Question: Given the unity - feedback system with open - loop transfer function ( ) = ( + 2 ) ( + 4 ) ( +

Given the unity-feedback system with open-loop transfer function ()=(+2)(+4)(+6)(+8). a. 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, with a damping ratio of 0.5, and improve the steady-state error by a factor of 30. The compensator zero is at -5. b. Write the compensated open-loop transfer function in zero-pole-gain (ZPK) form. c. Justify any 2nd order approximations or verify the design through simulation.

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