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B-6-8. Consider a unity-feedback control system with the following feedforward transfer function: K G(s) = - s ( 52 + 45 + 8 ) Plot the root loci for the system. If the value of gain K is set equal to 2, where are the closed-loop poles located? Supplementary Problems 13.42. Determine the angle and magnitude of 16( s + 1) GH = s ( s + 2 ) ( s + 4 ) at the following points in the s-plane: (a) s=j2, (b) s= -2+j2. (c) s = -4+j2. (d) (e) s = -3. 13.43. Determine the angle and magnitude of GH = - 20( s + 10 + /10)(s + 10 -10) (s + 10)(s+ 15)(s + 25) at the following points in the s-plane: (a) s =/10, (b) s =j20, (c) s= -10 + j20. (d) s= -2 (e) s = -15 + j5. 13.44. For each transfer function, find the breakaway points on the root-locus: K K(s + 5) K(s + 1) (a) GH - s ( s + 6) (s + 8) ' (b) GH = ( s + 2 ) (s + 4) ' (c) GH = s' ( s + 9 )