The transfer function between the elevator input and the pitch attitude of a plane is given by:
G(s)=[160(s+2.5)(s+0.7)] / [(s^2 +5s+40)(s^2 + 0.03s + 0.06)]
Design an autopilot controller (using a lead compensator) for the system so that the response to a step input (pitch command) has a rise time of 1sec or less and an overshoot less than 10%. Assume a unity feedback system and cascade compensation. Show all your design steps and also perform a validation of your final design.