Given the unity feedback system of Figure 2 with G (s) = K/(s + 2) (s + 4) (s + 6) (s + 8) Design a lead-lag compensator that will yield a settling time 0.5 second 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. Also, find the compensated system's gain. Justify any second-order approximations and verify the design through simulation