Question

7. a) Sketch the root-locus Ris) C(s) diagram for the system S(5+) shown in figure when Ge=1. 6) Design phare- lead be compensator such that the system time constant is 0,25 see and != 0,45. Assume compensator at s=-4. Sketch the root-locus diagram of compensated system. c) Find the unit step responses of COMPENSATED and WN COMPENSATED systems and plot these responses. zero

Answer 1

(a) RIS) ces) Gc SIST) Root locuri It is unity Negative feedback given Go = 1 G(S) = G(S). SCS+1) SCS+1) s(5+1) poles: Zeros : R) None Intersection point E Poles (read) - Zeros (red) Poles Zeros constant -1-(0) 2-o. - No. if Asymptotes P-2 = 2-0=2. Angle of Asymptotes (29+1) 180 q = 0, -P-z 3x180 180 2 2 Root locus 90, 270. Im s plane 1996 kao Re %0.5 ko kya 270'

(6) Phase lead Compensator Ja 0.25 sec Time constant datus q=0.us lead compensator Yes HH Vo(s) Ra 11 BI Vils) Zhr Wics) R2 ( 1+SGR) (B, +R2) (It RL SGR) (1+55) (1 + 5,3) where T=R, C = Time constant R2 RitR2 ته R, G = 0.25 = 0.45 Rit R2