+ All Categories
Home > Documents > Chapter8_2_Ahmadi_notes.pdf

Chapter8_2_Ahmadi_notes.pdf

Date post: 02-Jun-2018
Category:
Upload: jonthemes
View: 218 times
Download: 0 times
Share this document with a friend

of 9

Transcript
  • 8/10/2019 Chapter8_2_Ahmadi_notes.pdf

    1/9

    M|nf

    4soo

    -

    f."Jbodr contol

    Equev.q

    Resporu

    nsfeJ

    -pl

    l r .

    N.1

    q,rr's

    f

    sto l;1,'{.,,

    Cn'I+nirlr-r

    .

    .

    7s

    o'"J lo

    **^::

    tLr

    st"b;li\

    .f

    "1o1al-tooy sTsternr

    n

    freluarg

    olo:nah

    I

    ,

    fr/lo,nts

    delorning

    tl^t

    nunbqr

    4

    p"la

    in

    fl,* r'6ht-hf etav*

    6f

    tt"

    .lrte r"t-

    slJttn

    ftn-

    tAq

    " -l"t?_

    y.

    Fcsponsq-

    . lJnnlgez

    -rxpa'innb/16

    .bloiw./

    {rq.

    rapon*

    eon

    bq

    usal.

    -

    /o

    racqd {o

    {ns-r

    ttc

    leafrba

    of

    4A

    poles.

    Jn

    5ho.t

    termt

    3

    koowig)

    t1,t)l4Qa1

    *'+q5-*ffi,

    o"

    7,a4

    f

    =r6,t

    h,'"^V

    L-{ilJ

    uact'oblL

    Poles

    (o7r

    rlcts

    u

    F

    kQH=oa;lh

    prr,t,'^er'crl

    rrt).

    ,fte

    fr//0,,'41

    rfuoreln

    f's

    7'-

    7o.-tolJ.

    {o-

    +ts

    rt"st

    'f

    &

    ru[ert'

    /-layTtg

    Throrw,,

    if

    Ffs)

    r's

    a

    r^t,o

    of

    'f,t"

    71"4'oni"lJ

    in

    s,

    ,f

    /:

    S

    zeros

    rntide a

    elot"ol

    conlatr

    )n

    tlbnl-

    o^"1

    P

    =

    #

    polu

    n';de

    a

    clatJ

    coa'loat

    in

    s-7hl.a

    '

    'A"on

    TAe'

    'tlt

    .tosd

    anlour

    af

    Fts)

    enclr.leJ

    +_:W-I*-Z-P

    timel

    clockvb,

    , "

    -t

    h

    aarvlo

    r

    p

    3-

    Tbac

    ts a

    /"rays

    se/ec

    t/

    z:/acktuse

    '

    Nofes

    \".ir;t*)"i-'

    counlor-clock-tt,b,

    rwos

  • 8/10/2019 Chapter8_2_Ahmadi_notes.pdf

    2/9

    T . ) - . / ' - .

    l r r \

    f

    a t \ , ) ) t -

    -

    t . -

    \

    f 1 n , r ' i ; ,

    6 i r ; f l { t ) =

    I t t

    ,

    t .

    -

    , - l

    I

    t

    Figure8-47

    Closedcontours n the s

    plane

    nd heir

    corresponding

    losed urves

    in the F(s)

    plane. vhete

    F ( . r ) :

    ( s

    + 1 ) / ( s 1 ) .

    MappingTheorem. Let -F(s) ea ratioof two

    polynomialsn s.Let P be he nunr

    ber

    of poles ndZ be henumber f zeros f

    ,/?(s)hat ie nside ome losed ontour n

    the s

    plane,

    with multiplicity f

    poles ndzeros ccountedor.Let the contourbe such

    that t doesnot

    pass

    hroughany

    polesor zerosof F(s).This closed ontour n the s

    plane

    is

    thcn

    mappednto the F(.s)planeasa closed u Ne.

    he otalnumberN of clockwise

    encirclementsf the originof

    the F(s) plane, sa rcprcsentati -

    oint

    {

    traccs ut thc

    entire

    ontour n the clockwise ircction,

    s equal o Z

    -

    P.

    (Note

    hatby thismapping

    theorem,lhenumbersof zerosand

    of polescannotbe found-only their diflerence.)

    544

    chapter 8

    /

    Frequency-ResponseAnalysis

  • 8/10/2019 Chapter8_2_Ahmadi_notes.pdf

    3/9

    Ap/tkail6>

    to

    -rtq

    ,tlU

    days/r

    N"e/

    lb

    )"f;nt-

    a

    pfe"

    a.re

    avstzd

    as

    shoon

    ;

    Nak.

    ^:,1 unst"bb

    bt

    o/=*ot

    .f

    /+Gr9

    Ha)

    w,ll

    be

    iuide

    -fhis

    se.,ni

    ivle

    conttuf

    rh

    S-ylane

    '"c1,

    +t^o*

    all

    fn1,^enu'at

    7h;s

    Fo

    t

    v.fe1

    Z'/' h

    Po4

    *hroylh

    ts

    ^i)

    ca//d

    l*"Nyqwif

    pafi,

    tu

    fS

    sho^ld

    not

    uf

    +b

    pot"s

    or

    z-e"aS

    f

    /+

    Q0

    tlts)'

    On4-

    64

    1'tolc

    l:

    .>-4

    4

    /+

    61i,.riltj"r)

    is

    o

    s{if+e,o{

    A"

    4"

    to

    TL' ptant

    A^,

    1dht.

    fl.,uLfa4.

    onz

    c4h

    onl&

    ficus

    on

    enjrdwnzafs

    o/ +1"

    ofen-loo7

    f,

    ettjal Htl,a)

    b**

    rhslial

    cons''dtr

    g^o

    sa,ab

    N

    t6-r

    p'rt

    "(

    +tr

    1V1l"is'l-

    .*h

    l"cole-ol

    enur.lzme/rrfs

    Jr /+

    4t14Htj")

    Q

    fl

    gtaM

    5

    am( aJ

    l+

    qrr)H(jNl

  • 8/10/2019 Chapter8_2_Ahmadi_notes.pdf

    4/9

    .

    7hL

    Pt'"n

    ,

    f

    tl-

    is /A/

    n/r/ar

    i,lye

    posihw

    s,'dt

    and

    f^p"r*.n|

    rnlus

    fiof

    c,w.

    nctft.

    "f

    ov;6,ibff

    qd

    -

    +

    of (,u .

    ewir6,

    l '-1*oi"

    nr.n

    ^ t ^ P

    N '.-

    *f

    fir

    hVa'li'P

    \'*ncio't

    -a1t'J1o

    ,

    -f

    +lt p @

    rM

    a

    j,i

    H{1d

    louJ, as

    to

    vanet

    {rovtr

    encl'r-.le

    lLo

    pont

    -'(

    l< t;mt't

    in

    lL,l

    R.rrtor(

    s

    1.

    TAe.

    q H

    d o e s

    zgrol

    on

    +

    C.L.

    s1rtern..

    e

    to

    &,

    mnst

    C.C"W

    direcio

    n .

    ertlenbn

    c4n

    b

    e,

  • 8/10/2019 Chapter8_2_Ahmadi_notes.pdf

    5/9

    T' /'

    N= o

    P - o

    +

    '

    Uso-.'llq

    q

    shool /

    n

    ."tJ

    no+

    6 ) o

    ,

    7lo*

    rl .)sh"

    +.r

    . _ L

    1 1 t ^ t t

    '

    plan,('

    Qe

    I t u

    ,-%

    a N

    c f l

    Z = N

    )

    f o .

    4e-

    p

    lof is

    6t

    b