^ (rr.rclb +e)
+ -7h;.* e.Yon-s-n:lab.-L
.'o *n 1x&. 1ructb +t) - Ltrn ',[]" t*s(t*:*U to) =o
- Qwnve C+) € I I E *^ ^,},Cu{olb
+*) - uJ*-g" ces6.',ue'9
1-: L'
CPs (t^:clb + Q)
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i;)
3t
ta-n g' = *ta-r, (wdb+e)
bq-n (krcl-b
wt>lt
ruct_t
tNdY
+e) 5 ba-n ( trr+ ts)
+C rs n-ff*&'
=., nTf +gr' g
F nTf
?u-b b=+DI
to=t,
t = nTI-
L,l..loL
nTr
cAffl
.StrL t*" + 7 r1'= I
wcL
+P= Tr-- *Tr.d..-^+
uuoL rr-rn ',[E"
l"1ax-Lr.a-1.,.-y.n Aves*hoob / f "nx' ove:t"sh@t "'
--:. L* .;a *+ep'vlea '-a'/s cfr42- *'o*i S moiai'n@,n
e^ra.,tge- *o 'fr/& vo'Lua-7 ld* &,.P- rn-a-}
'-W-o'y\/ Va!^c- ja qn/,a*vou.,A' foe V.]'LL.' '
I
,h "pe-o*, overt sh-oob = g C+f) - c CaD 1 ro oCC".D
&Pr-cloo*L '-&<lt-Q-'$t W?
*Tt4p* $&rulg *Wf "*TnrL'a- *f
c SrwnbC C-t, E l- e.
rFq>I tr:eLa" +*)
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db
P,*
M7
b = t P2
Lt*) =
* 8 fr) e-e) t CCAD E I '-
= l_ D s t [_
{ln=
4^in C*& bp + I
,T-Y6E-
vaG '7rv+,
(rr+*)
'- E uJal ao
e dn f,*et,o + e) i
,- 1*"+pC-C+f) = t -i- ?
.IIT=
*P =Et^bl
woL= rx)n .[Q= = - 7*l
?*.,Y*aFI*P; o
= -\)g)
,lE"
\J;q,
c (+p) F r r ;qT/ G*[,. a]
w',
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? (erw
.|'r\-C-Dn&*:r.-t"ue-fou11 tr \-&tLffi dtTi .-,r"*iU't-
JA"le- fl*
G"
,r'*3, G € =J-E,
0*g*n 6;r =
U.6potorr;tau-S .1*&
ryc&r)s rr;qn/JEE- W,m-
cc+p)= r+;9*irr@'1
'-.9Y
E /r+ e EE'rrk toc?
I
'/, Mp > -r tTr' 'l- * -*---
X IOO
e\E=
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iv) SeL+
req.dp-ry
ccL) €
Or
i"'..** -X-t-7u[NefLr*n T:JJYLQ,.
-.}..7
I
--i'--L-J..r lA-.'
\frr-a*6
JA
d-a
-Eunbl-e-
grg*,
frrre-
-ndeLo"rA/&j eyon-o.r^*r1oL ^:tryt-r'a' /_ed'/ucsst
cJ.11c.q.,1 ry /L;v"L^/wi"L*f '-cor?onr,nt
&,ur-ve- JbD ,L,t::rL) r 'Ltl-t^ lo f e>t cnc-q bo"o'l' ^
(
* NesLrns-tt/H ) 2- */ " .^pE& 5 ,l , '.btgga.-nce- ba*d*
ery{> Y* .c-r"* t +s) :*
+ The- =
16.- *,^t-,i* '*x7 *t A%-@
*bl [war +s)
\JE92
+ 'Tnlo- JLQ-8forL'lA- -$ *Btnn-d- 'e't-oLorr *f"-" '?/"a-L
?m Um e*f o& b*f'^xn*t'.reAL t)
.- 9 u:nt
I
e) AfurdsL c'nn-,oo",enL'n'
+ A,& (( reLt +s).
+ Z* #ilA
19.&dUo.,H"qrt1-\
* Hqxtcut -t'7,1e
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35
?la,- ** Jdj,'M- 4-aJrc bP- $o* 'Du'k "1
"1p* e,-f. r.'-e-'.'f,,;- 'tDrufrw* J*b /' d'oLe>to-nce-
,YtSt-*t ,
) Fo.li g-'/ ' Jr>tesr-cl,,"tec av<:<*t ba-nA* a"b € -- bs
* Q
trrnLL 2 O'O9-'
rl r _e"1
, Fe.r, J-c-aAt V*U^i- ''$ q )
--Qrrlnhs = D.og,e
+ E',rd ***n Na'fi^'.qiL *iduLrn t *u
-Qrunts F L'n(u'os)
Iek '
/qwnr6 - /4
$r^rntE F + ,
tg= *9*n
) Foq .s{-o()}LJ_ "s'ceL!}t *^p'be-rn ' 'fr'\2- *-;''e- 4D'AA'to-rr-L
0
oo-rw be- t = -l-1*n
t3 ; 1T I t"= L.f . e.rutet)
' ) Fo" 6'/' *pte-rto-nce- exeLsq ba-' -d' o-'U t= bS )
- Q urntsg = O'O5.E-
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E,
? tro+a "/ iu--c'A? Va"trl,^e- '^& q ,
r $*ubsg '= 0 c Ob- .
) U*( @"? Ncr-la,tslat 'to?o,Leti";"n , *L X*jr
I *^*6
{ q trentg
E t,,6rts
; ltu LD'oC
tgF
/3
3
3
9*"*c,*,c*.-ax trero )
,fr\L *fi-lv & C-cYr'Lg-gnb
* Fo"sr Ae,rcr-rL
La-vv ba
'T- =I
q*n
bS = 3T ( {o= 6- *l ' E-n L^s"{)
Dgl&ve- #'a-
-krcn& *x-da:+
ryflq<r
n $"- .b^v\*-
**Xae,be-J-
t @
ft c,-
--,fulA€-Ye.-ru&
tuIE'gJA
I
cL-
CI.*
.rsq-8UQ=,IYL
.l o I
.xo.h."b
+ Th-a-, A^e@rvd- tre;vu '*+ M t"*P
dt),rry Yat{^ons
uI-&
ccs) tUn2^
S i 9-& UnS+ tr)I
RCs) (\
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3Y
o
> 1+.,&- yd4o.2lqlbj&s+%- e4fa*bD "[E s+ "q
u)nS *-t^3n2 = o ;
uJ+lDLe-A = el-rl-r
G--1 - dy? a+-,
=TI4,a- 'rt-ootb 'a{. {'J^iu
sr tfiz s *b +.'lF+^L2a*
A- = I
b = 9-Ecun
? - &)nL\J -
=Si e-32 = -_L€,LrlP +t
7Sr rss = -9*r.t *, G{St .9z=-gbn:turn{-q*
J^y?l't^a ,
Ed = r-rJa ,lE{, Lsi)
. t^,'L y r^,n tJI1*
€r)Ss= -qq.rntj*,eL.
Ca.t*. t :- g <t ,t-undat< Aar^f e-"L
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* A.puootu 3 fY .rwffiil,rrrilb o
I
.,_ RCs) : I
Ccs) = RCs) t^r n*d+ l-eturns+t'L' f
CCg) * uru=
f+2Etr;nS* t'trnL
,Affin q"*nz,
CCs) = L^ir,*
** z\ur,S *9Ln" 4Lt-r n'- E'*nt
C Cs) s Lunt
(s*E*nf+ un2 (t-q')
C;Cs) E wnL
(s+ t*.0* wd2-
Md${* a;*d- divi'd"Q-- t'L} L /
CCs)= urnz.,r^lA
ecs) E
uu&r
lrqr,ltrc&
s+EulQi:*q
b tx s[-
@)h-,r-roL2 :
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c cs) = 3f d
t,,ttd-
Cr+) = f'
CCA s wnz-
;
Cct) = qlltt^)d VT!"
Cs+€l *0=+ t*,,"L2
usd,
f c cs)] = lr"1 ;- l
t t"tCL
F q.'nb8-' /L,f')
e u:A\L (s +\*n)* +r-,){
t^reLb
kAu ii :-
+ -rl'\e-
9T:^
+T1r',-o*
oJA
r.ql^lnL og v ,.3;.n t,trcLb
Ovwt ol-a-r,.pe-"[ \> t
*t oota o'lu- -'oLeal '{.,\ Jne1o*Lv Q-
-ur.iu- -r: W ryRCs) = r
.rz,,,rud- i-orucr-,,,.-- 3 ry 1*,.tl"t"
C CS) t^,)nL
Rfs) uft "qu.r6rs+.^: r|
Sl s * So,--
Sz = "-gb ,
S I E g t*)p1 'j-r (A:n al q"- t
sz : - 9*n t,-n {S-r .
CC+) = La-:n - e L$ab oe- L /YJa t''LjoLt
t*E"
![Page 42: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/42.jpg)
Sr ?sz = qt^lntwn..[g;-r]'t
CCS) = RCs) wr,-
?hCs-r-sr)[sts*) ,
W? fa"diat {a-a-c,tr^on ,
?-,CCS) = [^)n- =-- A , + B o,LCs{€,)Cs+s, s+ s t s+8 L
ccs) = DnL r ACS+S!-)+B(s+sr)
Cs+s,) fs+s2) Cs+sr ) (s+SO .
CCs) = ta)n2 = 4 Cs+sz) + B(s+S) .
?Luts g= -Slbn, -- A(-s, *S-)+B (-{r*g,)
= t,( 1,/" + ur^ \ry'-r - #^ + *",1F-,)
runL = A (e u.rp1 Wr)A: pnt
F .rE tl 6 A=tOnarff*,ay6$r
-sF"|
P*s=+Sg-
t,nz = A (* ?L+sd) + Bc--s2 +s,)
F A(Efr,E,.rn1@l ..- gy/r"rF(-urndpr) ,
![Page 43: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/43.jpg)
4l
wnL: A (* rcwn \4-t)
13 = L, tl) n/
&fiw
B E _ t{JD
&,q_r
Su--bs tibr-u- fr/t-a;o-L Vq-Lr-Le^ -':n eq/-th;n O
ccs)F*fu +fu
s+sl g+8.e-.
CCs)= c!4 f t- - I Ie, {f- r f-*+s ' t* *l
A farcfnq -tr,veru,-e- Jo.flqce- Tb{ rrL
t' L"c*)] = wn ,
srlF-'
1-l e I - | ?
I s+-s 1 S+s21
Cc+)= Lr:n t -srb -.-Il&\F-, Lt e I
![Page 44: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/44.jpg)
b,
U*t:k -*fu-lxe, .
"{LU)
,t9'' ( t"r-n-et-esr
el-antp€J-)
Llr
A*oek,Y ,l4gA c\tL 3* J*[email protected],oL frrrL sr;AL
ync*ton , erc*) = to f e (s+z) , F*nd frt^-e- '27r'v'
hfrrbl ?*d*n. ove*'ushne:r_, l*h "dt""' 4-' & ^"*"?
&cs) ccs)
Sotr",ton'.-
&Iv e;.T lDa.fq- i-
Gcs) E,D
Wad.-
SC+D,
SDa-bcu'-
tiae, "k*^.r."- ) r/.Ov ) f€-cLJ,e
.-,t1-nas
t9* Ltndh e@4-d- ^*n &-u- fl *? *"f.^k %
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Fo,:+-'*tu,/-,o*:-
T}&e, -L-i-r"Le- tv rd
OV€-P{-,& h"OOb ..'*
?g*3c 't na{- *p
*\- -J- I, - bwi, urJlruoLL A
F qu/,[q" x roo=Q
Tr- otu cL
^/, nnr
d *rr
.3& *,ta-n4-s- tg(
t .:OL !
-bsts
Zr
4Tfw 5 */' -Tole:to*r1 cqlSa-n
ft 2-'/ ,"To\rytance- Bo-^d'
? aW "^cJ,es+-d- *rern-ry* 'd-t-rnct{'o/'] 'c-cs) s &rs)Prs) 1r qts)
ht cs)
&ivetw **tr--b, &Ca)r tDf s(s+z)
= to/ S5s+z)C CS)
ecs)
=, $*"c -"*'&\ 1eod"a'ci&'
= to/ s c$DsG+, +jD
s (st-c)I +.,,,to
SG+r)
Ccs) IO
ecs) Siz s +roto,
,l+Ajtubnnt)
![Page 46: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/46.jpg)
cLs) tJ-, n 2-
R-cs) LSI+ tE v)nstru n>
@
?@rv 'w-Y'*t,tJ NL =
@" O -h @ r)re- trlo
wn =- /*
2I tl;pl
q=
o-
tl-
e)-25
2 tLt6 9.x3,lgc-
til&
fN&
= trr^ rEz
= 3,162
fs
tr s;,
qvi n
O.3tb K 2.169-
g E o.gqql
![Page 47: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/47.jpg)
)+5
Find* *y = *fT*&
wcL
e= *odi;'*l ,.-;av t- el
9
g s -l:e.nl
II
*v
,-lt,8.^n
t n LBg
T:J-UJoL
s.3lt,
r o,Qol\{"--lot o.g tb )'Pt&oL . -
F Tr * I'a33
-._ [barr (z'85 t)
= ?'l+ -- '"' 3b3.
*v = 0.63T $ec-,
ryl,o FrhA ./r ny =
-Ey/tfqg / Xloo .
-O ,Ztb-ff / K looE
ts a *3 l& x 3'lty / O ' q 8l= g, I x loo
-o.gq9/o.q8l?- x loO.
rE [* Otte, x tgO
A, 3511 x too
O. B lbL
/,Mo s 35'}-1-l '|
I
![Page 48: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/48.jpg)
?esx Trt,a.:*t- Tr = ?'t4- i2r w& a.
I = I Sf.*,c_
1*n o'31& x3'lb2
Fcv 2'f . €!'tJ.t-.19'L, ts = 4T '- +Cl) = +ry
tro-rr. 5./- ?>r><-o,et, ts = 3r = >(-t) = 3 Al2"
Q.ea utb : -
'/. +ed< oves-a,hnst '/- nop = 36'2' / 'I
PeAX +1r.rr;*- tp = l. o 4t -\ecI
,eJ*t,ti1-? *rrvt^L +s =- L*/, s 18ec.5^*f-€g4ec,
![Page 49: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/49.jpg)
8. .U$l,bd Fe:e;-bacK
*p^e**s"ryf*etrsnD #"a*
Jtoi& 'h^*VU vtu
*oQvMOb .u^e -lJJvt-e-,
s^it
&?ve;z Sa-|11.,'*
&r Cs) E
SCs+t o)
?zqi*tecl .}cr.*c}-;*
3@r-rT W, Ao ,frq-oe
--%,*er* 3;
t/A{ E trrn 1@t
F 4-T- ( r$o, e_y.
r- 3r C -F.,aL E */.
= ,Jf,rucL .
w)@-
TI,ri-
,.OJL
de-rYf>t*<.t
*f rynv
ld
pec-le,
Feo-le
SoLrfion'--
e*-.c, ;rt*cbee{i4 a& %arc) =3 ,- r
S CS-r- t o)
c*5
Va-l,,tlg K- D fl
-a-b @ @ob flI
$eM;nfl -b;"^L , Y-ofu c-ov o'--L *T-curue-
o',b L{r1-oJ<, ,ove-eu,hor1c_ A6a1- a- .-'*r&t 4LaP -^?t* '
troM:-ave*+,shno E y, M? € nn*/'@ ,. roo
&f-lr'.rt*- tbp) -.*r-- ,I..*r"r4-€- Cfs)
![Page 50: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/50.jpg)
l'+CS) E I
Ccs> = Grds) = &c.s)Lts) lrF+G)&ds) ,+e,f-)
tu Hcs) Gr ffi d *f **,elion
&rs) F _j!s Cs+-r")
C{$ .F t<ls c s+{ o) K/s C sTao)Rcs) t+ K/s G-uo) s(snQ +rc/s Lyro)
C Cs) K" oR(3) ^2s + rDs+K
* T^L Vo-l-u-o- .,g-t K L,Lo*rL be, ,a_vo-L,t.o,*eol b*,T v: u(-.\ Cl;-ra{iryvw'
n
'L ,*Yo..nffua- tr^^^c*L" a,^,rt:e,u
.s.tanAo,yd- j-;o-* *t Xeeon/-- .-e%o1.4-x- br?n'\ey
c_!S2= t-un2 _ ^ i
tcs) *?"9ur,.,s+uu n2- ---@ I
I
vLDt*P
#4R-
flc-tt^on
![Page 51: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/51.jpg)
+q
0^3n 2 F- k- .
P;;-"'"1t___
e- ELtJn = tD
g= lD, ;;.
.-.-"-,€'*-{t!
s tD
& tfl.
A, = D.5 -h L"u6 =I
C,6- = ,A
* Th-e- Varl,ut*, t^B-l K € t o$T
ltrn E \ru= too
&, dE.
. !_?_
e, Io,E)
Fy-I
{I
€i ae?w.4
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'/. PecLJc
'i, n<p
OV Q*lAl7.;.Ot .'-
iF gn/ffi2-F e, I X lo0
* 0.5 xTl- I;g/ 9-[- D '5' xlDDl
E 0.1b3 X loO
Qealc fu'-W& = u-rrn ,rEt
=to
= lD
= lo,,IlTt
= lo K o,Sbba
= o' B g6 ,ha.d-l *l€e-
I "6bo
= 3.t4Etbo
ItP= cGBb3 rsec
l * o.45
txt cl.,
![Page 53: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/53.jpg)
Se-t*td*fr ry'| *{_frL€, :*
&s=47 t $a"u **l !
_l ._.- ,
D.5 + to
w)
Frt*l.-F
€,LD nl
5
e;*oIa
'/. FEg-*q-
tr?\
S a*f-L*"-u(j
S \d€""p{** lnfre: h
**1p- '-I-*t*v'ua- bD =f
T**,t*tfl, b6 2
/" rp F lb"3*/!
D" 3 &3 Aec
D -8 3ec LL.l '
o. b -8ec L 5 */ +
Qgre<-fr*t)
@,
![Page 54: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/54.jpg)
q. Dex.rfue- ..i}1&
tu &e;cg;'n^d-
^ef-P.qfui,'
S*, uhSo A
? lrchnn- w R(s) = t/s,
R-(s ) .b)-nL
CS+c^rOt
trJnl - tr,nl"S
u-prLL-r^-Lrcr, tr d*'*P ef
-v.-,d,#u Y ffie-ebd- f,*t,
O.-
o.* "l;.-mjlb
ry Y E=I? @ & dxI
Wa
? Th-e- ata-nda-*d- $*,* *t ,c-l'*Sed' J"Yto
*ec,nA --Wda*, W 'rtz ,
ccs) 5+rE---r-r-_
wn'gCS) 5;1+ e-q uns +tnnL
Cvi*:tcr..;u17 q=r
qcs:- u
ets)tr)n'
2.g+2 t-trns -Ful-:nL
.9CF) ,= Lj.nL
Rrs) (s*r*ni)'
Si e-rups + trr*Z = Cs{r-u'D'
o?+ 2o.b Jr- 62 = C cr:rb)-
r cs)
CCS)
CS+urO2 SCs)+r-,,-irlo
![Page 55: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/55.jpg)
lr?.
) B1 ^fffi fW fo"d;"n ',
C Cs) .= _*^oSCs+w6o
FAr :.S
+c o,(s**r,)o S+t;r rf
Tb #AA=
,-
sx ccs) l(s=o.
;f,x wn? )'fi (s+u)
-)e-
[ . EO
€ Yl=. \C 8+wp1)z \ I =O
; tLrnl =lt J nt
To Y& E .--
B s (s+ ur6** c C-s) {
l*= -(r)6 ,
a Ce "/D"^ t,).,o
s(s"/O"S s -ulf.1 1
tL, ntls *s - t-L)n .
![Page 56: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/56.jpg)
* -Yn,{.,wvl
/
# t^)n-.
To #ct--C = .L
B = -* tJ.)6
ots
= .L f Ldnl)E L - jl*E-t$6
= - oL [ (u* {,1'.^ k)",L 1 1ots L %*/b=llu=-r!^-
-- t-t)1..L \
S2- \S = --rr)n
= - y"i = - t*t.)n 2
+ S,rb-slil':'r,n*, A2
Ls
B) L
tun?
------
-sV o-r\rt t^g-s uJn-
*l#
E+tsn
e-l/-o*/r., O,
CS*rD-ccs)s
![Page 57: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/57.jpg)
+EX *^t".'? itve:o+'e- ;a-p-l-o'c-e- ffiL- 1..",J =r'f*] wni I#{ -L: Itt
c-c+) = t- ,,n+;trrftbf rr
^*-Jl,r-=bzlI a .
-l' cs tct>L JL
,
cc+) = [-r,.,nba*t"t: Ctrunb
cc+) = I- e-wnL fr + Lunq
xnyub *rarlAL=
AWJr*iW
ilrr6, ffi..3ote;.}i-on..*
ja 4fPt *"L ;15 o'- wlLbd f*"""GrCs) = tv/e[s+r) . f ind- fr'12- e@A'Pn+'P- $
C CS) s acs)R"cs) l+Fl cs) G4cs)
![Page 58: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/58.jpg)
n- l2_
s(s+Y)
t+ t2- Cr)S Cs+r)
= r2-/s6s /t>s,(s{_r)+ tt/s{l
€ lL
S 6.s+-t)+ 19 ,
ccs) E" tLRfs) si -1 s + te-
CCs) E 12 'Rfs)2_
S +T s+l2-
*r1x-*.
gCq) = l2 '.,-
Rfs5 (s ++)(s+3)
CCs) = le- R.CS)
G+O(St,
CCs) r , lLCs+a) Cs+$
+81 ffi f& ffin't2- =- A ,F B,t_
4l. r---,+ t -..-r,
Cs++) fs+3) s+4 s1=3
![Page 59: Biological control systems - Time Response Analysis - S.Mathankumar-VMKVEC](https://reader037.fdocuments.in/reader037/viewer/2022103010/58754f2b1a28abb8208b8097/html5/thumbnails/59.jpg)
51
-1$
t2 4G+t + BGs+4)
(s+4)rft+a) 6S*s)
l2 s A Cs{-})+ rZ fs++)
Q*b =S= B
re- s A?,il+{>+BC-B++)
tz = B€rr)
?ur-,tS=_+,
t2 = A (*++s)+BC*/*f0
12 = A (* t)
A = -12
C(s) s L- l9- + 12*
S++ S+g
* B"d -rertl'r,n Jn reor-t+- -fl*"*- -fro-ruf m
*+v -3b,CCt) = r,E l> g + tg- s