Question
Asked Nov 19, 2019
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A unity-feedback control system has the forward path transfer function as

G(s) = K / s(s2+6s+25)

Construct the root locus diagram for K ≥ 0 . Find values of K for all the breakaway points.

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Expert Answer

Step 1

The given transfer function is rewritten as follows:

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K G(s)= s(52 +6s+25) К G(s)= s(s+3-4 s3+ j4) 1. Poles are s-0, -3+j4, -3-j4 2. Angle of asymptotes n- Number of poles is '3' and m-Number of zeros is '0 t180(2 1 0 = ,9%3 0,1, п-т п — т +180 (2(0)+1) = +600 3 0 Likewise e2 180°, 0±120°, 0, = T60°

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Step 2
  1. Centroid:
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Sum of poles Sum of zeros п — т 0 34 3j4 - 0 3-0 - -2 4. Since there is not more than one pole in the real axis. Therefore, no existence of breakaway or breakin point

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Step 3
  1. Angle of departure.
...
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(1) e 90° tan 4 126.86° , 90° 0=180° -(00) =180- (126.86°+90°) 0 =-36.86°

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