The block diagram of a speed control system is shown in Figure P12.6. For a particular system with proportional control, G1(s) = KP, the open-loop transfer function is
G(s) = Kp / s (s + 2)
With Kp = 4, the damping ratio is ( = 0.5, the natural frequency is (n = 2 rad/sec, and Cu = 2/sec. Design a compensator that will give a static velocity error coefficient of Cu = 20/sec, a phase margin of at least 40o, and a gain margin of at least 6 dB.

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Tais) Ω(s) Controller Motor