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Control systems, classification, effects of feedback
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T k
wC) (^) = +k WeOL Band w idth iS Icreased by a^ factor (^) (1+k). he (^) system sesponse is fosE (^) becaLUSE NNre Siqnals wi|lPa SS ihiD^ band^ limitE Etect (^) f feed (^) back (^) on (^) Parame (^) ter (^) yar iation Open loop
G+ (^) cCs)c(s)+4^ C(S) F1g OuCS (^) wIth (^) paramete variatioD C(S) R(S) E(S) A (^) c(S) (^) R(S) aG(s) CLCS RS) (^) G+AG cCs)+Ac(s)
H Fig (^) CLCS with (^) Parame ter (^) yoariationn
Grt (^) A (^) R(S) cSR(S)R(S) 1 1+G GH
C(S)+AC(S = +CH+AGHG+AEIR(S)
AC +EH-+A GH^ +6H4^ AGHeS) HG>HAG Simce AGKG cCS) +A c(S)=| (^) +GH +^ +GHAG^ e(S)
AcCS) AG^ R (s)
s Summary OLCS CLCS 1Gain I+H(redues^ in^ geneal to Satisfy remaining al Parameters 2NOise a (^) C- N Noise^ Pathin^ fpruuad Noisefeedback^ in patr disturbance (^) C N C -9,6HN
4Time cons tant (^) T-T (^) T (^) I+KH S Band widthb
pifferences ettue cn OLCS and CLCS OLCS (^) CLCS
and complex
less no^ Of^ Com^ ponents^ Ore^ no^ of^ comPonên^ ts
and cunaeliable
the due tO^ externol^ due^ to^ externoN
matitally. More sensitive^ to^ noire and exrerral^ disturbances^ extenal^
disturbances
Physia) Syst em It is^ a^ collection^ of^ physical^ Connet
objectr
lectrical Systems^ ConsistS^ OF^ SOurecOurces esistOs, inductorS, Capacitors Mechanical SystemsConsists OF mas sprin and dam per Mattematical Re piesen tation ot Physical stemg
Trons fer fuhcthon
De pending upon^ the^ chbice^ of^ variables^ andand^ thethe CO-Ordinare (^) sy Stem a^ aiven physic^ al^ mOdel
a (^) set (^) Of (^) model (^) equations (^) ut'ing kcL or as a set of mesh equahont using kVL
TAMaMatemahc^ model^ is^ linear^ it^ salisfies^ the Priniples of^ superposition^ and^ homogeneity.
and pordig
*V Alowr^ into^ the^ block^ and^ Vo^ OSOuto
floeIs. t(V; is^ nmoditied^ by^ the^ block) modellng 1nto represent^ ear^ susystem
sto Use^ transfer^ function.s^ o^ EPrEJenE iables
The classiccal laY^ OF mput output^ xeationships^ between^ ariahia
t) (^) LTI C
St)>împulse ilp
t) ip cCt) olp LC9C= G(S)
Transfer function is de fined as the ratio of
c(s) =^ LT (^) of (^) O|p R(S)=L.T 0+ ilp CCS RS) zero initial
S)=TF Condtim
li In (^) pLut uli (^) Out (^) puut {nMt t (^) Va rbe (^) sst em)
S) GS) CiCS) RS) C2(S) Fi9Multi varia ble system CiS)= (^) Gn(S) (^) R, (S)+ GpS) A(S)
Ghiolis C(S) R(S) In General (^) C(S) ) = CS) SS)^ SiS^.^ .pS)^ (S) CS) G(S)(S)^ GapS)^ P^ (S qpSJRp(S)
whese Pilp
ranster Function^ is^ de^ fined^
only for not de^ Fhed^ For
for The non-l1near
not de^ hed^ FOr
nm-linear
Sustems
(a) R RART V;tE) (^) C VoE) L SL
APPying l.T SC Sol de s v{S)
vis)
NLS)= Vi(s) R+
TF NoCs)^ CS Vi(s) R+ NoCS) stRI-SCR v; (S)
2
Sol
v(S) R^ VoCs)
By uslmg^ voltage^
divÍsion ru^ te By (^) Vi(s) R Vo (S)
TF VaCc); (s) SCR SCR+
Deterrmine he^ trans^ fer^ function
VCS)
Sol
APPlyng kvL,
IC) VS) SC SCR+
Determine (^) TF b(S) (^) Iven RER - cCa= |u
N Nolt)
812 h ind the Tansf^ crFLuNCEion
L
Sel Applying^ laplace^ Trensform MM
Applying KVL Vi (S) = RiI + 1 (I-I)+LS LI OD
CSCIS -4)+^ ItRI^ =0^ >
yis)asC R+
Cs t+C +R R2 CIC2SkVe.ls) Vi(S)CS+ Vc,(S)Cs
C R,Cis+LiS^ R,Cs+LCIS
V.(s)C,StC1S+Ra C1C1SCa.S V;S)^ CS C RCS+LCs)^ R,CS^ +Li^ Ls
Vi(S) (^) RCIt CCs+RcdRLIC1SCC1S
C's RS+LCICc-CCS+t cPsR+Lchs-cicas +RRccs+Ruc?c,a- RCPc?}s C
+RRaCICs+ R,uCC,srCICES C
+RIRaCICS-CIc?
APplying MP (^) M C
M Es) F)^ ,
z Ratls CS
R C+ RaIC2S+C,S +CS CLS C2S +RC2S CS+CS+R CIC2S APPlyIn9 voltoge^ divis^ iom^ rule V= E(S).z Z+R,
ElS) (^) CIS Eo)
CS
E(S). FCs) +R+,^ (,S) CS+C+RCIC2S ES) (^) +R(+R4)
+RS+R,CS+RIC2S +RIICsLD4T)
RCytCS+IC+ R,s+ Find TF Vos)
N (^) Vo
Sol (^) Applyin9 (^) Lopla ce Transorm LS LS
Vi(s)
FoCS
R+PaCl+R,CS) 1+RCS
RtRtR,RaCS
RtR1+ RICS)
1H
Y s)
Z I+S||
+S+ +S2+S
Aplying Voltage division^ rule
S+z vi(S) St SSt
S+3s+ NoS) VS Vi(s)(s+1)S Vo (S)= S+3s+I +S Vo (S) iS) s (CT) S+3s41+S) VoS) (^) S v;(s) s+35t
4 Find T-F
m B MM- (^) N- ww s
A ItS+1S+ PA =A PB =^ A^ (S-+1)