Given the unity feedback system of Figure P9.1 with

Find the transfer function of a lag-lead compensator that will yield a settling time 0.5 second shorter than that of the uncompensated system. The compensated system also will have a damping ratio of 0.5, and improve the steady-state error by a factor of 30. The compensator zero is at -5. Also, find the compensated system’s gain. Justify any second-order approximations or verify the design through simulation.

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K G(s) = (s + 2)(s + 4)(s +6)(s+ 8) %3D