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Given the unity feedback system of Figure P9.1 with K, find the transfer function of a lag-lead compensator that will yield a settling time 0.5 seconds shorter than that of the uncompensated system. The compensated system will also 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. [Section: 9.4]R(s)E(s)C(s)G(s)FI
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