For a system with block diagram shown in Figure 2 where G(s) = G (s) = 1 3s + 2 H(s) = 2 (a) Obtain the expression of open-loop transfer function. (b) Obtain the expression of close-loop transfer function. (c) Use MATLAB to plot the close-loop system time response under a unit step input. (d) Manually sketch the polar plot of the open-loop transfer function on a graph paper (please list data in a table for at least 15 points to construct the plot, you can use Excel or CAD, as long as it shows clearly how you calculate and get the points for polar plot). (e) Check the system stability by Nyquist criterion. R(S) + G(s) H(s) Figure 2 G (s) C(s)