Question

Sketch the root locus for the control system shown in Figure Q3(b). b) Calculate the breakaway value of K and its location. Comment on the stability of the system. 1 G(s) and Ge(s) K (s+ 1) (s+2) where K is a positive constant C(s) R(s) G(s) Ge(s) Figure Q3(b) If the control system is modified by an addition of an open loop pole at s - 6 ii) 1 sketch the new root locus showing such that G(s) (s+1) (s+2)(s + 6) clearly; the breakaway point a) point of intersection with the imaginary axis b) comments on the system stability c)

Answer 1

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K (4t2)4) 4 Breat away foin d 0 g4 18 5420 co th1- 91-b $1 4.52 -18 t 2 (3 But 452doent erist in Rost loctus dingnam 47) is Bvea away paint 9-3, A-180 1.2, OA30 P-2 r point 0f Ihtersechun twith axis fo staiy hasedenshic en a Ha) Ruh-Hunuidty eitenia for By 400 O

33 20 12 12+K for Kmar (max for Stiy) 3/ 12-(n+) 12tK 4(20)-(12+0 3ubsitute Kin 180-12- K Aux eauakon 891 () Rouo (24 16) 20 y The system is Conditional stable and 13 Stable for 0KI68 for K63 3ystem unstable Con dusion additon of 2eno to open losp transfer funcho dareases the Stabiuhy