This document provides instructions to sketch the root locus and analyze the characteristics of a unity feedback control system with a transfer function of G(s)=K/(s-1)(s+3)(s+6) as the gain K varies from 0 to infinity, without using MATLAB. It asks the reader to identify parts of the real axis containing the root locus, asymptotes, break-in/away points, the range of K for stability, intersections with the imaginary axis, and the value of K for a pair of complex poles with a damping ratio of 0.5, then compare the sketch to a MATLAB plot.

1. Please show all work! Consider a unity feedback control system with the transfer function G(s)
in the forward path. For each of the following transfer function, sketch the root locus as K varies
from 0 to infinity and find the following: Parts of the real axis that have root locus; Number of
asymptotes, their angles, and their intersection with the real axis; Break-in and breakaway points
(if any); The range of K for stability; Points of intersection with the imaginary axis (if any);
The value of K to yield a stable system with a pair of complex poles having a damping ratio of
0.5 (if possible). G(s) = K/(s - 1)(s + 3)(s + 6) Solve the problem without using MATLAB.
Then plot the root locus using MATLAB and compare with your sketch. Include the plots in
your solution.
Solution
Sorry to say plz check question once . this problem is unstable as one pole came in right side . we
are doing root locus only for stable systems.