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Control system unit 1, Study notes of Control Systems

VIT-AP University Control Systems

Control systems, classification, effects of feedback

Typology: Study notes

2020/2021

Uploaded on 08/24/2021

amrutha-nagalingam 🇮🇳

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T=I

wC)

WeOL

factor

(1+k).

Band

idth

Icreased

fosE

becaLUSE

NNre

system

ses

ponse

ihiD

band

limitE

Siqnals

wi|lPa

Etect

feed

back

Parame

ter

yar

iation

Open

loop

e(S)

G+

c(s)+4

(S)

cCs)

F1g

OuCS

wIth

paramete

variatioD

C(S)

R(S)

E(S)

c(S)

R(S)

aG(s)

CLCS

cCs)+Ac(s)

RS)

G+AG

Fig

CLCS

with

Parame

ter

yoariationn

Partial preview of the text

Download Control system unit 1 and more Study notes Control Systems in PDF only on Docsity!

= 1+ LO

T=I

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

e(S)

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)+ A C(S)=

H(G+aG)H

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)

(+GH)

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

Sensithivity =| M=^ chang^ inG]

-Hchengg+GH in HJ

4Time cons tant (^) T-T (^) T (^) I+KH S Band widthb

pifferences ettue cn OLCS and CLCS OLCS (^) CLCS

These ale simple ad

econoMI Cal The^ se^ re Costlier

and complex

These consume less 2 The se cOSUMe^ móre

owe Power

The se are eatier tO (^5) These are not easier^ to

constrtcE because of Cons truct be^ cause^ of

less no^ Of^ Com^ ponents^ Ore^ no^ of^ comPonên^ ts

required requived

Stabi lity^ is^ nott^ a^ +.^ Stabiliy^ is^ a^ maoor

Problem he re SneedePro^ blermd^ hereto Moredeclgn^ carea

Stable closed-lOop^ System

These are^ inaccurate^ 5Theand reliaase ble.^ accu^ rate

and cunaeliable

6The changes^ n^ the^6 The^ changes^ in^

the due tO^ externol^ due^ to^ externoN

Outdisturban put ces are not disautomatically, tubances are esscorrected

Corre cted^ auto^ Sensite to noise^ ond

matitally. More sensitive^ to^ noire and exrerral^ disturbances^ extenal^

disturbances

Matheatical Models^ Of^ Physi(al^ ysten

Physia) Syst em It is^ a^ collection^ of^ physical^ Connet

objectr

tagetheJ to^ Se^ Ve^ a^ object

lectrical Systems^ ConsistS^ OF^ SOurecOurces esistOs, inductorS, Capacitors Mechanical SystemsConsists OF mas sprin and dam per Mattematical Re piesen tation ot Physical stemg

Diferential equaion

Trons fer fuhcthon

3. Stoate Spoao ce AhalystS

Voaol

De pending upon^ the^ chbice^ of^ variables^ andand^ thethe CO-Ordinare (^) sy Stem a^ aiven physic^ al^ mOdel

may tead^ todifterene^ ma^ the^ mati^ cal^ mcdle

A eleCtical networs May be mode^ l^ td^ as

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.

Differentia Eauahons Of Physical SYstems

De pends upon physical s tems, a differentid equation is obtained by utilizing Physicaphyico laus tike Newton's (^) lawS, (^) kcL, kvL

and pordig

hus V; COuld^ be^ V(oX)VA^ arn^ COrcorres

Could be^ VT (or)^ VA

*V Alowr^ into^ the^ block^ and^ Vo^ OSOuto

floeIs. t(V; is^ nmoditied^ by^ the^ block) modellng 1nto represent^ ear^ susystem

Transfer^ Func^ tion:

sto Use^ transfer^ function.s^ o^ EPrEJenE iables

The classiccal laY^ OF mput output^ xeationships^ between^ ariahia

One ay^ to^ de^ fine^ the^ ttonsfer^ function^ is

to use^ the^ impulse^ sesponse^ Jhich^ is

defined^ as^ follons

t) (^) LTI C

gCt)

St)>împulse ilp

gt)> 'mpulse sesponse

t) ip cCt) olp LC9C= G(S)

Single Tn put-sîngle output

Transfer function is de fined as the ratio of

Laplace Transform Of olp to tthe loplale ttons form

of ip with al1 initial conditions ero.

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)

C(S)=G1(S) R\CS) +GnaS) R,()

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

Propex hes^ Of^ Transfer^ fFunc^ hon

ranster Function^ is^ de^ fined^

only for not de^ Fhed^ For

Pvoperty-1 only^

for The non-l1near

LTI Systems.^ IE^ is^

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)

velt VS)S

vis)

Using Vo^ ltaqe-livisi^ om^ xuue

NLS)= Vi(s) R+

TF NoCs)^ CS Vi(s) R+ NoCS) stRI-SCR v; (S)

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

i(s)

VCS)

Sol

v(S) ICS) R

APPlyng kvL,

VS)= ( +R).IC)

IC) VS) SC SCR+

TF ICS)^ Sc

v(S) I+SCR

Determine (^) TF b(S) (^) Iven RER - cCa= |u

M V^ (S)

P C

N Nolt)

NeSV;(S) for the

figue 'belou

812 h ind the Tansf^ crFLuNCEion

olocoiny netcuOrK sho

Te R

Sel Applying^ laplace^ Trensform MM

T

LIS

Applying KVL Vi (S) = RiI + 1 (I-I)+LS LI OD

CSCIS -4)+^ ItRI^ =0^ >

,(S)=

0 Vi(S)^ =^ SR,-+ +LSI

Vi(S)+ = Ri+^ +L,s)I

yis)asC R+

R+ CS +LIS

Cs t+C +R R2 CIC2SkVe.ls) Vi(S)CS+ Vc,(S)Cs

RIC1S+LSCS

C+CS+ RCICs/Ve.(s)= Vi(S)C1S + N(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

NcS) CIS

Vi(S) (^) RCIt CCs+RcdRLIC1SCC1S

CCRICItLE)

C's RS+LCICc-CCS+t cPsR+Lchs-cicas +RRccs+Ruc?c,a- RCPc?}s C

RaC2S-+ LCS-c2s+CSR 4+LCS-CCS

+RRaCICs+ R,uCC,srCICES C

+RIRaCICS-CIc?

APplying MP (^) M C

M Es) F)^ ,

z Ratls CS

Rt +

R C+ RaIC2S+C,S +CS CLS C2S +RC2S CS+CS+R CIC2S APPlyIn9 voltoge^ divis^ iom^ rule V= E(S).z Z+R,

AM NM^22

ElS) (^) CIS Eo)

cs

E(S). FCs) +R+,^ (,S) CS+C+RCIC2S ES) (^) +R(+R4)

+Ba

+RS+R,CS+RIC2S +RIICsLD4T)

1+RC1S+-RCaS+G+RRCICSs

RCytCS+IC+ R,s+ Find TF Vos)

N (^) Vo

Sol (^) Applyin9 (^) Lopla ce Transorm LS LS

viS R

Vi(s)

FoCS

P

R+PaCl+R,CS) 1+RCS

A(1+RC)

RtRtR,RaCS

Pa(1+RICs)

RtR1+ RICS)

3. Find^7 F^ T

1H3 Vol+

Sol Applyinq laplace Tians form

Y s)

Z I+S||

1+S).

+S+ +S2+S

Aplying Voltage division^ rule

V; (s). z

S+z vi(S) St SSt

Vs (s+

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)

Control system unit 1, Study notes of Control Systems

Related documents

Partial preview of the text

Download Control system unit 1 and more Study notes Control Systems in PDF only on Docsity!

= 1+ LO

T=I

e(S)

c(S)+ A C(S)=

H(G+aG)H

(+GH)

-Hchengg+GH in HJ

These ale simple ad

econoMI Cal The^ se^ re Costlier

These consume less 2 The se cOSUMe^ móre

owe Power

constrtcE because of Cons truct be^ cause^ of

required requived

Stabi lity^ is^ nott^ a^ +.^ Stabiliy^ is^ a^ maoor

Problem he re SneedePro^ blermd^ hereto Moredeclgn^ carea

Stable closed-lOop^ System

These are^ inaccurate^ 5Theand reliaase ble.^ accu^ rate

6The changes^ n^ the^6 The^ changes^ in^

Outdisturban put ces are not disautomatically, tubances are esscorrected

Corre cted^ auto^ Sensite to noise^ ond

Matheatical Models^ Of^ Physi(al^ ysten

tagetheJ to^ Se^ Ve^ a^ object

Diferential equaion

3. Stoate Spoao ce AhalystS

Voaol

may tead^ todifterene^ ma^ the^ mati^ cal^ mcdle

A eleCtical networs May be mode^ l^ td^ as

Differentia Eauahons Of Physical SYstems

hus V; COuld^ be^ V(oX)VA^ arn^ COrcorres

Could be^ VT (or)^ VA

Transfer^ Func^ tion:

One ay^ to^ de^ fine^ the^ ttonsfer^ function^ is

to use^ the^ impulse^ sesponse^ Jhich^ is

defined^ as^ follons

gCt)

gt)> 'mpulse sesponse

Single Tn put-sîngle output

Laplace Transform Of olp to tthe loplale ttons form

of ip with al1 initial conditions ero.

C(S)=G1(S) R\CS) +GnaS) R,()

Propex hes^ Of^ Transfer^ fFunc^ hon

Pvoperty-1 only^

LTI Systems.^ IE^ is^

velt VS)S

Using Vo^ ltaqe-livisi^ om^ xuue

i(s)

v(S) ICS) R

VS)= ( +R).IC)

TF ICS)^ Sc

v(S) I+SCR

M V^ (S)

P C

NeSV;(S) for the

figue 'belou

olocoiny netcuOrK sho

Te R

T

LIS

,(S)=

0 Vi(S)^ =^ SR,-+ +LSI

Vi(S)+ = Ri+^ +L,s)I

R+ CS +LIS

RIC1S+LSCS

C+CS+ RCICs/Ve.(s)= Vi(S)C1S + N(S) CS

NcS) CIS

CCRICItLE)

RaC2S-+ LCS-c2s+CSR 4+LCS-CCS

Rt +

AM NM^22

cs

+Ba

1+RC1S+-RCaS+G+RRCICSs

viS R

P

A(1+RC)

Pa(1+RICs)