Problem 2. Role of Zeros (12 pts.) A standard second order system has the transfer function G = 1 s+s+1 Another second order system is similar, but has a zero: G = s+1 s+s+1* a. For each transfer function, derive the time-domain response to a unit step input. your answer b. In MATLAB, plot the unit step response for each transfer function. Overlay the responses on a single plot. Submit your plot, but you do not need to submit your code. Note that you can check to part (a) by using the MATLAB step function and comparing this to plots generated directly from your time-domain solutions. C. Read the 10-90% rise time (t), the 1% settling time (ts), and percent overshoot (Mp) from each plot, and give the values. To help you read these specs from the plot in MATLAB, you can use the data point marker or generate lines representing the thresholds overlaid on your plot. d. Explain the effect of the zero on the performance specifications (hint: look at rise time and overshoot). Based on your derivations in part a, how are these changes expected?