L R 50000 v(t) ( vc (1) i(t) 3 Applying the same concept to analyze this open loop system used in class perform the following analysis. a. This physical system in Fig 2.4.1 is the open loop system to be analyzed. Using the last three digits of your school ID, for example (Your name ID: xxxxx123) assign the digits accordingly. Inductor L = 1, the second last digit to the resistor R = 2 and that last digit to the capacitor C = 3 in Fig 2.4.1. b. Find the original design ODE of this system. c. Find the open loop transfer function G(s). d. Find the poles and zeros and plot them using MATLAB. e. Calculate and find the output step response of this system. (Use Partial fraction expansion). f. Use MATLAB to plot the open loop output step response. g. Assuming the output response is not what you are looking for add a negative feedback loop H(s) to this system. This time add proportional feedback. Use two different values for H(s) and compare both results. h. Find the closed loop transfer function. i. Plot the poles and zeros using MATLAB. j. Calculate and find the closed loop output step response. k. Plot the output response using MATLAB. I. Conclusion, what are your findings? Is your final design a stable system? Explain all your findings.