3. Sketch the root locus for the unity feedback system as shown in the figure below for the following transfer functions: K(s+2)(s+6) a. G(s) 5² +8s+25 b. G(s) = c. G(s) C(s) R(s) = = K(s² + 4) (²+1) K(s²+1) 5² G(s)

1. Consider the unity feedback system given below The system will be stable fora) K >-2 b) -3 < K < 0 c) K < -2 d) -3 < K < -2

Q5 Sketch the root loci for the system with G(s)=K/ s(s + 0.5)(s2 + 0.6s + 10) , H\S) = 1. Q6 Consider a unity feedback control system with the following open-loop transfer function G(s) =K/s(s2 + s + 4). Determine the value of the gain K such that the phase margin is 50 What is the gain margin for this case?

Ex. 363. Consider a unity feedback system with the forward transfer function G(s) = K (s+34)/(s(s+1)(s+20)(s+70)). Find K for a marginally stable closed-loop system. See the lecture videos which use the Routh table and calculator. ans:1