Unless otherwise stated, the following block diagram (Figure 5.1 from the textbook) is assumed in this homework. W Controller Plant U RO O Y DAs) G(s) OV Sensor H(s) Figure 1: Bkock dingram ud in this huwork Assume W = 0 and V =0 unless otherwise specified. (d) Assume that H(s) = (i) Sketch the root locus assuming a proportional controller, De(s) = K. (ii) Find the gain for which the root locus crosses the imaginary axis. Please show your working (do not use Matlab to find this gain). (iii) We wish to see the effect of a lead compensator on the system stability. Use MATLAB to plot the root locus for D,(s) = K(e+4) (iv) From the plot, find the gain at the imaginary axis crossings with the lead compensator. What advantage does using a lead compensator confer on the system?