1. This question refers to the system drawn in Figure 1. A table of transforms is given at the end of this exam booklet in Table 1. + 1- e-Ts S K 1+ TS Figure 1. Closed loop control system. a) Determine the transfer function of the open-loop system and closed-loop system in the z-domain. [5 marks] 0.3935 b) Show that H(z) equals z+0.3935K-0.6065 for T 1 second and T = 2 seconds. Draw the root locus of the system's pole(s) on the z-plane by plotting the following gain values: K = -2, 0, 0.5, 1.54, 3, 5. [4 marks] c) Based on the root locus diagram, consider the response of the system to a unit step input, assuming zero initial conditions. For each of the pole locations plotted in b), either sketch a time-plot of the response or briefly describe the key characteristics. You do not need to calculate exact values. [12 marks]