The control system G(s) = Kp / s (s+2) (s+6) has a unity feedback a. Kp is variable, discuss stability by using Routh Hurwitz method. Mark the poles of the system on root-locus curve below.  b. When Kp = 26.7 , roots of the characteristic equation becomes s1= -0.6-1.89i, s2= - 0.6+1.89i and s3= -6.8. Are you happy about this case? How do you evaluate, why ? c. How the root locus and step response would be effected by adding a controller Gc = Kp ( s + 0.5)2 / s . Give a comment about the addition of Gc on root locus and on step response.

17. For the unity feedback system of Figure P9.1, with G(s) = K (s²+20s101) (s +20) the damping ratio for the dominant poles is to be 0.4, and the settling time is to be 0.5 second. [Sec- tion: 9.3] a. Find the coordinates of the dominant poles. b. Find the location of the compensator zero if the compensator pole is at -15. c. Find the required system gain. d. Compare the performance of the uncompensated and compensated systems. e. Use MATLAB or any other computer program to simulate the system to check your design. Redesign if necessary. MATLAB ML