Question

© Determine stability for giver system with plent transfu function G(s); using the RH criterion. G(s) = 5 sa_9 G6)= 2521 sh+58-19st 11s +30 ©

Answer 1

À Clivene Transfer function doo zag Comparing as culth, 5 bostbit.nut bm. a seg a sata stalas..tan Here, m=0, na 5 - bo siis²- g alos?+ a,stang clo = 1, a = 0, clo=-9 Now, houth Array, 82 I llo da sliai a so I bi ba ² 1 -9 about a, 42 - Collz al In First negetive Column of Routh correy, there is no value So, system is stable. 0 .5 l & Tremsfer function aco) = - 34+93 - 1994+ 113 +30 Comparing with bost bismit-tbm aosta, soltantan Here, m=1 , n-4 - as t1 sh453-195² + 118 +30 bost bi closh + a, 5 + A2 5² + 93 3+ an ...Co=1, a = 1, C12 = -19 , caz=11, a = 30

b = (-191 -(1181 Routh arras, 34 4 -19 30 S3 1 11 0 s²-30 30 s 1a 11 is is is bg --30 b2 = (11830) - [ox Eig)] (b2 = 30). c;= €30x11) = (1+30) (c, = 12] = As we can see, there is one negative value in the first column of Routh corruy. So, this system is not Steble. and one negative vare shows that there are two poles shifted to left.
As per Ruth criterion , if there is no negative value in the first column of Ruth array then system is know as stable but if there is one or more negative values in first column then it will be unstable system.