1. The document contains questions related to biological control systems for an assignment. Questions cover topics like block diagram reduction, signal flow graphs, transfer functions, feedback control systems. 2. Detailed notes are requested on rules for signal flow graphs and their properties. Conversion of block diagrams to signal flow graphs and determining transfer functions using different techniques are also asked. 3. Closed loop transfer functions for various feedback control systems shown in block diagrams and signal flow graphs need to be determined using block diagram reduction and Mason's formula.

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

2. IvMU/VMKVEC/ELECTRONTC SCTENCES/BME/EVEN SEM/FOURTH SEM/
2OL$-2OL6I CBCS-R2012- FU LL T! M EJ
6. The signal flow graph for a feedback control system is shown in figure. Determine the Closed
loop transfer function C(S)1R(S) using Manson's formula.
7. Convert the block diagram
mason's gain formula.
to signal flow graph
H=
and determine the transfer function using
8. Discuss Signal flow graph with example. Mention its effectiveness.
9. The block diagram of a closed loop system is shown in the figure. Using the block reduction
technique determine the closed loop transfer function C(S)/R(S).
L0. Obtain the closed loop transfer function C(S)/R(S) of the
shown in figure. Use Block diagram reduction technique
with signal flow graph technique.
system whose block diagram is
and verify the transfer function
C(S)
R($
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P,(r)
S+ef J_:-
W A-Y19-
trCt() s e
&(1)
, I 3* 13
Arcs)
?L = * Qa
qp.s gg
6tr)

24. S{-e,p 9- :- 'T-s
I
@ 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"'W
J€€?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'*f
bn
',o,.jre
Vq
(
L",,1
C- q,H)
l+ &r H
o
J.-'5
-rfuj-o- ,,oJ-e- r/1-o fe % ar*P'w
e
-t r:tn;*d.T A-O/t -
,)@4
o'rt-oL

25. 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-l
t+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:o
4
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.345L
o>clo >o>-olo
G{ | Gr &3 &a &s fis)
'3 f"nl;o;-ad Yowu
Cx t &sGg &a 6rs
_ro

26. Prt>)
&a;*
D,fu
-/IJ}LSteo 2;*I
Cst
I
[+g
b"p A
,/1
oL ?*
hs
1 e- sf'.s L
G-+--O#L cu > c
&, &t 'C*1 G (r)
*fi. fffi'L
c 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- *t
Pr, = 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-b
fu- 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€76
T*?
bof @.
'gt chr:o u/u.,n cE- soercl,.-&*q J€6fg

27. &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!
#
J
1
l{
4,k- ?*
A*-- PK,

28. 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 "ae
a -"3"k
'
*
"u% ry*
"4
b"N1ct1-
o*
€)
ffi
R (s)
t
t

29. 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 I
o ) o |'o ) o ) o ) c > C>-> o > o
R CS)
/
FoYLuq:ud- PoWv
r-r
'
Pr '; Glt ., EL'&gi
tq
'#
Rprrutrr-rd" ?a*+w -9-
PsE4,o&14,
,fr^tu
(Dt
d-t
C C s) (tl'r1
C cs)

30. 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

31. 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 '

32. .S*% 5;- -i-*
I
-1,,t*& Txrcmxf** f**cJn#n
;*
ff at<- PK
fult
_J*- c
&'*
*-t- I
| -
<-----d
A [arn t Ae Pil
l*..
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
T
9 A" W $*uu
&voYw -f" a- -r*?rqe*rn 'fr'ee
fu *t-qe-br?c-
(
wn
98nryry*-*:y:o-.n*lorm/,nvl.,t-&-r*e
d-orno,ir<,
@na/,-#'t"
fo"e>t-,"i*3 "& coftt:.ol
eal-r-d--" i^ g - oL^ornai-n '
drrcr3 dever-sper",U /*d I'r ' f'rtaAcn
;- -u*rd'-
**-,"u* i"b
-*..',,;-.*.-:i,.-.i;'',l].'"'i'i$,-'.'::n";,4!']*i.is:!';M"n*']"E-*

33. 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,u
hluJ€*o,-,.-
VM ar4-aL-
',4raO '-fied-LA otck
* Eorc'u bvcrr'u.*t- Ja-x ? ?*
wwts- du}xe:r,&" '}
OJ{L-
o
Jr'
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-
o
J*r)
41so;
sr{- *ff
IBx'a-nch
"-
)A
,A
?" J^,V 1
,u Va-ar-abl
-o
BvancJa- .& di-re-obe-d* J;^4- 'L
SrYLe-ftV

34. 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- 1
v,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--,:,
I
dA
bv@ (A'L")d rr'ot*-) rrb
o
JA
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*V
tub
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,/- %
.&l
T
,g.}6ujd- *yag,l
a-b
u4A4

35. 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 oPe-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

36. 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)'

37. St€-p A- :- E
I
ffil,r* Fee6,tl61.cj<. 'l>ofr"L
rl
I
_t
I
I
I
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*L
lt
(}
blr,&k t $'
P++-4
*T:tr #1r-
bJ"@^c,' 'i
l+ rtcs) e$s)

38. R(s)
Bbef 6 ;- Etilr^-8^atu3"n Feelaark' fail.L- + FePt Foruuzct
{_*r_i
rI
I
?-$) rtr-. I
+,
Grz Cs)
i+urCOar&)
l-1
-{ G'Gtl
,
q)- CE)
l+.qz{s)Qz(s)
6'tC9,14ttS)
r+urlG) &7
6t:s), Ht CA)
Q"3
I ; He- Cs) &rc$Crtr Cs) 6 r-C$) H r ts)

39. sef L :-
Rfs)
f-
I
I
1_
I
I
I
c cs)
JJ/
tr(b-
-^
TyG.-n'sJz-€+4 Funcl=tbn
Sb"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:f
Gtfs)+ 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)

40. 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,n
I
EL,r-rYufl-cr*-*c
il
F€-e.*clb a"*,
€1
PaJJ4-
-f"* wry

41. cca
SLeD 3 :-
I
*? rfl.L We PoZ^t Y '#'La- btoeto
C Cs)
+Frt&r
S+of 4 :- brvt"bni,-? d@e*)r

42. r-
I
I
S+epT.'- EJrryar'*ej dnr- FeeAba;}y PqJJ'
r- I
c c€)
i+ t+ tQzHrGrQS
*
t

43. 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* 1
ru

44. 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 + t4 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
ccq
R#)
&t&E-88+ &'a
F*nc-U.on E'
,rn
Fu-rn c-Abn
C Cs)
R CS)
a Cs)