Root Locus & Routh-Hurwitz: Complete Solved Problem Guide

R o o t L o cu s & R o u t h - H o r w it z S t a b il it y C r it e ri o n

C o n s id e r t h e u n it y F e ed b a c k c o n t ro l s y s t e m s h o w n in t h e f ig u re
b e lo w . T h e s y s t e m h a s a v a r ia b le g a in K in t h e F o rw a rd p a t h .




R I S ) C is ) U n it y Fe e d b a c k s y s t e m
t G c s )
R C s ) : R e f e re n c e I n p u t
( ( s ) : F o rw a r d t r a n s f e r f u n c t io n



a ) D e t e r m in e t h e s t a r t in g p o in t s o f t h e R o o t L o cu s

b ) D e t e r m in e t h e n u m b e r a n d lo c a t i o n o f t h e
O p e n - lo o p z e ro s o f t h e s y s t e m .

C ) C a lc u la t e t h e n u m b e r o f a s y m p t o te s r e q u ir e d t o
s k e t c h t h e R o o t L o c u s . D e t e r m in e t h e ir in t e r s e c t i o n
p o in t ( c e n t r o i d ) a n d a n g le s .

, break-away point




Open Loop transfer function

K
G( s ) = s( s + 2) ( s + 3)
S 1 = 0, S 2 = - 2, S 3 = - 3 3 2
s( s + 2) ( s + 3) = s + 5s + 6 s
O
Numo
Loca at



Exp Function
G( s ) has no f.

n-m =