Please use MATLAB only
For problems involving MATLAB, you must submit screenshots of your code and results.
1. [15 points] Pre Lab:
The following values of a are 1, 2, 3, and 4. Also, make a plot of the poles for each system.
a) Evaluate the percentage of overshoot, settling time, and peak time when a = 4 and b = 25. Also, make a plot with the poles of the system.
b) Calculate the values of a and b so that the imaginary part of the poles remains the same. Evaluate the percentage of overshoot, settling time, and peak time.
c) Calculate the values of a and b so that the imaginary part of the poles remains the same, but the real part is decreased by one half over the poles found in part b1. Evaluate the percentage of overshoot, settling time, and peak time.
d) For the system of part b1:
1. Calculate the values of a and b so that the real part of the poles remains the same. Evaluate the percentage of overshoot, settling time, and peak time.
2. Calculate the values of a and b so that the real part of the poles remains the same, but the imaginary part is increased four times over the poles found in part b1. Evaluate the percentage of overshoot, settling time, and peak time.
e) For the system of part b1:
1. Calculate the values of a and b so that the damping ratio remains the same, but the natural frequency is increased two times over that of part b1. Evaluate the percentage of overshoot, settling time, and peak time.
2. Calculate the values of a and b so that the damping ratio remains the same, but the natural frequency is increased four times over that of part b1. Evaluate the percentage of overshoot, settling time, and peak time.