Question

Question #2 (20 pts): Transfer function of a causal system is given as s²-s-6 56 + 1955 + 14954 + 60353 + 1310s2 + 1418s + 580* a) Examine the stability of the system without using the information given in (b). How many poles does it have in the right half plane if it is not stable? b) Sketch the complete graphical demonstration of this system by utilizing previously given information and the additional information given with the following items, Possible ROCs: Re{s} <-5.-5 < Re{s} <-3, -3 < Re{s} < -2,-2 < Re{s} <-1.. Re{s} > -1. Transfer function of the system has complex conjugate pole pair that are in the following form 4 2. j where c and cy denote the positive or negative constant terms.

Answer 1

( characteristics equation is; q (s) = go+1995+ lyg g +6035²7 13105²+ 14185 +580 By Routh hurwitz's ; Method So 95 I 19 149 603 1310 1418 580 o 19x149-603xl 19x1310-1418 19x580-0 19 19 Ele tl1 = 896.5 E61 = 085 = 53 1324 0 117.263x603-19X1335.368 117.263 = 402.83 849.95 s 580 o o s' go 1049.11 580 0 0 0 0

All the signs of 1st column are positive So number of right hand side Poles = 0. so Left hand side Poles = 6. 1 (6) → → → → for Re(s) -5 5L Re(s) 2-3 < Re(s) <-2 - < Re(s) <-1 Recs) >-1. causal system Re(s) >-1.

T -5 -3 -2 -1 X Note :- g=-1 live 4 5=-2 characteristics are satisfying equation. the