Root Locus

Question 1

Root Locus:

1. Definition
2. Closed loop transfer function of Proportional Gain
3. Purpose
4. Design

Answer 1

1. Plot of the locations of all possible closed-loop poles with some parameter (proportional gain), varied between 0 and infinity.
2. Y(s)/R(s) = KH(s)/(1+KH(s))
   for H(s) = b(s)/a(s) then a(s) + K*b(s) = 0 or a(s)/K + b(s) = 0
3. Helps choose value of gain to achieve type of desired performance
4. Given the root locus, there is a tolerable design of the damping factor and the natural frequency