A unity feedback control systems for a robot submarine has a plant with a third-order transfer function
G(s) = K / (s(s + 10)(s +50))
We want the overshoot to be approximately 7.5% for a step input and the settling time (with a 2% criterion) of the system be 400ms. Find a suitable phase-lead compensator by using root locus methods. Let the zero of the compensator be located at s = -15, and determine the compensator pole. Determine resulting Kv.