A unity feedback control system for a robot submarine has a plant with a third-order transfer function [20]:

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 400 ms. 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 the resulting system Kv.

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G(s) s(s 10)(s 50)