Write a MATLAB program that will design a lead compensator assuming second-order approximations as follows:

a. Allow the user to input from the keyboard the desired percent overshoot, peak time, and gain required to meet a steady-state error specification

b. Display the gain-compensated Bode plot

c. Calculate the required phase margin and bandwidth

d. Display the pole, zero, and gain of the lead compensator

e. Display the compensated Bode plot

f. Output the step response of the lead compensated system to test your second order approximation

Test your program on a unity feedback system where

and the following specifications are to be met: percent overshoot = 10%, peak time = 0.1 second, and K_v = 30.

K(s+ 1) S(s+ 2)(s+ 6) G(s) =