biological control systems - system concepts-mathankumar.s, vmkvec

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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*,{w trt""ture of the Tutor $i{nature of the Coordintrtor

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Page 1: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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

Page 2: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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($

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

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

,./a

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.: PL -h Pg- '|

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t

P,(r)

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W A-Y19-

trCt() s e

&(1)

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qp.s gg

6tr)

Page 24: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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-

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J*y, Valr-t,e- +

.5 cLlr "*

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

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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

Page 25: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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- &'

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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

Page 26: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

Prt>)

&a;*

D,fu

-/IJ}LSteo 2;*I

Cst I

[+g

b"p A,/1

oL ?*

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W A,-vu-

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toop8

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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 *\

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bof @.

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

Page 27: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

&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

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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!

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Page 28: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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

Page 29: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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)

Page 30: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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

Page 31: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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 '

Page 32: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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

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

ff at<- PK

fult_J*- c&'*

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8.

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f { Qr&rqs tq,&q

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.,tta Wv€-n-!J"& I

Nleyr*fen

jtb

T9 A" W $*uu

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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-*

Page 33: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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

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eJAry Lfr^L brrs-n&1' '

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Page 34: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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

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brra-nclL '

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J;nf t1'od-a*

o%r*Vtub

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g A ?o'#L rA

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Page 35: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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--

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tffi? ea;,'1

+

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

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

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,-U&

otSQA Jfi-at M av

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

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

.,.tpq J-DT*'

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

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

Llrfl+e,oLr.-b *t

Page 36: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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)'

Page 37: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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)

Page 38: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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

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, q)- CE)

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

Page 39: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

sef L :-

Rfs)

f-

I

I

1_

II

I

c cs)

JJ/

tr(b--^

TyG.-n'sJz-€+4 Funcl=tbnSb"1" 1 .-

c,

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

, t nr,6 hvcs)

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)e,&eCs)t-f'Hs

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(erCs)tr ) QvCs)

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t t-4y{s)

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

Page 40: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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::

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ldn-V aed-

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

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F€-e.*clb a"*,€1

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Page 41: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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

Page 42: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

r-I

I

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

I

c c€)

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t

Page 43: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

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;

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l+HrQaf Hr&r4sr",fl:

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Page 44: Biological control systems - System Concepts-Mathankumar.S, VMKVEC

G t&2-GL3

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

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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

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q tq,eGts + qq

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

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

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