root locus notes
DESCRIPTION
Root Locus notesTRANSCRIPT
o
lFoo{ L.-s -J.^- zo B
MeoSa ,)r. TerALt4 c*L( l*f
r (t)
dg or- tary
closqLJ-'tp
Flr,- cr)
H ".
rs)
t"l CCs) Gr b) e G6
F ccr) fi{g
I + k c($G/s>
= l/6\Dcs)
l-1", r s) = raoh oF DG)
-fosb oL 1t ts\
e\t*!' l*i, ,vspt^'e-
a
oy<'- luop
qzr, (uoy
Hu() =
P"6
$*
ol-
V=o
lvG)
D6) f l< ̂ rcs)
r^,/. ol- Dc) *k /dc)
rao| ol- >cs)
oPt^ lag pob>."6oL
loo, p6t
6t (= ab cbral l-O poLs fdb 6 6{- ^tG)
q + l * e I ' o r
{lnr, J'l- &t rrob-
f o D F
s{rbl*P
c l s
ofe^ t *[,
t l -
K U)es ilr^-
Tobs e,'-!-
/ t d
a( ofr*o
o*rls
?-11A Hr. (r) = S Z
S E P
P = oW l * f ? "6/ - oW L*? k/D
P,r t Loc us
K'2 E=o, y '
Rub.#z
%L a.(D Drn h,l nu, ltt
d\
o l
hcu
( o t -
r^f loutOL ?9,0t
x -o -
Oyn-', L*f)
i ( J4" n,ul,-+D rtel^ l- al
P o Qe/1)
o{ pobs
?or+ ,\ olA.
florO s
e1o l-f. tr) =
fu*vf el'r# h,us /ut-ri $^ ruoL aJ<,E
Is (s- p)
s ' (s -p \e? . l / \
l - L , / \ l :a , o L L - l -
;- d"tLt, P"te
f Ff,^- af rvr.(G '
eFr) (rb\ m( l,zus
Rub 3
of, osv-y hLt ,) eq,*L
, l
ncrl- W$lc-
Car\kr- tr * ot
Scr,G =
rn usl- /rrr*
el,\y-tW
e&l1o,ct; =
*'JLuo qtyrYLl;- teaL cUF') D aol-
I r492, f lrJe: is
2 o L b b s - 2 o L & n s
f n,,-.t,-ol ou.
t @ras ,
&Dl- &,>"sLocrts
l"not otkt
fl/oL J,l*l-D a \ a ,9\,nn.',
Ofr*la
"(( dt'
rw( lcr, u,r.
/u^[ a*D-fl, ,D6
It. r')€ -o)s'
L €nll'' rst-
. 0J+?l*y't
*
# , = ? bC^l- t,r*'t-
d.^hb '^f ot
s-+ t
EK^rL
t'lotrls) --€niX'il
ps^* HorG\ :-Ez-l g- t)(s+t)
hrQ 3
6ic'+iYsi:l
C'n') Cs-s')
9. r - ! " - - g i t$ ' rO - : -
3 3
iloril= s t r
Q + e ) ?
sL!;l,v ^ h*erLJ
A- iG*O
Mft nof,^sL\,L o-
woL at
*t-3rr-.L(2
ol"*.1'sLLQ .
G6l
S L T
ln2yu\nL IPIk*L a,
O t ?olo>
U - *.lo*d-.
o - a L
t -F kD P obs ot+- u/Lr
Rol l*,, f" lio,(.s): k;+
W re2{ c^nrovl loru, rr,d
|n J4 "LHP dD "af/*tt( J4oL gn
Ltl ?
H". ( r )= k s -? .
ca LL e"il,>,Js"[A>u]1 'r,.-t"
B"l' wc c a^rnol'butlclal6,
@ ^ t - 7 , _z- ?"
PrtL'i\6P.,
tob, ffJ-L 4 ?
b co-, pril" Ct pLt
Co'Vnsft- ?'D 4 )/sI'{, r1/" /-
d"l"*.4l-'
c";l'L *5
ltofu -;^ ttF
/
5 (S- P)
L)LL rol-bu,, oLtL-t)=
hlrl ar-gu.rfuf2;,,vl"tl^'.^ g o Lb^-
^dJ
%a
J4
lnl lorus
@
fut-l^ il LJ '^,t
fal"L h Wl o"{- crrL
u.,ll orlrn-., L clo*t /.1e-
.j^,, cN6B +; P, lh-
ilL cornpn>cL h"1. /4CL Nyaxsc- S/ruea.
a> L PLL , lJ^L t ,r-.L /4
t>P- 9, HQtta tile ,aA 1r,^(ctv\ms,rf,
k .2-
rc)'I lt.u5 Ho, (s) -
un>LtL [* u7 k
auV 4 gL @D b> d4 a g'a {" Ct"pe^sc-tl.-,
H r , - ( s ) = X ( s - )g3
+t f ( t /nsL(6 t -
s
(?^,1^ to,.a
4 t ,
A)nL n to,rLL &, @ s ^
ILTL CI- V-jr,rtu y"L, crrrs
) ' - ' aY i .