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This document delves into the analysis of root locus plots and stability assessment in control systems. it explores methods for determining system stability based on the location of poles and zeros in the s-plane, utilizing techniques such as the routh-hurwitz criterion and root locus plotting. The document guides the reader through the steps involved in constructing root locus diagrams and interpreting them to assess system stability and performance.
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eveg
poxt.
Gennaliy (^) ime (^) and te hot e pbrn eoche)
the toartiert^ sospone^ ess
Apan Aeady
ote do
If the^ syern oeachey^
to eaches to^ Aeady^
tate (^) te
dbonsent ponae Comletely^
esout
Aoble onh rouon andable^
em.
Stoele nn-^
f A^ yemeon^
% said^
be stoble
bounded output^
tt
hounded,
nput (meoku e)
utabe
even thoughn^
iput s
bounded
tunbounded
otut
poe Qocatfon^
tn S-pone
:
stablty
bakd
the (^) pdes
in
ooe (^) pho
poles locaton^ fn Splone
) LHS
RHS
Stade
untoble
On the^
(monaupt) uoikhg
*) Japeated^ poles^
untoble
RH Ctteia;Routh-toruotta)
Bacd on RH^ Cltea^ Q em AAaid^ t^ be^ hul
4 foltased,
the
Cord foM.
gl (^) 1)
all the^ C.n^ the gien^ chatactelt
mtairg
torn (^) the (^) gren
chaacteytte eouotfon.
a)
inthe (^) 4inat coleurnn tr
C8) outh^ table^ ortve rou th^ orray^ o)
d4us^ 3Y4 s^ +16-
(^16 )
46
frtcdaum (utab
Oit S0dts,^2 gn chang, so
2 oot^
n
5
S 1
2
decida be^ stabrliby
magnay stable Jnlan
fn outh tod,^ Cart be (^) toble ( )
3-
gnothe^ gemahg^ tuo^ Moota
, tob..
etetmne the^ tobi.
o a y<Cn
usho chaaceate^ enuotorntgRn Taoxoa g+s5+ 23Y4 2s> +aS+G3St^6.
2 u
3
3
3€-G
3-(3$ -6)
0 cheek^ tu^ tobty^
a to
Aoth A lern^
turtoble
0Ytd th valu k,^ t ounft^
yslen .otot^
loop tarnfe^
tntbn ts
G)HS)
Ka toble sylem
chaocetc equattn^
=cloee)
0
colet S(S+0(St2)
0
fs)Cs+) (^) +K 20
2
K
Ko (thun^
sto Me^ end^
+re)
6>K
S
s i
( a 1 i b )
L T o u r 9 | L h n
g n s t , 5 ]
o l o q w w
d
3 . C o
k a j o b u n g Q
3
8
S
w b r s p c r s , o n
S H 4 0 0 o 5 P 0 S
d r
Root (^) laus
& the^ docu^
f th
Oot
the charoda At.
eqqhcohen the^ arm ,gorvd
(k) he
Steps odaau ooot lawse
and Zens^ Calcuofs
tuncton
poles ond s0^ tha^ an
tnong
TodRate (^) poles coth^
ond (^) ee (^) Lth
oml) mak
On o^
qnaph ahet.
soot the total mo^
dh pole,(n)
un
feedback Cortrolylero^
Open Doop^
Cortol
tom Bgen
G)H(s). s(stus+13)
step1:
docatton pole^ andl 7do
G1(5)- H(S)
poles ae^ O, S'+UStI
-btb-uac
be-4 " (^) 4CX3)
2
)-9t 3
Thenoy
-d- co (^) le bio
B taal^ (elb)
o, tol^ (al3)/^ lb)
florl b)
(tos
clb)
ctep6: -^
1eectbn
pofot
aloq Jo^
Calcuol
Bowr
cotthyl
otou sectfon^ pofnth nten nteg
teog the^ characterstic^
eauatfon
putS
choracteute eaoton.
-)seperato^
th
eal
loe uOo
Calut the
Shetch
he20ot locuuo^ tha^ tollocna
uny
teedback^
Cortio glkn^
drante tunction^ hgven .)
G[s) H()o^
koosi
(susts)
slep1 Locaton^ of^ ole^ and^ Totos ole ao (^) O, -9tjuo (n=3)
e o4 (n-0)
glep dous^
on th^ 9eala 4
slep 3:
Colauoton ot^ Certnoidard^
ang q
@ m ptoe,
Cent xoicd^ <p-^2 =-l- 3-
mptots
z 8o (o+1)^ D^ -6o o 3
O q1 e^ 8ol t) 3
2 180(441),^800
3
3 t
stepu Calcuaton^
t
mot oris
b 2-^ e9S.tenos^ & 2-poles Ao,brake
awoy polot
pofot^ doendt
(Preal soot)
af depatie^ (nag
Atep (^5) ng
180- ta2)
2
1-56.S
on the
step
3 Certotd
Centotd
ond ang 1 Auymp totes
D-nm
3-
onge 4^ agmpetes
9, =6o
fO -2 -3-3o
Bxak
auy
Beak
Bmeakausay pont (tas)H)) chaolete equcttor
S(5+2) CS^ )+
h-ss+2)(S+ ) --S(S4 S+2S+8)
= 63-
= -(s+6s^
dk
ds
(3s +12s+8)^ >o
-btb-^ ac
S,--0. Kubtlu
-6ses)
2(3)
toots e -o84, -8-
The beakauay^ cofot^ -o^
Step5: Caluaton^ ange^ deparhiol^ and
Th em^ do^ yo^ rave^ Conpler^ pole^ Ko
angla depasrtial^ ond^ ang
mot exis
kep6i Totekato pofot coft juw axiA
chara ctestic eauaton.
Pt S) (s+2)(stu)tk= Characeut (^) s (^) t (^) 65+85+k eo
put (^) szjo
Cjo+ (^) 6jo)' +8(je)+h"
(k-b)+j(-w+8)o
( n@;e) au
