Question

Given the systems below, sketch the root locus: R(S) K C(s) s(s+2)(s+5)

Answer 1

Dete Pogo Ans Following are the steps to construct a Root-locus : R(s) C(s) k s(st2) (345) 1. Starting of Root-locus :- Starts at open loop pole's At { -2, -5 2. Number of Branches at infinity: N = P-2 3-0 N = 3 . Three branches at infinity. 3 Root locus at Real axis - 2 R-L exists at dashed part of real line

Pog H Angle of Asymptote : As three poles there with i Asymptotic angle 601 180 are no zero's are 300 5. Centroid:- C = SP- Ez P-2 c = of-2t - 5 3 - 2.33 3 6. Break away point: - (14 It GH + k sts+2) (5+5)) = 0 k= -s(st2) (St 5) k= -s3-78²-los dk ds 35² + lustlo=0 so -14 4 / (14) 2_463) (10) 263)

Date Page, s = -14 1 g. 71 6 S - 3.785 -0.88 SE -0.88 Valid Break away point Iraganary 7. Intersection at Axis : Cjw 'w axis) s3+75²t lost kao 3 7 t 70-t 7 k * 75² tkm = 0 752 + 70=0 S = .

Date Page Considering all the steps Root-locus looks like:- pjw sto -2.33 jso 180 300