For the system of Problem 6, do the following:

a. Use frequency response methods to find the gain, K, required to yield about 15% overshoot. Make any required second-order approximations.

b. Use frequency response methods to design a PI compensator to yield zero steady-state error for a ramp input without appreciably changing the transient response characteristics designed in Part a.

c. Use MATLAB or any other computer program to test your second order approximation by simulating the system for your designed value of K and PI compensator.