Given the characteristic equation:
F(s) = s^3 + 8s^2 + (8 + K p )s + Ki = 0
a) Show the region of stability in the Kp vs. Ki plane. Shade region which is stable and clearly show if boundaries are included on not included. Colored pens are a must for this picture!
b) Describe the type of response that would exist if the values of Kp and Ki placed the roots on the boundaries determined in part 1. Note consider each boundaries may exhibit a different performance
c) Determine if the system can be made to oscillate at 500 radians/sec. If so, what values of Kp and Ki will make this happen. Show this point on the appropriate boundary.